Scheme_Modules_nonempty_iso_tensorUnit_of_pullback_three_slices.lean

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.ThreeSlices
attribute [-instance]
  AlgebraicGeometry.SmoothOfRelativeDimension.fiberToSpecResidueField
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_snd
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_fst
  AlgebraicGeometry.SmoothOfRelativeDimension.smooth_one
  AlgebraicGeometry.SmoothProperCurve.isIntegral_pullback_Spec_field
  AlgebraicGeometry.IsProper.fiberToSpecResidueField
  AlgebraicCurve.CurveModel.isProper
  AlgebraicCurve.CurveModel.isIntegral
  AlgebraicCurve.CurveModel.smooth
  AlgebraicCurve.Place.instIsScalarTowerSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Divisor.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instSMulAlgEquiv
  AlgebraicCurve.Place.instIsPrincipalIdealRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instIsDiscreteValuationRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Pic0.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instAlgebraSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instMulActionAlgEquiv
  AlgebraicCurve.Pic0.instSMulAlgEquiv
  TwoChartCech.Sections.M0_moduleA
  TwoChartCech.Sections.M1_module
  TwoChartCech.Cover.A01_algebra
  TwoChartCech.Cover.A0_algebra
  TwoChartCech.Cover.A1_commRing
  TwoChartCech.Cover.A1_algebra
  TwoChartCech.Sections.M01_module
  TwoChartCech.Sections.M0_addCommGroup
  TwoChartCech.Sections.M0_tower
  TwoChartCech.Sections.M01_addCommGroup
  TwoChartCech.Cover.A0_commRing
  TwoChartCech.Sections.M1_tower
  TwoChartCech.Sections.M01_moduleA
  TwoChartCech.Sections.M0_module
  TwoChartCech.Sections.M1_moduleA
  TwoChartCech.Sections.M1_addCommGroup
  TwoChartCech.Cover.A01_commRing
  TwoChartCech.Sections.M01_tower
  CoherentBaseChange.TwoTermComplex.C0_module
  CoherentBaseChange.TwoTermComplex.C0_addCommGroup
  CoherentBaseChange.TwoTermComplex.C1_module
  CoherentBaseChange.TwoTermComplex.C1_addCommGroup
attribute [-instance]
  CoherentBaseChange.TwoTermComplex.C0_free
  CoherentBaseChange.TwoTermComplex.C1_finite
  CoherentBaseChange.TwoTermComplex.C0_finite
  CoherentBaseChange.TwoTermComplex.C1_free
  AlgebraicCurve.IsCurveOver.instNontrivialKaehler
  AlgebraicCurve.IsCurveOver.instFreeKaehler
  AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
  AlgebraicCurve.IsCurveOver.instFiniteResidue
attribute [-instance]
  instIsLocallyInjectiveFunUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsLocallySurjectiveUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsOpenImmersionToGlued
attribute [-instance]
  instIsIsoSheafZariskiTopologyTypeUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.RelPicard.isOpenImmersion_toGlued
  AlgebraicGeometry.Scheme.Modules.preservesBinaryProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback_monoidal
  AlgebraicGeometry.Scheme.Modules.sheafify_isLocalization'
  AlgebraicGeometry.Scheme.Modules.preservesTerminal_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback₀_monoidal
  AlgebraicGeometry.Scheme.Modules.preservesFiniteProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.sheafifyPullback_lifting
  PresheafOfModules.PullbackMonoidal.pullback_monoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ
  PresheafOfModules.pushforward_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_η
  PresheafOfModules.free_monoidal
  PresheafOfModules.restrictScalars_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ_gS
  PresheafOfModules.pullback_oplaxMonoidal
attribute [-instance]
  instPreservesColimitsOfSizeCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierPb
attribute [-instance]
  PresheafOfModules.pullback_monoidal'
  AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
  AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
  AlgebraicCurve.Place.instIsPrimeCenter
  AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
  instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
  AlgebraicCurve.Pic0.instModuleZModTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instSMulTorsion
  AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
  AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
  AlgebraicCurve.RationalFunctionField.instNontrivialInftyValueGroup
  PresheafOfModules.ExteriorPower.instModulePresheafAb
  AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
  AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
  AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
  AlgebraicGeometry.isClosedImmersion_graphOver
  AlgebraicGeometry.FGSubalgebra.instIsDirectedLe
attribute [-instance]
  instQuasiSeparatedSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsCofilteredOpposite
  AlgebraicGeometry.FGSubalgebra.instIsAffineObjOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instNonempty
  AlgebraicGeometry.FGSubalgebra.instNonemptySubtypeLeSubalgebraValFG
attribute [-instance]
  instCompactSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsDirectedSubtypeLeSubalgebraValFG
  AlgebraicGeometry.FGSubalgebra.instIsAffineHomMapOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instIsFiltered
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instNeg
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulInt
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAddCommGroup
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAdd
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSub
attribute [-instance]
  instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
  AlgebraicCurve.instHasLocalResidue_of_hasCanonicalLocalResidueK
  AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
  AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
  ModularCurve.KwF4gRRTate.instAlgebraKAdicCompletionIntegers
  AlgebraicCurve.Place.kw_ffgc_continuousSMul_adicCompletionComap
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersCompletionCompletion
attribute [-instance]
  instLiesOverSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegersCompletionIdealAsIdeal
attribute [-instance]
  AlgebraicCurve.instHasCanonicalLocalResidueK
  AlgebraicCurve.Place.instAlgebra_restrictResidueField
  AlgebraicCurve.Place.instIsScalarTower_restrictResidueField
  AlgebraicCurve.instHasLocalResidue
  AlgebraicCurve.HasSeparableResidue.of_perfectField_of_isCurveOver
  AlgebraicCurve.HasSeparableResidue.of_perfectField
  AlgebraicCurve.Place.instIsLocalHom_restrictSubringHom
  AlgebraicCurve.instHasCanonicalLocalResidueKStar
  ModularCurve.KwNo6Pin.isLocalRing_completion
  SheafOfModules.isIso_ihomModelToIhom
  AlgebraicGeometry.OModulePresheaf.isScalarTower
  AlgebraicGeometry.Scheme.OrderedAffineCover.instLinearOrder
  AlgebraicGeometry.OModulePresheaf.module
  AlgebraicGeometry.Scheme.OrderedAffineCover.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCover.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.addCommGroup
  AlgebraicGeometry.Scheme.OrderedAffineCover.instDecidableEqIdx
  AlgebraicGeometry.OModulePresheaf.moduleSections
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.instSubsingletonObjZero
attribute [-instance]
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
  AlgebraicGeometry.OModulePresheaf.Leray.biC_module
  DoubleComplex.instModuleE₂I
  DoubleComplex.Bounded.modR
  DoubleComplex.instModuleE₂II
  DoubleComplex.instAddCommGroupE₂II
  DoubleComplex.Bounded.abGrp
  DoubleComplex.instAddCommGroupE₂I
  AlgebraicGeometry.ChowDatum.hι_closed
  AlgebraicGeometry.ChowDatumProj.hιN_closed
  AlgebraicGeometry.ChowDatumProj.hp_proper
  AlgebraicGeometry.ChowDatum.hp_isoU
  AlgebraicGeometry.ChowDatum.hp_proper
  AlgebraicGeometry.ProjSpace.algebraAway
  AlgebraicGeometry.ProjSpace.instIsProperProdOverπ
  AlgebraicGeometry.ChowDatumProj.hp_isoU
  AlgebraicGeometry.ProjSpace.isProper_π
  AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
  ProjSpaceCech.GradedModule.H.module
  ProjSpaceCech.GradedModule.H.addCommGroup
  ProjSpaceCech.GradedModule.sec.instAdd
  ProjSpaceCech.GradedModule.sec.instNeg
  ProjSpaceCech.GradedModule.acg
  ProjSpaceCech.GradedModule.Frac.setoid
  ProjSpaceCech.GradedModule.modR
  ProjSpaceCech.GradedModule.sec.instModule
  ProjSpaceCech.GradedModule.sec.instAddCommGroup
  ProjSpaceCech.GradedModule.sec.instZero
  ProjSpaceCech.GradedModule.Presentation.fJ
  ProjSpaceCech.GradedModule.sec.instSMul
  ProjSpaceCech.Twist.H.module
  ProjSpaceCech.Idx.instFintype
  ProjSpaceCech.Twist.H.addCommGroup
attribute [-instance]
  ProjSpaceCech.Idx.instDecidableEq
  ProjSpaceCech.Twist.Mon.instDecidableEq
  ProjSpaceCech.Twist.cochain.instAddCommGroup
  ProjSpaceCech.Twist.cochain.instModule
  AlgebraicGeometry.FGSubalgebra.tensorStage_directedSystem
  AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
  AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
  AlgebraicCurve.CurveModel.locallyOfFiniteType_gluedToBase
  AlgebraicCurve.CurveModel.isFractionRing_overlap
  AlgebraicCurve.CurveModel.isLocallyNoetherian_glued
  AlgebraicCurve.CurveModel.jacobsonSpace_glued
  AlgebraicCurve.CurveModel.isOpenImmersion_ι₀
  AlgebraicCurve.CurveModel.isIntegral_glued
  AlgebraicCurve.CurveModel.quasiSeparated_gluedToBase
  AlgebraicCurve.CurveModel.compactSpace_glued
  AlgebraicCurve.CurveModel.isIntegral_adjoin_chartRing
  AlgebraicCurve.CurveModel.isFractionRing_overlap_functionField
  AlgebraicCurve.CurveModel.isProper_gluedToBase
  AlgebraicCurve.CurveModel.isOpenImmersion_ιU
  AlgebraicCurve.CurveModel.isOpenImmersion_f₀
  AlgebraicCurve.CurveModel.isOpenImmersion_fInf
  AlgebraicCurve.CurveModel.isOpenImmersion_ιInf
  AlgebraicCurve.CurveModel.algebra_overlap_functionField
  AlgebraicCurve.CurveModel.quasiCompact_gluedToBase
  AlgebraicCurve.CurveModel.algebraAdjoin
  AlgebraicCurve.CurveModel.isDedekindDomain_chartRing
  AlgebraicCurve.CurveModel.isIntegralClosure
  AlgebraicCurve.CurveModel.finite_chartRing
  AlgebraicCurve.CurveModel.centre_isPrime
  AlgebraicCurve.CurveModel.isFractionRing_chartRing
  AlgebraicCurve.CurveModel.finiteType_chartRing
  AlgebraicCurve.CurveModel.isNoetherianRing_chartRing
  AlgebraicCurve.CurveModel.isScalarTower_base_adjoin
  AlgebraicCurve.CurveModel.isScalarTower_adjoin
  AlgebraicCurve.CurveModel.chartRing_finitePresentation
attribute [-simp]
  GoodReductionJacobian.RelativePic0Designation.mk.sizeOf_spec
  GoodReductionJacobian.AvatarSchemeBridge.mk.injEq
  GoodReductionJacobian.AvatarSchemeBridge.mk.sizeOf_spec
  GoodReductionJacobian.RelativePic0Designation.mk.injEq
  GoodReductionJacobian.schemeHomOverComp_coe
  NeronModelInfra.schemeHomOverEquivOverHom_apply
  GoodReductionJacobian.RelativeGroupLaw.mk.sizeOf_spec
  NeronModelInfra.schemeHomOverEquivOverHom_symm_apply
  NeronModelInfra.overHomToSchemeHomOver_coe
  GoodReductionJacobian.RelativeGroupLaw.mk.injEq
  NeronModelInfra.overHomToSchemeHomOver_schemeHomOverToOverHom
  NeronModelInfra.schemeHomOverToOverHom_left
  NeronModelInfra.schemeHomOverToOverHom_overHomToSchemeHomOver
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.sizeOf_spec
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
  AlgebraicCurve.CurveModel.mk.injEq
  AlgebraicCurve.CurveModel.mk.sizeOf_spec
  AlgebraicCurve.Place.mk.injEq
  AlgebraicCurve.Divisor.degree_single
  AlgebraicCurve.Divisor.smul_single
  AlgebraicCurve.Place.smul_toValuationSubring
  AlgebraicCurve.Place.heightOneSpectrum_asIdeal
  AlgebraicCurve.Place.coe_algebraMap
  AlgebraicCurve.Place.ord_one
  AlgebraicCurve.Place.coe_smulRingEquiv_apply
  AlgebraicCurve.Pic0.coe_degZeroSMulHom
  AlgebraicCurve.Place.deg_smul
  AlgebraicCurve.Pic0.mk_zero
  AlgebraicCurve.Place.mk.sizeOf_spec
  AlgebraicCurve.Divisor.degree_smul
  AlgebraicCurve.Pic0.mk_add
  AlgebraicCurve.Place.ord_zero
  AlgebraicCurve.Place.ofHeightOneSpectrum_toValuationSubring
  AlgebraicCurve.mulAdele_apply
attribute [-simp]
  AlgebraicCurve.residuePairing_apply_coe
  AlgebraicCurve.mem_adeleBdd
  AlgebraicCurve.weilSmul_one
  AlgebraicCurve.diagonalHom_apply
  AlgebraicCurve.weilSmul_apply
  AlgebraicCurve.adeleSpaceMul_coe
  AlgebraicCurve.mulAdele_one
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U1
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.injEq
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U0
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.mk.injEq
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.pullback_U1
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.pullback_U0
  TwoChartCech.Sections.mk.injEq
  TwoChartCech.Cover.mk.injEq
  TwoChartCech.GrothendieckComplex.mk.injEq
  TwoChartCech.Sections.mk.sizeOf_spec
  TwoChartCech.Cover.mk.sizeOf_spec
  TwoChartCech.Cover.lineBundle_r0_apply
  TwoChartCech.GrothendieckComplex.mk.sizeOf_spec
  TwoChartCech.Cover.lineBundle_r1_apply
  CoherentBaseChange.TwoTermComplex.mk.sizeOf_spec
  CoherentBaseChange.TwoTermComplex.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
  AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
  CategoryTheory.Functor.OverTotal.ofFibre_fst
  CategoryTheory.Functor.overTotal_map_fst
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_J
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYoneda_toGlued_uliftYonedaGluedToSheaf
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t'
attribute [-simp]
  uliftYoneda_toGlued_uliftYonedaGluedToSheaf_assoc
attribute [-simp]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_toGlued
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_openCover_map
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_comp
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_V
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_U
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_f
attribute [-simp]
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_P
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_toBase
  AlgebraicGeometry.RelPicard.rigSection_snd
  AlgebraicGeometry.RelPicard.RigidifiedLineBundle.ofInvertible_L
  AlgebraicGeometry.RelPicard.rigSection_snd_assoc
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
  GoodReductionJacobian.relativeGroupLawOfGrpObj_inv
  GoodReductionJacobian.relativeGroupLawOfGrpObj_mul
  GoodReductionJacobian.overHomEquivSchemeHomOver_apply_coe
  GoodReductionJacobian.relativeGroupLawOfGrpObj_one
  GoodReductionJacobian.overHomEquivSchemeHomOver_symm_apply_left
  PresheafOfModules.freeεIso_hom_app
  PresheafOfModules.freeμIso_hom_app
  AlgebraicCurve.coe_cechH0Equiv_apply
  AlgebraicCurve.cechH1ToH1_mk
  AlgebraicCurve.lSpaceOn_univ
  AlgebraicCurve.lSpaceOn_empty
  AlgebraicCurve.Place.congrEquiv_symm_apply
  AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
  AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
  AlgebraicCurve.Place.congrEquiv_apply
  AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
  AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
  AlgebraicCurve.Divisor.mapRestrict_single
  AlgebraicCurve.Divisor.pushforward_single
  AlgebraicCurve.Place.coe_restrictInclusion
  AlgebraicCurve.Place.mem_fiber
  AlgebraicCurve.Place.restrict_toValuationSubring
  AlgebraicCurve.Divisor.degree_pushforward
  AlgebraicCurve.Place.restrictResidueMap_residue
  AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
  AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
  AlgebraicCurve.Place.placeOfPrime_toValuationSubring
  AlgebraicCurve.Place.mem_fiberOver
  AlgebraicCurve.Place.fiberEquiv_symm_apply
  AlgebraicCurve.Place.fiberEquiv_apply
  AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
attribute [-simp]
  AlgebraicCurve.Divisor.degree_pushforwardAlong
  AlgebraicCurve.Pic0.coe_degZeroCorrespondence
  AlgebraicCurve.Place.mem_fiberAlong
  AlgebraicCurve.SemilinearAut.toRingAut_inv
  AlgebraicCurve.SemilinearAut.smul_def
  AlgebraicCurve.SemilinearAut.smul_single
  AlgebraicCurve.SemilinearAut.smul_toValuationSubring
  AlgebraicCurve.SemilinearAut.baseAut_inv
  AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_one
  AlgebraicCurve.SemilinearAut.deg_smul
  AlgebraicCurve.SemilinearAut.degree_smul
  AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
  AlgebraicCurve.SemilinearAut.baseAut_mul
  AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
  AlgebraicCurve.SemilinearAut.baseAut_one
  AlgebraicCurve.SemilinearAut.ofAlgAut_smul
  AlgebraicCurve.SemilinearAut.coe_torsion_smul
  AlgebraicCurve.SemilinearAut.toRingAut_mul
attribute [-simp]
  AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeInfty
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_some
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeOfPoint
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_none
  AlgebraicCurve.Divisor.evalFun_zero
  AlgebraicCurve.Place.evalAt_one
  AlgebraicCurve.Place.differentialCoeff_zero
  AlgebraicCurve.Place.differentialCoeff_dCoord
  AlgebraicCurve.TranscendenceTower.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
  AlgebraicCurve.TranscendenceTower.mk.injEq
  AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec
  AlgebraicCurve.PoleDivisorPackage.mk.injEq
  AlgebraicGeometry.RelPicard.thetaBundle_def
attribute [-simp]
  AlgebraicGeometry.RelPicard.picardBundle_def
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_ofRelEffDivisor
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_I
  AlgebraicGeometry.mapOnProdOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.mk.sizeOf_spec
  AlgebraicGeometry.RelEffCartierDiv.mk.injEq
  AlgebraicGeometry.mapOnProdOver_snd
  AlgebraicGeometry.mapOnProdOver_fst
  AlgebraicGeometry.mapOnProdOver_snd_assoc
  AlgebraicGeometry.mapOnProdOver_id
  AlgebraicCurve.RelEffDivisor.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_fst
  AlgebraicCurve.mapOnProd_fst_assoc
  AlgebraicCurve.mapOnProd_snd
  AlgebraicCurve.UnivDivisorPack.mk.injEq
  AlgebraicCurve.RelEffDivisor.mk.injEq
  AlgebraicCurve.UnivDivisorPack.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_snd_assoc
  AlgebraicGeometry.Scheme.Modules.exteriorPower_obj
  PresheafOfModules.exteriorPower_map_ιMulti
  PresheafOfModules.ExteriorPower.appₗ_apply
  AlgebraicGeometry.prodKerGraph_one
  AlgebraicGeometry.fibrePowOver.proj_comp
  AlgebraicGeometry.prodKerGraph_zero
  AlgebraicGeometry.RelEffCartierDiv.empty_I
  AlgebraicGeometry.fibrePowOver.proj_comp_assoc
  AlgebraicGeometry.graphOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
  AlgebraicGeometry.graphOver_fst
  AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
  AlgebraicGeometry.graphOver_snd
  AlgebraicGeometry.graphOver_snd_assoc
  AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
  AlgebraicCurve.SymmetricPowerPackage.mk.injEq
  AlgebraicGeometry.FGSubalgebra.cocone_ι_app_apply
  AlgebraicGeometry.RelPicard.fst_toProdSpec
  AlgebraicGeometry.RelPicard.toProdSpec_fst_assoc
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_cons
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_nil
attribute [-simp]
  AlgebraicGeometry.RelPicard.fst_toProdSpec_assoc
  AlgebraicGeometry.RelPicard.toProdSpec_fst
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.sizeOf_spec
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.injEq
  AlgebraicCurve.adeleSingle_coe
  AlgebraicCurve.kaehlerResidueTermKFam_apply
  AlgebraicCurve.Place.LocalResidueData.mk.injEq
  AlgebraicCurve.Place.LocalResidueData.mk.sizeOf_spec
  AlgebraicCurve.Place.kw_ffgc_adicCompletionComapIntegers_coe
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.sizeOf_spec
  AlgebraicCurve.Place.mem_simplePoleSubmodule
  AlgebraicCurve.Place.coe_uniformizerSubring
  ModularCurve.Lg37.Lg37CompletionSection.mk.injEq
  AlgebraicCurve.Place.CoefficientFieldSection.mk.injEq
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.injEq
  ModularCurve.Lg37.Lg37CompletionSection.mk.sizeOf_spec
  AlgebraicCurve.Place.CoefficientFieldSection.mk.sizeOf_spec
  AlgebraicCurve.Place.poleSubmodule_one
  AlgebraicCurve.Place.mem_poleSubmodule
  AlgebraicGeometry.Scheme.Modules.toUnitSection_ofUnitSection
  AlgebraicGeometry.Scheme.Modules.pullbackSection_def
  AlgebraicGeometry.Scheme.Modules.ofUnitSection_toUnitSection
  PresheafOfModules.InternalHom.IsSheafAux.appAt_toPresheafHom
attribute [-simp]
  SheafOfModules.ihomSectionsEquivFamily_unit
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_apply
  SheafOfModules.ihomEval_unit_app
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_right
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_left
  AlgebraicGeometry.Scheme.Modules.homOfFamily_app_apply
  SheafOfModules.unit_ihomSectionsEquivFamily
  AlgebraicGeometry.Scheme.Modules.familyOfHom_app
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_hom_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_inv_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomOfFamily_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_symm_apply
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_right
  AlgebraicGeometry.Scheme.Modules.map_unitSection
  AlgebraicGeometry.Scheme.Modules.tensorSectionsBilin_apply
  AlgebraicGeometry.Scheme.Modules.tensorPowSection_zero
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_left
  AlgebraicGeometry.Scheme.Modules.tensorPow_zero
  AlgebraicGeometry.Scheme.Modules.tensorPow_succ
  AlgebraicGeometry.Scheme.OrderedAffineCover.mk.injEq
  AlgebraicGeometry.OModulePresheaf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCover.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.mk.injEq
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_neg
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_zero
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_sub
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_add
  AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
  AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U
  AlgebraicGeometry.OModulePresheaf.Hom.mk.injEq
  AlgebraicGeometry.OModulePresheaf.Hom.id_app
  AlgebraicGeometry.OModulePresheaf.AffHom.appSections_apply
  AlgebraicGeometry.OModulePresheaf.AffHom.comp_app
  AlgebraicGeometry.OModulePresheaf.AffSES.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.AffHom.kerMap_coe
  AlgebraicGeometry.OModulePresheaf.AffHom.id_app
  AlgebraicGeometry.OModulePresheaf.Hom.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.Hom.toAffHom_app
attribute [-simp]
  AlgebraicGeometry.OModulePresheaf.SES.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.AffHom.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.Hom.comp_app
  AlgebraicGeometry.OModulePresheaf.SES.mk.injEq
  AlgebraicGeometry.OModulePresheaf.AffHom.mk.injEq
  AlgebraicGeometry.OModulePresheaf.Hom.appSections_apply
  AlgebraicGeometry.OModulePresheaf.AffSES.mk.injEq
  AlgebraicGeometry.OModulePresheaf.prod_obj
  AlgebraicGeometry.OModulePresheaf.restrOpen_obj
  AlgebraicGeometry.OModulePresheaf.DevissageStep.mk.injEq
  AlgebraicGeometry.OModulePresheaf.pushforward_obj
  AlgebraicGeometry.OModulePresheaf.im_obj
  AlgebraicGeometry.OModulePresheaf.pow_obj
  AlgebraicGeometry.OModulePresheaf.fstHom_app
  AlgebraicGeometry.OModulePresheaf.ker_obj
  AlgebraicGeometry.OModulePresheaf.coker_obj
  AlgebraicGeometry.OModulePresheaf.DevissageStep.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCover.preimage_U
  AlgebraicGeometry.OModulePresheaf.sndHom_app
  AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
  DoubleComplex.Bounded.mk.injEq
  DoubleComplex.Bounded.mk.sizeOf_spec
  DoubleComplex.Convergence.mk.injEq
  DoubleComplex.Convergence.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.injEq
  AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatumProj.mk.injEq
  AlgebraicGeometry.ChowDatum.mk.injEq
  ProjSpaceCech.GradedModule.mk.injEq
  ProjSpaceCech.GradedModule.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Presentation.mk.injEq
  ProjSpaceCech.GradedModule.Frac.mk.injEq
  ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.shift_toLinearMap
  ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.mk.injEq
  TwoChartCech.Mumford.dK_apply
attribute [-simp]
  TwoChartCech.Mumford.ι0_apply
  TwoChartCech.Mumford.ι1_apply
  TwoChartCech.KerCoprod.dK_apply
  TwoChartCech.KerCoprod.ι1_apply
  TwoChartCech.KerCoprod.ι0_apply
  AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
  AlgebraicGeometry.RelPicard.algEquivZeroGroupCut_toSubPicCondition
  AlgebraicGeometry.RelPicard.LFP.stageHom_val
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_hom_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_inv_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.restrict_P
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp
  AlgebraicGeometry.RelEffCartierDiv.functor_map_fst
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_pullbackAlong
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_symm_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp_assoc
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top
  AlgebraicGeometry.RelEffCartierDiv.mem_supportedIn_iff
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top_eq
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
  CoherentBaseChange.FibreH0Family.mk.sizeOf_spec
  CoherentBaseChange.FibreH0Family.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.sizeOf_spec
  AlgebraicCurve.CurveModel.coe_gInf
  AlgebraicCurve.CurveModel.coe_tInvChart
  AlgebraicCurve.CurveModel.ιInf_gluedToBase_assoc
  AlgebraicCurve.CurveModel.ιInf_gluedToBase
  AlgebraicCurve.CurveModel.primeOfι₀_asIdeal
  AlgebraicCurve.CurveModel.coe_tChart
  AlgebraicCurve.CurveModel.ι₀_gluedToBase_assoc
  AlgebraicCurve.CurveModel.primeOfιInf_asIdeal
attribute [-simp]
  AlgebraicCurve.CurveModel.ι₀_gluedToBase
  AlgebraicCurve.CurveModel.coe_tma
  AlgebraicCurve.CurveModel.coe_primeEquivChartPlaces
universe u
noncomputable section
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.CategoryTheory.CartesianMonoidalCategory
open _root_.AlgebraicGeometry.RelPicard
open _root_.NeronModelInfra
namespace P2mCubeAssembly
section Triv
variable {S T V : Scheme.{u}}

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.ThreeSlices
attribute [-instance]
  AlgebraicGeometry.SmoothOfRelativeDimension.fiberToSpecResidueField
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_snd
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_fst
  AlgebraicGeometry.SmoothOfRelativeDimension.smooth_one
  AlgebraicGeometry.SmoothProperCurve.isIntegral_pullback_Spec_field
  AlgebraicGeometry.IsProper.fiberToSpecResidueField
  AlgebraicCurve.CurveModel.isProper
  AlgebraicCurve.CurveModel.isIntegral
  AlgebraicCurve.CurveModel.smooth
  AlgebraicCurve.Place.instIsScalarTowerSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Divisor.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instSMulAlgEquiv
  AlgebraicCurve.Place.instIsPrincipalIdealRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instIsDiscreteValuationRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Pic0.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instAlgebraSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instMulActionAlgEquiv
  AlgebraicCurve.Pic0.instSMulAlgEquiv
  TwoChartCech.Sections.M0_moduleA
  TwoChartCech.Sections.M1_module
  TwoChartCech.Cover.A01_algebra
  TwoChartCech.Cover.A0_algebra
  TwoChartCech.Cover.A1_commRing
  TwoChartCech.Cover.A1_algebra
  TwoChartCech.Sections.M01_module
  TwoChartCech.Sections.M0_addCommGroup
  TwoChartCech.Sections.M0_tower
  TwoChartCech.Sections.M01_addCommGroup
  TwoChartCech.Cover.A0_commRing
  TwoChartCech.Sections.M1_tower
  TwoChartCech.Sections.M01_moduleA
  TwoChartCech.Sections.M0_module
  TwoChartCech.Sections.M1_moduleA
  TwoChartCech.Sections.M1_addCommGroup
  TwoChartCech.Cover.A01_commRing
  TwoChartCech.Sections.M01_tower
  CoherentBaseChange.TwoTermComplex.C0_module
  CoherentBaseChange.TwoTermComplex.C0_addCommGroup
  CoherentBaseChange.TwoTermComplex.C1_module
  CoherentBaseChange.TwoTermComplex.C1_addCommGroup
attribute [-instance]
  CoherentBaseChange.TwoTermComplex.C0_free
  CoherentBaseChange.TwoTermComplex.C1_finite
  CoherentBaseChange.TwoTermComplex.C0_finite
  CoherentBaseChange.TwoTermComplex.C1_free
  AlgebraicCurve.IsCurveOver.instNontrivialKaehler
  AlgebraicCurve.IsCurveOver.instFreeKaehler
  AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
  AlgebraicCurve.IsCurveOver.instFiniteResidue
attribute [-instance]
  instIsLocallyInjectiveFunUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsLocallySurjectiveUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsOpenImmersionToGlued
attribute [-instance]
  instIsIsoSheafZariskiTopologyTypeUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.RelPicard.isOpenImmersion_toGlued
  AlgebraicGeometry.Scheme.Modules.preservesBinaryProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback_monoidal
  AlgebraicGeometry.Scheme.Modules.sheafify_isLocalization'
  AlgebraicGeometry.Scheme.Modules.preservesTerminal_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback₀_monoidal
  AlgebraicGeometry.Scheme.Modules.preservesFiniteProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.sheafifyPullback_lifting
  PresheafOfModules.PullbackMonoidal.pullback_monoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ
  PresheafOfModules.pushforward_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_η
  PresheafOfModules.free_monoidal
  PresheafOfModules.restrictScalars_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ_gS
  PresheafOfModules.pullback_oplaxMonoidal
attribute [-instance]
  instPreservesColimitsOfSizeCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierPb
attribute [-instance]
  PresheafOfModules.pullback_monoidal'
  AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
  AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
  AlgebraicCurve.Place.instIsPrimeCenter
  AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
  instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
  AlgebraicCurve.Pic0.instModuleZModTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instSMulTorsion
  AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
  AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
  AlgebraicCurve.RationalFunctionField.instNontrivialInftyValueGroup
  PresheafOfModules.ExteriorPower.instModulePresheafAb
  AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
  AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
  AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
  AlgebraicGeometry.isClosedImmersion_graphOver
  AlgebraicGeometry.FGSubalgebra.instIsDirectedLe
attribute [-instance]
  instQuasiSeparatedSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsCofilteredOpposite
  AlgebraicGeometry.FGSubalgebra.instIsAffineObjOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instNonempty
  AlgebraicGeometry.FGSubalgebra.instNonemptySubtypeLeSubalgebraValFG
attribute [-instance]
  instCompactSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsDirectedSubtypeLeSubalgebraValFG
  AlgebraicGeometry.FGSubalgebra.instIsAffineHomMapOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instIsFiltered
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instNeg
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulInt
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAddCommGroup
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAdd
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSub
attribute [-instance]
  instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
  AlgebraicCurve.instHasLocalResidue_of_hasCanonicalLocalResidueK
  AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
  AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
  ModularCurve.KwF4gRRTate.instAlgebraKAdicCompletionIntegers
  AlgebraicCurve.Place.kw_ffgc_continuousSMul_adicCompletionComap
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersCompletionCompletion
attribute [-instance]
  instLiesOverSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegersCompletionIdealAsIdeal
attribute [-instance]
  AlgebraicCurve.instHasCanonicalLocalResidueK
  AlgebraicCurve.Place.instAlgebra_restrictResidueField
  AlgebraicCurve.Place.instIsScalarTower_restrictResidueField
  AlgebraicCurve.instHasLocalResidue
  AlgebraicCurve.HasSeparableResidue.of_perfectField_of_isCurveOver
  AlgebraicCurve.HasSeparableResidue.of_perfectField
  AlgebraicCurve.Place.instIsLocalHom_restrictSubringHom
  AlgebraicCurve.instHasCanonicalLocalResidueKStar
  ModularCurve.KwNo6Pin.isLocalRing_completion
  SheafOfModules.isIso_ihomModelToIhom
  AlgebraicGeometry.OModulePresheaf.isScalarTower
  AlgebraicGeometry.Scheme.OrderedAffineCover.instLinearOrder
  AlgebraicGeometry.OModulePresheaf.module
  AlgebraicGeometry.Scheme.OrderedAffineCover.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCover.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.addCommGroup
  AlgebraicGeometry.Scheme.OrderedAffineCover.instDecidableEqIdx
  AlgebraicGeometry.OModulePresheaf.moduleSections
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.instSubsingletonObjZero
attribute [-instance]
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
  AlgebraicGeometry.OModulePresheaf.Leray.biC_module
  DoubleComplex.instModuleE₂I
  DoubleComplex.Bounded.modR
  DoubleComplex.instModuleE₂II
  DoubleComplex.instAddCommGroupE₂II
  DoubleComplex.Bounded.abGrp
  DoubleComplex.instAddCommGroupE₂I
  AlgebraicGeometry.ChowDatum.hι_closed
  AlgebraicGeometry.ChowDatumProj.hιN_closed
  AlgebraicGeometry.ChowDatumProj.hp_proper
  AlgebraicGeometry.ChowDatum.hp_isoU
  AlgebraicGeometry.ChowDatum.hp_proper
  AlgebraicGeometry.ProjSpace.algebraAway
  AlgebraicGeometry.ProjSpace.instIsProperProdOverπ
  AlgebraicGeometry.ChowDatumProj.hp_isoU
  AlgebraicGeometry.ProjSpace.isProper_π
  AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
  ProjSpaceCech.GradedModule.H.module
  ProjSpaceCech.GradedModule.H.addCommGroup
  ProjSpaceCech.GradedModule.sec.instAdd
  ProjSpaceCech.GradedModule.sec.instNeg
  ProjSpaceCech.GradedModule.acg
  ProjSpaceCech.GradedModule.Frac.setoid
  ProjSpaceCech.GradedModule.modR
  ProjSpaceCech.GradedModule.sec.instModule
  ProjSpaceCech.GradedModule.sec.instAddCommGroup
  ProjSpaceCech.GradedModule.sec.instZero
  ProjSpaceCech.GradedModule.Presentation.fJ
  ProjSpaceCech.GradedModule.sec.instSMul
  ProjSpaceCech.Twist.H.module
  ProjSpaceCech.Idx.instFintype
  ProjSpaceCech.Twist.H.addCommGroup
attribute [-instance]
  ProjSpaceCech.Idx.instDecidableEq
  ProjSpaceCech.Twist.Mon.instDecidableEq
  ProjSpaceCech.Twist.cochain.instAddCommGroup
  ProjSpaceCech.Twist.cochain.instModule
  AlgebraicGeometry.FGSubalgebra.tensorStage_directedSystem
  AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
  AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
  AlgebraicCurve.CurveModel.locallyOfFiniteType_gluedToBase
  AlgebraicCurve.CurveModel.isFractionRing_overlap
  AlgebraicCurve.CurveModel.isLocallyNoetherian_glued
  AlgebraicCurve.CurveModel.jacobsonSpace_glued
  AlgebraicCurve.CurveModel.isOpenImmersion_ι₀
  AlgebraicCurve.CurveModel.isIntegral_glued
  AlgebraicCurve.CurveModel.quasiSeparated_gluedToBase
  AlgebraicCurve.CurveModel.compactSpace_glued
  AlgebraicCurve.CurveModel.isIntegral_adjoin_chartRing
  AlgebraicCurve.CurveModel.isFractionRing_overlap_functionField
  AlgebraicCurve.CurveModel.isProper_gluedToBase
  AlgebraicCurve.CurveModel.isOpenImmersion_ιU
  AlgebraicCurve.CurveModel.isOpenImmersion_f₀
  AlgebraicCurve.CurveModel.isOpenImmersion_fInf
  AlgebraicCurve.CurveModel.isOpenImmersion_ιInf
  AlgebraicCurve.CurveModel.algebra_overlap_functionField
  AlgebraicCurve.CurveModel.quasiCompact_gluedToBase
  AlgebraicCurve.CurveModel.algebraAdjoin
  AlgebraicCurve.CurveModel.isDedekindDomain_chartRing
  AlgebraicCurve.CurveModel.isIntegralClosure
  AlgebraicCurve.CurveModel.finite_chartRing
  AlgebraicCurve.CurveModel.centre_isPrime
  AlgebraicCurve.CurveModel.isFractionRing_chartRing
  AlgebraicCurve.CurveModel.finiteType_chartRing
  AlgebraicCurve.CurveModel.isNoetherianRing_chartRing
  AlgebraicCurve.CurveModel.isScalarTower_base_adjoin
  AlgebraicCurve.CurveModel.isScalarTower_adjoin
  AlgebraicCurve.CurveModel.chartRing_finitePresentation
attribute [-simp]
  GoodReductionJacobian.RelativePic0Designation.mk.sizeOf_spec
  GoodReductionJacobian.AvatarSchemeBridge.mk.injEq
  GoodReductionJacobian.AvatarSchemeBridge.mk.sizeOf_spec
  GoodReductionJacobian.RelativePic0Designation.mk.injEq
  GoodReductionJacobian.schemeHomOverComp_coe
  NeronModelInfra.schemeHomOverEquivOverHom_apply
  GoodReductionJacobian.RelativeGroupLaw.mk.sizeOf_spec
  NeronModelInfra.schemeHomOverEquivOverHom_symm_apply
  NeronModelInfra.overHomToSchemeHomOver_coe
  GoodReductionJacobian.RelativeGroupLaw.mk.injEq
  NeronModelInfra.overHomToSchemeHomOver_schemeHomOverToOverHom
  NeronModelInfra.schemeHomOverToOverHom_left
  NeronModelInfra.schemeHomOverToOverHom_overHomToSchemeHomOver
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.sizeOf_spec
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
  AlgebraicCurve.CurveModel.mk.injEq
  AlgebraicCurve.CurveModel.mk.sizeOf_spec
  AlgebraicCurve.Place.mk.injEq
  AlgebraicCurve.Divisor.degree_single
  AlgebraicCurve.Divisor.smul_single
  AlgebraicCurve.Place.smul_toValuationSubring
  AlgebraicCurve.Place.heightOneSpectrum_asIdeal
  AlgebraicCurve.Place.coe_algebraMap
  AlgebraicCurve.Place.ord_one
  AlgebraicCurve.Place.coe_smulRingEquiv_apply
  AlgebraicCurve.Pic0.coe_degZeroSMulHom
  AlgebraicCurve.Place.deg_smul
  AlgebraicCurve.Pic0.mk_zero
  AlgebraicCurve.Place.mk.sizeOf_spec
  AlgebraicCurve.Divisor.degree_smul
  AlgebraicCurve.Pic0.mk_add
  AlgebraicCurve.Place.ord_zero
  AlgebraicCurve.Place.ofHeightOneSpectrum_toValuationSubring
  AlgebraicCurve.mulAdele_apply
attribute [-simp]
  AlgebraicCurve.residuePairing_apply_coe
  AlgebraicCurve.mem_adeleBdd
  AlgebraicCurve.weilSmul_one
  AlgebraicCurve.diagonalHom_apply
  AlgebraicCurve.weilSmul_apply
  AlgebraicCurve.adeleSpaceMul_coe
  AlgebraicCurve.mulAdele_one
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U1
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.injEq
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U0
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.mk.injEq
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.pullback_U1
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.pullback_U0
  TwoChartCech.Sections.mk.injEq
  TwoChartCech.Cover.mk.injEq
  TwoChartCech.GrothendieckComplex.mk.injEq
  TwoChartCech.Sections.mk.sizeOf_spec
  TwoChartCech.Cover.mk.sizeOf_spec
  TwoChartCech.Cover.lineBundle_r0_apply
  TwoChartCech.GrothendieckComplex.mk.sizeOf_spec
  TwoChartCech.Cover.lineBundle_r1_apply
  CoherentBaseChange.TwoTermComplex.mk.sizeOf_spec
  CoherentBaseChange.TwoTermComplex.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
  AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
  CategoryTheory.Functor.OverTotal.ofFibre_fst
  CategoryTheory.Functor.overTotal_map_fst
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_J
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYoneda_toGlued_uliftYonedaGluedToSheaf
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t'
attribute [-simp]
  uliftYoneda_toGlued_uliftYonedaGluedToSheaf_assoc
attribute [-simp]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_toGlued
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_openCover_map
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_comp
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_V
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_U
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_f
attribute [-simp]
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_P
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_toBase
  AlgebraicGeometry.RelPicard.rigSection_snd
  AlgebraicGeometry.RelPicard.RigidifiedLineBundle.ofInvertible_L
  AlgebraicGeometry.RelPicard.rigSection_snd_assoc
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
  GoodReductionJacobian.relativeGroupLawOfGrpObj_inv
  GoodReductionJacobian.relativeGroupLawOfGrpObj_mul
  GoodReductionJacobian.overHomEquivSchemeHomOver_apply_coe
  GoodReductionJacobian.relativeGroupLawOfGrpObj_one
  GoodReductionJacobian.overHomEquivSchemeHomOver_symm_apply_left
  PresheafOfModules.freeεIso_hom_app
  PresheafOfModules.freeμIso_hom_app
  AlgebraicCurve.coe_cechH0Equiv_apply
  AlgebraicCurve.cechH1ToH1_mk
  AlgebraicCurve.lSpaceOn_univ
  AlgebraicCurve.lSpaceOn_empty
  AlgebraicCurve.Place.congrEquiv_symm_apply
  AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
  AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
  AlgebraicCurve.Place.congrEquiv_apply
  AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
  AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
  AlgebraicCurve.Divisor.mapRestrict_single
  AlgebraicCurve.Divisor.pushforward_single
  AlgebraicCurve.Place.coe_restrictInclusion
  AlgebraicCurve.Place.mem_fiber
  AlgebraicCurve.Place.restrict_toValuationSubring
  AlgebraicCurve.Divisor.degree_pushforward
  AlgebraicCurve.Place.restrictResidueMap_residue
  AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
  AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
  AlgebraicCurve.Place.placeOfPrime_toValuationSubring
  AlgebraicCurve.Place.mem_fiberOver
  AlgebraicCurve.Place.fiberEquiv_symm_apply
  AlgebraicCurve.Place.fiberEquiv_apply
  AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
attribute [-simp]
  AlgebraicCurve.Divisor.degree_pushforwardAlong
  AlgebraicCurve.Pic0.coe_degZeroCorrespondence
  AlgebraicCurve.Place.mem_fiberAlong
  AlgebraicCurve.SemilinearAut.toRingAut_inv
  AlgebraicCurve.SemilinearAut.smul_def
  AlgebraicCurve.SemilinearAut.smul_single
  AlgebraicCurve.SemilinearAut.smul_toValuationSubring
  AlgebraicCurve.SemilinearAut.baseAut_inv
  AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_one
  AlgebraicCurve.SemilinearAut.deg_smul
  AlgebraicCurve.SemilinearAut.degree_smul
  AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
  AlgebraicCurve.SemilinearAut.baseAut_mul
  AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
  AlgebraicCurve.SemilinearAut.baseAut_one
  AlgebraicCurve.SemilinearAut.ofAlgAut_smul
  AlgebraicCurve.SemilinearAut.coe_torsion_smul
  AlgebraicCurve.SemilinearAut.toRingAut_mul
attribute [-simp]
  AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeInfty
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_some
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeOfPoint
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_none
  AlgebraicCurve.Divisor.evalFun_zero
  AlgebraicCurve.Place.evalAt_one
  AlgebraicCurve.Place.differentialCoeff_zero
  AlgebraicCurve.Place.differentialCoeff_dCoord
  AlgebraicCurve.TranscendenceTower.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
  AlgebraicCurve.TranscendenceTower.mk.injEq
  AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec
  AlgebraicCurve.PoleDivisorPackage.mk.injEq
  AlgebraicGeometry.RelPicard.thetaBundle_def
attribute [-simp]
  AlgebraicGeometry.RelPicard.picardBundle_def
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_ofRelEffDivisor
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_I
  AlgebraicGeometry.mapOnProdOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.mk.sizeOf_spec
  AlgebraicGeometry.RelEffCartierDiv.mk.injEq
  AlgebraicGeometry.mapOnProdOver_snd
  AlgebraicGeometry.mapOnProdOver_fst
  AlgebraicGeometry.mapOnProdOver_snd_assoc
  AlgebraicGeometry.mapOnProdOver_id
  AlgebraicCurve.RelEffDivisor.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_fst
  AlgebraicCurve.mapOnProd_fst_assoc
  AlgebraicCurve.mapOnProd_snd
  AlgebraicCurve.UnivDivisorPack.mk.injEq
  AlgebraicCurve.RelEffDivisor.mk.injEq
  AlgebraicCurve.UnivDivisorPack.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_snd_assoc
  AlgebraicGeometry.Scheme.Modules.exteriorPower_obj
  PresheafOfModules.exteriorPower_map_ιMulti
  PresheafOfModules.ExteriorPower.appₗ_apply
  AlgebraicGeometry.prodKerGraph_one
  AlgebraicGeometry.fibrePowOver.proj_comp
  AlgebraicGeometry.prodKerGraph_zero
  AlgebraicGeometry.RelEffCartierDiv.empty_I
  AlgebraicGeometry.fibrePowOver.proj_comp_assoc
  AlgebraicGeometry.graphOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
  AlgebraicGeometry.graphOver_fst
  AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
  AlgebraicGeometry.graphOver_snd
  AlgebraicGeometry.graphOver_snd_assoc
  AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
  AlgebraicCurve.SymmetricPowerPackage.mk.injEq
  AlgebraicGeometry.FGSubalgebra.cocone_ι_app_apply
  AlgebraicGeometry.RelPicard.fst_toProdSpec
  AlgebraicGeometry.RelPicard.toProdSpec_fst_assoc
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_cons
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_nil
attribute [-simp]
  AlgebraicGeometry.RelPicard.fst_toProdSpec_assoc
  AlgebraicGeometry.RelPicard.toProdSpec_fst
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.sizeOf_spec
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.injEq
  AlgebraicCurve.adeleSingle_coe
  AlgebraicCurve.kaehlerResidueTermKFam_apply
  AlgebraicCurve.Place.LocalResidueData.mk.injEq
  AlgebraicCurve.Place.LocalResidueData.mk.sizeOf_spec
  AlgebraicCurve.Place.kw_ffgc_adicCompletionComapIntegers_coe
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.sizeOf_spec
  AlgebraicCurve.Place.mem_simplePoleSubmodule
  AlgebraicCurve.Place.coe_uniformizerSubring
  ModularCurve.Lg37.Lg37CompletionSection.mk.injEq
  AlgebraicCurve.Place.CoefficientFieldSection.mk.injEq
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.injEq
  ModularCurve.Lg37.Lg37CompletionSection.mk.sizeOf_spec
  AlgebraicCurve.Place.CoefficientFieldSection.mk.sizeOf_spec
  AlgebraicCurve.Place.poleSubmodule_one
  AlgebraicCurve.Place.mem_poleSubmodule
  AlgebraicGeometry.Scheme.Modules.toUnitSection_ofUnitSection
  AlgebraicGeometry.Scheme.Modules.pullbackSection_def
  AlgebraicGeometry.Scheme.Modules.ofUnitSection_toUnitSection
  PresheafOfModules.InternalHom.IsSheafAux.appAt_toPresheafHom
attribute [-simp]
  SheafOfModules.ihomSectionsEquivFamily_unit
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_apply
  SheafOfModules.ihomEval_unit_app
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_right
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_left
  AlgebraicGeometry.Scheme.Modules.homOfFamily_app_apply
  SheafOfModules.unit_ihomSectionsEquivFamily
  AlgebraicGeometry.Scheme.Modules.familyOfHom_app
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_hom_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_inv_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomOfFamily_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_symm_apply
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_right
  AlgebraicGeometry.Scheme.Modules.map_unitSection
  AlgebraicGeometry.Scheme.Modules.tensorSectionsBilin_apply
  AlgebraicGeometry.Scheme.Modules.tensorPowSection_zero
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_left
  AlgebraicGeometry.Scheme.Modules.tensorPow_zero
  AlgebraicGeometry.Scheme.Modules.tensorPow_succ
  AlgebraicGeometry.Scheme.OrderedAffineCover.mk.injEq
  AlgebraicGeometry.OModulePresheaf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCover.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.mk.injEq
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_neg
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_zero
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_sub
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_add
  AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
  AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U
  AlgebraicGeometry.OModulePresheaf.Hom.mk.injEq
  AlgebraicGeometry.OModulePresheaf.Hom.id_app
  AlgebraicGeometry.OModulePresheaf.AffHom.appSections_apply
  AlgebraicGeometry.OModulePresheaf.AffHom.comp_app
  AlgebraicGeometry.OModulePresheaf.AffSES.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.AffHom.kerMap_coe
  AlgebraicGeometry.OModulePresheaf.AffHom.id_app
  AlgebraicGeometry.OModulePresheaf.Hom.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.Hom.toAffHom_app
attribute [-simp]
  AlgebraicGeometry.OModulePresheaf.SES.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.AffHom.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.Hom.comp_app
  AlgebraicGeometry.OModulePresheaf.SES.mk.injEq
  AlgebraicGeometry.OModulePresheaf.AffHom.mk.injEq
  AlgebraicGeometry.OModulePresheaf.Hom.appSections_apply
  AlgebraicGeometry.OModulePresheaf.AffSES.mk.injEq
  AlgebraicGeometry.OModulePresheaf.prod_obj
  AlgebraicGeometry.OModulePresheaf.restrOpen_obj
  AlgebraicGeometry.OModulePresheaf.DevissageStep.mk.injEq
  AlgebraicGeometry.OModulePresheaf.pushforward_obj
  AlgebraicGeometry.OModulePresheaf.im_obj
  AlgebraicGeometry.OModulePresheaf.pow_obj
  AlgebraicGeometry.OModulePresheaf.fstHom_app
  AlgebraicGeometry.OModulePresheaf.ker_obj
  AlgebraicGeometry.OModulePresheaf.coker_obj
  AlgebraicGeometry.OModulePresheaf.DevissageStep.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCover.preimage_U
  AlgebraicGeometry.OModulePresheaf.sndHom_app
  AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
  DoubleComplex.Bounded.mk.injEq
  DoubleComplex.Bounded.mk.sizeOf_spec
  DoubleComplex.Convergence.mk.injEq
  DoubleComplex.Convergence.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.injEq
  AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatumProj.mk.injEq
  AlgebraicGeometry.ChowDatum.mk.injEq
  ProjSpaceCech.GradedModule.mk.injEq
  ProjSpaceCech.GradedModule.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Presentation.mk.injEq
  ProjSpaceCech.GradedModule.Frac.mk.injEq
  ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.shift_toLinearMap
  ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.mk.injEq
  TwoChartCech.Mumford.dK_apply
attribute [-simp]
  TwoChartCech.Mumford.ι0_apply
  TwoChartCech.Mumford.ι1_apply
  TwoChartCech.KerCoprod.dK_apply
  TwoChartCech.KerCoprod.ι1_apply
  TwoChartCech.KerCoprod.ι0_apply
  AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
  AlgebraicGeometry.RelPicard.algEquivZeroGroupCut_toSubPicCondition
  AlgebraicGeometry.RelPicard.LFP.stageHom_val
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_hom_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_inv_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.restrict_P
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp
  AlgebraicGeometry.RelEffCartierDiv.functor_map_fst
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_pullbackAlong
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_symm_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp_assoc
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top
  AlgebraicGeometry.RelEffCartierDiv.mem_supportedIn_iff
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top_eq
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
  CoherentBaseChange.FibreH0Family.mk.sizeOf_spec
  CoherentBaseChange.FibreH0Family.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.sizeOf_spec
  AlgebraicCurve.CurveModel.coe_gInf
  AlgebraicCurve.CurveModel.coe_tInvChart
  AlgebraicCurve.CurveModel.ιInf_gluedToBase_assoc
  AlgebraicCurve.CurveModel.ιInf_gluedToBase
  AlgebraicCurve.CurveModel.primeOfι₀_asIdeal
  AlgebraicCurve.CurveModel.coe_tChart
  AlgebraicCurve.CurveModel.ι₀_gluedToBase_assoc
  AlgebraicCurve.CurveModel.primeOfιInf_asIdeal
attribute [-simp]
  AlgebraicCurve.CurveModel.ι₀_gluedToBase
  AlgebraicCurve.CurveModel.coe_tma
  AlgebraicCurve.CurveModel.coe_primeEquivChartPlaces
universe u
noncomputable section
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.CategoryTheory.CartesianMonoidalCategory
open _root_.AlgebraicGeometry.RelPicard
open _root_.NeronModelInfra
namespace P2mCubeAssembly
section Triv
variable {S T V : Scheme.{u}}

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.ThreeSlices
attribute [-instance]
  AlgebraicGeometry.SmoothOfRelativeDimension.fiberToSpecResidueField
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_snd
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_fst
  AlgebraicGeometry.SmoothOfRelativeDimension.smooth_one
  AlgebraicGeometry.SmoothProperCurve.isIntegral_pullback_Spec_field
  AlgebraicGeometry.IsProper.fiberToSpecResidueField
  AlgebraicCurve.CurveModel.isProper
  AlgebraicCurve.CurveModel.isIntegral
  AlgebraicCurve.CurveModel.smooth
  AlgebraicCurve.Place.instIsScalarTowerSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Divisor.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instSMulAlgEquiv
  AlgebraicCurve.Place.instIsPrincipalIdealRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instIsDiscreteValuationRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Pic0.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instAlgebraSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instMulActionAlgEquiv
  AlgebraicCurve.Pic0.instSMulAlgEquiv
  TwoChartCech.Sections.M0_moduleA
  TwoChartCech.Sections.M1_module
  TwoChartCech.Cover.A01_algebra
  TwoChartCech.Cover.A0_algebra
  TwoChartCech.Cover.A1_commRing
  TwoChartCech.Cover.A1_algebra
  TwoChartCech.Sections.M01_module
  TwoChartCech.Sections.M0_addCommGroup
  TwoChartCech.Sections.M0_tower
  TwoChartCech.Sections.M01_addCommGroup
  TwoChartCech.Cover.A0_commRing
  TwoChartCech.Sections.M1_tower
  TwoChartCech.Sections.M01_moduleA
  TwoChartCech.Sections.M0_module
  TwoChartCech.Sections.M1_moduleA
  TwoChartCech.Sections.M1_addCommGroup
  TwoChartCech.Cover.A01_commRing
  TwoChartCech.Sections.M01_tower
  CoherentBaseChange.TwoTermComplex.C0_module
  CoherentBaseChange.TwoTermComplex.C0_addCommGroup
  CoherentBaseChange.TwoTermComplex.C1_module
  CoherentBaseChange.TwoTermComplex.C1_addCommGroup
attribute [-instance]
  CoherentBaseChange.TwoTermComplex.C0_free
  CoherentBaseChange.TwoTermComplex.C1_finite
  CoherentBaseChange.TwoTermComplex.C0_finite
  CoherentBaseChange.TwoTermComplex.C1_free
  AlgebraicCurve.IsCurveOver.instNontrivialKaehler
  AlgebraicCurve.IsCurveOver.instFreeKaehler
  AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
  AlgebraicCurve.IsCurveOver.instFiniteResidue
attribute [-instance]
  instIsLocallyInjectiveFunUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsLocallySurjectiveUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsOpenImmersionToGlued
attribute [-instance]
  instIsIsoSheafZariskiTopologyTypeUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.RelPicard.isOpenImmersion_toGlued
  AlgebraicGeometry.Scheme.Modules.preservesBinaryProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback_monoidal
  AlgebraicGeometry.Scheme.Modules.sheafify_isLocalization'
  AlgebraicGeometry.Scheme.Modules.preservesTerminal_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback₀_monoidal
  AlgebraicGeometry.Scheme.Modules.preservesFiniteProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.sheafifyPullback_lifting
  PresheafOfModules.PullbackMonoidal.pullback_monoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ
  PresheafOfModules.pushforward_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_η
  PresheafOfModules.free_monoidal
  PresheafOfModules.restrictScalars_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ_gS
  PresheafOfModules.pullback_oplaxMonoidal
attribute [-instance]
  instPreservesColimitsOfSizeCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierPb
attribute [-instance]
  PresheafOfModules.pullback_monoidal'
  AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
  AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
  AlgebraicCurve.Place.instIsPrimeCenter
  AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
  instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
  AlgebraicCurve.Pic0.instModuleZModTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instSMulTorsion
  AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
  AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
  AlgebraicCurve.RationalFunctionField.instNontrivialInftyValueGroup
  PresheafOfModules.ExteriorPower.instModulePresheafAb
  AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
  AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
  AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
  AlgebraicGeometry.isClosedImmersion_graphOver
  AlgebraicGeometry.FGSubalgebra.instIsDirectedLe
attribute [-instance]
  instQuasiSeparatedSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsCofilteredOpposite
  AlgebraicGeometry.FGSubalgebra.instIsAffineObjOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instNonempty
  AlgebraicGeometry.FGSubalgebra.instNonemptySubtypeLeSubalgebraValFG
attribute [-instance]
  instCompactSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsDirectedSubtypeLeSubalgebraValFG
  AlgebraicGeometry.FGSubalgebra.instIsAffineHomMapOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instIsFiltered
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instNeg
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulInt
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAddCommGroup
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAdd
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSub
attribute [-instance]
  instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
  AlgebraicCurve.instHasLocalResidue_of_hasCanonicalLocalResidueK
  AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
  AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
  ModularCurve.KwF4gRRTate.instAlgebraKAdicCompletionIntegers
  AlgebraicCurve.Place.kw_ffgc_continuousSMul_adicCompletionComap
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersCompletionCompletion
attribute [-instance]
  instLiesOverSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegersCompletionIdealAsIdeal
attribute [-instance]
  AlgebraicCurve.instHasCanonicalLocalResidueK
  AlgebraicCurve.Place.instAlgebra_restrictResidueField
  AlgebraicCurve.Place.instIsScalarTower_restrictResidueField
  AlgebraicCurve.instHasLocalResidue
  AlgebraicCurve.HasSeparableResidue.of_perfectField_of_isCurveOver
  AlgebraicCurve.HasSeparableResidue.of_perfectField
  AlgebraicCurve.Place.instIsLocalHom_restrictSubringHom
  AlgebraicCurve.instHasCanonicalLocalResidueKStar
  ModularCurve.KwNo6Pin.isLocalRing_completion
  SheafOfModules.isIso_ihomModelToIhom
  AlgebraicGeometry.OModulePresheaf.isScalarTower
  AlgebraicGeometry.Scheme.OrderedAffineCover.instLinearOrder
  AlgebraicGeometry.OModulePresheaf.module
  AlgebraicGeometry.Scheme.OrderedAffineCover.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCover.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.addCommGroup
  AlgebraicGeometry.Scheme.OrderedAffineCover.instDecidableEqIdx
  AlgebraicGeometry.OModulePresheaf.moduleSections
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.instSubsingletonObjZero
attribute [-instance]
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
  AlgebraicGeometry.OModulePresheaf.Leray.biC_module
  DoubleComplex.instModuleE₂I
  DoubleComplex.Bounded.modR
  DoubleComplex.instModuleE₂II
  DoubleComplex.instAddCommGroupE₂II
  DoubleComplex.Bounded.abGrp
  DoubleComplex.instAddCommGroupE₂I
  AlgebraicGeometry.ChowDatum.hι_closed
  AlgebraicGeometry.ChowDatumProj.hιN_closed
  AlgebraicGeometry.ChowDatumProj.hp_proper
  AlgebraicGeometry.ChowDatum.hp_isoU
  AlgebraicGeometry.ChowDatum.hp_proper
  AlgebraicGeometry.ProjSpace.algebraAway
  AlgebraicGeometry.ProjSpace.instIsProperProdOverπ
  AlgebraicGeometry.ChowDatumProj.hp_isoU
  AlgebraicGeometry.ProjSpace.isProper_π
  AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
  ProjSpaceCech.GradedModule.H.module
  ProjSpaceCech.GradedModule.H.addCommGroup
  ProjSpaceCech.GradedModule.sec.instAdd
  ProjSpaceCech.GradedModule.sec.instNeg
  ProjSpaceCech.GradedModule.acg
  ProjSpaceCech.GradedModule.Frac.setoid
  ProjSpaceCech.GradedModule.modR
  ProjSpaceCech.GradedModule.sec.instModule
  ProjSpaceCech.GradedModule.sec.instAddCommGroup
  ProjSpaceCech.GradedModule.sec.instZero
  ProjSpaceCech.GradedModule.Presentation.fJ
  ProjSpaceCech.GradedModule.sec.instSMul
  ProjSpaceCech.Twist.H.module
  ProjSpaceCech.Idx.instFintype
  ProjSpaceCech.Twist.H.addCommGroup
attribute [-instance]
  ProjSpaceCech.Idx.instDecidableEq
  ProjSpaceCech.Twist.Mon.instDecidableEq
  ProjSpaceCech.Twist.cochain.instAddCommGroup
  ProjSpaceCech.Twist.cochain.instModule
  AlgebraicGeometry.FGSubalgebra.tensorStage_directedSystem
  AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
  AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
  AlgebraicCurve.CurveModel.locallyOfFiniteType_gluedToBase
  AlgebraicCurve.CurveModel.isFractionRing_overlap
  AlgebraicCurve.CurveModel.isLocallyNoetherian_glued
  AlgebraicCurve.CurveModel.jacobsonSpace_glued
  AlgebraicCurve.CurveModel.isOpenImmersion_ι₀
  AlgebraicCurve.CurveModel.isIntegral_glued
  AlgebraicCurve.CurveModel.quasiSeparated_gluedToBase
  AlgebraicCurve.CurveModel.compactSpace_glued
  AlgebraicCurve.CurveModel.isIntegral_adjoin_chartRing
  AlgebraicCurve.CurveModel.isFractionRing_overlap_functionField
  AlgebraicCurve.CurveModel.isProper_gluedToBase
  AlgebraicCurve.CurveModel.isOpenImmersion_ιU
  AlgebraicCurve.CurveModel.isOpenImmersion_f₀
  AlgebraicCurve.CurveModel.isOpenImmersion_fInf
  AlgebraicCurve.CurveModel.isOpenImmersion_ιInf
  AlgebraicCurve.CurveModel.algebra_overlap_functionField
  AlgebraicCurve.CurveModel.quasiCompact_gluedToBase
  AlgebraicCurve.CurveModel.algebraAdjoin
  AlgebraicCurve.CurveModel.isDedekindDomain_chartRing
  AlgebraicCurve.CurveModel.isIntegralClosure
  AlgebraicCurve.CurveModel.finite_chartRing
  AlgebraicCurve.CurveModel.centre_isPrime
  AlgebraicCurve.CurveModel.isFractionRing_chartRing
  AlgebraicCurve.CurveModel.finiteType_chartRing
  AlgebraicCurve.CurveModel.isNoetherianRing_chartRing
  AlgebraicCurve.CurveModel.isScalarTower_base_adjoin
  AlgebraicCurve.CurveModel.isScalarTower_adjoin
  AlgebraicCurve.CurveModel.chartRing_finitePresentation
attribute [-simp]
  GoodReductionJacobian.RelativePic0Designation.mk.sizeOf_spec
  GoodReductionJacobian.AvatarSchemeBridge.mk.injEq
  GoodReductionJacobian.AvatarSchemeBridge.mk.sizeOf_spec
  GoodReductionJacobian.RelativePic0Designation.mk.injEq
  GoodReductionJacobian.schemeHomOverComp_coe
  NeronModelInfra.schemeHomOverEquivOverHom_apply
  GoodReductionJacobian.RelativeGroupLaw.mk.sizeOf_spec
  NeronModelInfra.schemeHomOverEquivOverHom_symm_apply
  NeronModelInfra.overHomToSchemeHomOver_coe
  GoodReductionJacobian.RelativeGroupLaw.mk.injEq
  NeronModelInfra.overHomToSchemeHomOver_schemeHomOverToOverHom
  NeronModelInfra.schemeHomOverToOverHom_left
  NeronModelInfra.schemeHomOverToOverHom_overHomToSchemeHomOver
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.sizeOf_spec
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
  AlgebraicCurve.CurveModel.mk.injEq
  AlgebraicCurve.CurveModel.mk.sizeOf_spec
  AlgebraicCurve.Place.mk.injEq
  AlgebraicCurve.Divisor.degree_single
  AlgebraicCurve.Divisor.smul_single
  AlgebraicCurve.Place.smul_toValuationSubring
  AlgebraicCurve.Place.heightOneSpectrum_asIdeal
  AlgebraicCurve.Place.coe_algebraMap
  AlgebraicCurve.Place.ord_one
  AlgebraicCurve.Place.coe_smulRingEquiv_apply
  AlgebraicCurve.Pic0.coe_degZeroSMulHom
  AlgebraicCurve.Place.deg_smul
  AlgebraicCurve.Pic0.mk_zero
  AlgebraicCurve.Place.mk.sizeOf_spec
  AlgebraicCurve.Divisor.degree_smul
  AlgebraicCurve.Pic0.mk_add
  AlgebraicCurve.Place.ord_zero
  AlgebraicCurve.Place.ofHeightOneSpectrum_toValuationSubring
  AlgebraicCurve.mulAdele_apply
attribute [-simp]
  AlgebraicCurve.residuePairing_apply_coe
  AlgebraicCurve.mem_adeleBdd
  AlgebraicCurve.weilSmul_one
  AlgebraicCurve.diagonalHom_apply
  AlgebraicCurve.weilSmul_apply
  AlgebraicCurve.adeleSpaceMul_coe
  AlgebraicCurve.mulAdele_one
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U1
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.injEq
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U0
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.mk.injEq
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.pullback_U1
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.pullback_U0
  TwoChartCech.Sections.mk.injEq
  TwoChartCech.Cover.mk.injEq
  TwoChartCech.GrothendieckComplex.mk.injEq
  TwoChartCech.Sections.mk.sizeOf_spec
  TwoChartCech.Cover.mk.sizeOf_spec
  TwoChartCech.Cover.lineBundle_r0_apply
  TwoChartCech.GrothendieckComplex.mk.sizeOf_spec
  TwoChartCech.Cover.lineBundle_r1_apply
  CoherentBaseChange.TwoTermComplex.mk.sizeOf_spec
  CoherentBaseChange.TwoTermComplex.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
  AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
  CategoryTheory.Functor.OverTotal.ofFibre_fst
  CategoryTheory.Functor.overTotal_map_fst
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_J
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYoneda_toGlued_uliftYonedaGluedToSheaf
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t'
attribute [-simp]
  uliftYoneda_toGlued_uliftYonedaGluedToSheaf_assoc
attribute [-simp]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_toGlued
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_openCover_map
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_comp
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_V
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_U
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_f
attribute [-simp]
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_P
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_toBase
  AlgebraicGeometry.RelPicard.rigSection_snd
  AlgebraicGeometry.RelPicard.RigidifiedLineBundle.ofInvertible_L
  AlgebraicGeometry.RelPicard.rigSection_snd_assoc
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
  GoodReductionJacobian.relativeGroupLawOfGrpObj_inv
  GoodReductionJacobian.relativeGroupLawOfGrpObj_mul
  GoodReductionJacobian.overHomEquivSchemeHomOver_apply_coe
  GoodReductionJacobian.relativeGroupLawOfGrpObj_one
  GoodReductionJacobian.overHomEquivSchemeHomOver_symm_apply_left
  PresheafOfModules.freeεIso_hom_app
  PresheafOfModules.freeμIso_hom_app
  AlgebraicCurve.coe_cechH0Equiv_apply
  AlgebraicCurve.cechH1ToH1_mk
  AlgebraicCurve.lSpaceOn_univ
  AlgebraicCurve.lSpaceOn_empty
  AlgebraicCurve.Place.congrEquiv_symm_apply
  AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
  AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
  AlgebraicCurve.Place.congrEquiv_apply
  AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
  AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
  AlgebraicCurve.Divisor.mapRestrict_single
  AlgebraicCurve.Divisor.pushforward_single
  AlgebraicCurve.Place.coe_restrictInclusion
  AlgebraicCurve.Place.mem_fiber
  AlgebraicCurve.Place.restrict_toValuationSubring
  AlgebraicCurve.Divisor.degree_pushforward
  AlgebraicCurve.Place.restrictResidueMap_residue
  AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
  AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
  AlgebraicCurve.Place.placeOfPrime_toValuationSubring
  AlgebraicCurve.Place.mem_fiberOver
  AlgebraicCurve.Place.fiberEquiv_symm_apply
  AlgebraicCurve.Place.fiberEquiv_apply
  AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
attribute [-simp]
  AlgebraicCurve.Divisor.degree_pushforwardAlong
  AlgebraicCurve.Pic0.coe_degZeroCorrespondence
  AlgebraicCurve.Place.mem_fiberAlong
  AlgebraicCurve.SemilinearAut.toRingAut_inv
  AlgebraicCurve.SemilinearAut.smul_def
  AlgebraicCurve.SemilinearAut.smul_single
  AlgebraicCurve.SemilinearAut.smul_toValuationSubring
  AlgebraicCurve.SemilinearAut.baseAut_inv
  AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_one
  AlgebraicCurve.SemilinearAut.deg_smul
  AlgebraicCurve.SemilinearAut.degree_smul
  AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
  AlgebraicCurve.SemilinearAut.baseAut_mul
  AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
  AlgebraicCurve.SemilinearAut.baseAut_one
  AlgebraicCurve.SemilinearAut.ofAlgAut_smul
  AlgebraicCurve.SemilinearAut.coe_torsion_smul
  AlgebraicCurve.SemilinearAut.toRingAut_mul
attribute [-simp]
  AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeInfty
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_some
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeOfPoint
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_none
  AlgebraicCurve.Divisor.evalFun_zero
  AlgebraicCurve.Place.evalAt_one
  AlgebraicCurve.Place.differentialCoeff_zero
  AlgebraicCurve.Place.differentialCoeff_dCoord
  AlgebraicCurve.TranscendenceTower.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
  AlgebraicCurve.TranscendenceTower.mk.injEq
  AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec
  AlgebraicCurve.PoleDivisorPackage.mk.injEq
  AlgebraicGeometry.RelPicard.thetaBundle_def
attribute [-simp]
  AlgebraicGeometry.RelPicard.picardBundle_def
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_ofRelEffDivisor
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_I
  AlgebraicGeometry.mapOnProdOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.mk.sizeOf_spec
  AlgebraicGeometry.RelEffCartierDiv.mk.injEq
  AlgebraicGeometry.mapOnProdOver_snd
  AlgebraicGeometry.mapOnProdOver_fst
  AlgebraicGeometry.mapOnProdOver_snd_assoc
  AlgebraicGeometry.mapOnProdOver_id
  AlgebraicCurve.RelEffDivisor.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_fst
  AlgebraicCurve.mapOnProd_fst_assoc
  AlgebraicCurve.mapOnProd_snd
  AlgebraicCurve.UnivDivisorPack.mk.injEq
  AlgebraicCurve.RelEffDivisor.mk.injEq
  AlgebraicCurve.UnivDivisorPack.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_snd_assoc
  AlgebraicGeometry.Scheme.Modules.exteriorPower_obj
  PresheafOfModules.exteriorPower_map_ιMulti
  PresheafOfModules.ExteriorPower.appₗ_apply
  AlgebraicGeometry.prodKerGraph_one
  AlgebraicGeometry.fibrePowOver.proj_comp
  AlgebraicGeometry.prodKerGraph_zero
  AlgebraicGeometry.RelEffCartierDiv.empty_I
  AlgebraicGeometry.fibrePowOver.proj_comp_assoc
  AlgebraicGeometry.graphOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
  AlgebraicGeometry.graphOver_fst
  AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
  AlgebraicGeometry.graphOver_snd
  AlgebraicGeometry.graphOver_snd_assoc
  AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
  AlgebraicCurve.SymmetricPowerPackage.mk.injEq
  AlgebraicGeometry.FGSubalgebra.cocone_ι_app_apply
  AlgebraicGeometry.RelPicard.fst_toProdSpec
  AlgebraicGeometry.RelPicard.toProdSpec_fst_assoc
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_cons
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_nil
attribute [-simp]
  AlgebraicGeometry.RelPicard.fst_toProdSpec_assoc
  AlgebraicGeometry.RelPicard.toProdSpec_fst
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.sizeOf_spec
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.injEq
  AlgebraicCurve.adeleSingle_coe
  AlgebraicCurve.kaehlerResidueTermKFam_apply
  AlgebraicCurve.Place.LocalResidueData.mk.injEq
  AlgebraicCurve.Place.LocalResidueData.mk.sizeOf_spec
  AlgebraicCurve.Place.kw_ffgc_adicCompletionComapIntegers_coe
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.sizeOf_spec
  AlgebraicCurve.Place.mem_simplePoleSubmodule
  AlgebraicCurve.Place.coe_uniformizerSubring
  ModularCurve.Lg37.Lg37CompletionSection.mk.injEq
  AlgebraicCurve.Place.CoefficientFieldSection.mk.injEq
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.injEq
  ModularCurve.Lg37.Lg37CompletionSection.mk.sizeOf_spec
  AlgebraicCurve.Place.CoefficientFieldSection.mk.sizeOf_spec
  AlgebraicCurve.Place.poleSubmodule_one
  AlgebraicCurve.Place.mem_poleSubmodule
  AlgebraicGeometry.Scheme.Modules.toUnitSection_ofUnitSection
  AlgebraicGeometry.Scheme.Modules.pullbackSection_def
  AlgebraicGeometry.Scheme.Modules.ofUnitSection_toUnitSection
  PresheafOfModules.InternalHom.IsSheafAux.appAt_toPresheafHom
attribute [-simp]
  SheafOfModules.ihomSectionsEquivFamily_unit
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_apply
  SheafOfModules.ihomEval_unit_app
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_right
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_left
  AlgebraicGeometry.Scheme.Modules.homOfFamily_app_apply
  SheafOfModules.unit_ihomSectionsEquivFamily
  AlgebraicGeometry.Scheme.Modules.familyOfHom_app
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_hom_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_inv_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomOfFamily_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_symm_apply
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_right
  AlgebraicGeometry.Scheme.Modules.map_unitSection
  AlgebraicGeometry.Scheme.Modules.tensorSectionsBilin_apply
  AlgebraicGeometry.Scheme.Modules.tensorPowSection_zero
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_left
  AlgebraicGeometry.Scheme.Modules.tensorPow_zero
  AlgebraicGeometry.Scheme.Modules.tensorPow_succ
  AlgebraicGeometry.Scheme.OrderedAffineCover.mk.injEq
  AlgebraicGeometry.OModulePresheaf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCover.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.mk.injEq
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_neg
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_zero
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_sub
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_add
  AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
  AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U
  AlgebraicGeometry.OModulePresheaf.Hom.mk.injEq
  AlgebraicGeometry.OModulePresheaf.Hom.id_app
  AlgebraicGeometry.OModulePresheaf.AffHom.appSections_apply
  AlgebraicGeometry.OModulePresheaf.AffHom.comp_app
  AlgebraicGeometry.OModulePresheaf.AffSES.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.AffHom.kerMap_coe
  AlgebraicGeometry.OModulePresheaf.AffHom.id_app
  AlgebraicGeometry.OModulePresheaf.Hom.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.Hom.toAffHom_app
attribute [-simp]
  AlgebraicGeometry.OModulePresheaf.SES.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.AffHom.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.Hom.comp_app
  AlgebraicGeometry.OModulePresheaf.SES.mk.injEq
  AlgebraicGeometry.OModulePresheaf.AffHom.mk.injEq
  AlgebraicGeometry.OModulePresheaf.Hom.appSections_apply
  AlgebraicGeometry.OModulePresheaf.AffSES.mk.injEq
  AlgebraicGeometry.OModulePresheaf.prod_obj
  AlgebraicGeometry.OModulePresheaf.restrOpen_obj
  AlgebraicGeometry.OModulePresheaf.DevissageStep.mk.injEq
  AlgebraicGeometry.OModulePresheaf.pushforward_obj
  AlgebraicGeometry.OModulePresheaf.im_obj
  AlgebraicGeometry.OModulePresheaf.pow_obj
  AlgebraicGeometry.OModulePresheaf.fstHom_app
  AlgebraicGeometry.OModulePresheaf.ker_obj
  AlgebraicGeometry.OModulePresheaf.coker_obj
  AlgebraicGeometry.OModulePresheaf.DevissageStep.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCover.preimage_U
  AlgebraicGeometry.OModulePresheaf.sndHom_app
  AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
  DoubleComplex.Bounded.mk.injEq
  DoubleComplex.Bounded.mk.sizeOf_spec
  DoubleComplex.Convergence.mk.injEq
  DoubleComplex.Convergence.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.injEq
  AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatumProj.mk.injEq
  AlgebraicGeometry.ChowDatum.mk.injEq
  ProjSpaceCech.GradedModule.mk.injEq
  ProjSpaceCech.GradedModule.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Presentation.mk.injEq
  ProjSpaceCech.GradedModule.Frac.mk.injEq
  ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.shift_toLinearMap
  ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.mk.injEq
  TwoChartCech.Mumford.dK_apply
attribute [-simp]
  TwoChartCech.Mumford.ι0_apply
  TwoChartCech.Mumford.ι1_apply
  TwoChartCech.KerCoprod.dK_apply
  TwoChartCech.KerCoprod.ι1_apply
  TwoChartCech.KerCoprod.ι0_apply
  AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
  AlgebraicGeometry.RelPicard.algEquivZeroGroupCut_toSubPicCondition
  AlgebraicGeometry.RelPicard.LFP.stageHom_val
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_hom_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_inv_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.restrict_P
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp
  AlgebraicGeometry.RelEffCartierDiv.functor_map_fst
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_pullbackAlong
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_symm_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp_assoc
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top
  AlgebraicGeometry.RelEffCartierDiv.mem_supportedIn_iff
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top_eq
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
  CoherentBaseChange.FibreH0Family.mk.sizeOf_spec
  CoherentBaseChange.FibreH0Family.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.sizeOf_spec
  AlgebraicCurve.CurveModel.coe_gInf
  AlgebraicCurve.CurveModel.coe_tInvChart
  AlgebraicCurve.CurveModel.ιInf_gluedToBase_assoc
  AlgebraicCurve.CurveModel.ιInf_gluedToBase
  AlgebraicCurve.CurveModel.primeOfι₀_asIdeal
  AlgebraicCurve.CurveModel.coe_tChart
  AlgebraicCurve.CurveModel.ι₀_gluedToBase_assoc
  AlgebraicCurve.CurveModel.primeOfιInf_asIdeal
attribute [-simp]
  AlgebraicCurve.CurveModel.ι₀_gluedToBase
  AlgebraicCurve.CurveModel.coe_tma
  AlgebraicCurve.CurveModel.coe_primeEquivChartPlaces
universe u
noncomputable section
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.CategoryTheory.CartesianMonoidalCategory
open _root_.AlgebraicGeometry.RelPicard
open _root_.NeronModelInfra
namespace P2mCubeAssembly
section Triv
variable {S T V : Scheme.{u}}

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.ThreeSlices
attribute [-instance]
  AlgebraicGeometry.SmoothOfRelativeDimension.fiberToSpecResidueField
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_snd
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_fst
  AlgebraicGeometry.SmoothOfRelativeDimension.smooth_one
  AlgebraicGeometry.SmoothProperCurve.isIntegral_pullback_Spec_field
  AlgebraicGeometry.IsProper.fiberToSpecResidueField
  AlgebraicCurve.CurveModel.isProper
  AlgebraicCurve.CurveModel.isIntegral
  AlgebraicCurve.CurveModel.smooth
  AlgebraicCurve.Place.instIsScalarTowerSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Divisor.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instSMulAlgEquiv
  AlgebraicCurve.Place.instIsPrincipalIdealRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instIsDiscreteValuationRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Pic0.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instAlgebraSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instMulActionAlgEquiv
  AlgebraicCurve.Pic0.instSMulAlgEquiv
  TwoChartCech.Sections.M0_moduleA
  TwoChartCech.Sections.M1_module
  TwoChartCech.Cover.A01_algebra
  TwoChartCech.Cover.A0_algebra
  TwoChartCech.Cover.A1_commRing
  TwoChartCech.Cover.A1_algebra
  TwoChartCech.Sections.M01_module
  TwoChartCech.Sections.M0_addCommGroup
  TwoChartCech.Sections.M0_tower
  TwoChartCech.Sections.M01_addCommGroup
  TwoChartCech.Cover.A0_commRing
  TwoChartCech.Sections.M1_tower
  TwoChartCech.Sections.M01_moduleA
  TwoChartCech.Sections.M0_module
  TwoChartCech.Sections.M1_moduleA
  TwoChartCech.Sections.M1_addCommGroup
  TwoChartCech.Cover.A01_commRing
  TwoChartCech.Sections.M01_tower
  CoherentBaseChange.TwoTermComplex.C0_module
  CoherentBaseChange.TwoTermComplex.C0_addCommGroup
  CoherentBaseChange.TwoTermComplex.C1_module
  CoherentBaseChange.TwoTermComplex.C1_addCommGroup
attribute [-instance]
  CoherentBaseChange.TwoTermComplex.C0_free
  CoherentBaseChange.TwoTermComplex.C1_finite
  CoherentBaseChange.TwoTermComplex.C0_finite
  CoherentBaseChange.TwoTermComplex.C1_free
  AlgebraicCurve.IsCurveOver.instNontrivialKaehler
  AlgebraicCurve.IsCurveOver.instFreeKaehler
  AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
  AlgebraicCurve.IsCurveOver.instFiniteResidue
attribute [-instance]
  instIsLocallyInjectiveFunUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsLocallySurjectiveUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsOpenImmersionToGlued
attribute [-instance]
  instIsIsoSheafZariskiTopologyTypeUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.RelPicard.isOpenImmersion_toGlued
  AlgebraicGeometry.Scheme.Modules.preservesBinaryProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback_monoidal
  AlgebraicGeometry.Scheme.Modules.sheafify_isLocalization'
  AlgebraicGeometry.Scheme.Modules.preservesTerminal_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback₀_monoidal
  AlgebraicGeometry.Scheme.Modules.preservesFiniteProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.sheafifyPullback_lifting
  PresheafOfModules.PullbackMonoidal.pullback_monoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ
  PresheafOfModules.pushforward_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_η
  PresheafOfModules.free_monoidal
  PresheafOfModules.restrictScalars_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ_gS
  PresheafOfModules.pullback_oplaxMonoidal
attribute [-instance]
  instPreservesColimitsOfSizeCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierPb
attribute [-instance]
  PresheafOfModules.pullback_monoidal'
  AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
  AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
  AlgebraicCurve.Place.instIsPrimeCenter
  AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
  instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
  AlgebraicCurve.Pic0.instModuleZModTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instSMulTorsion
  AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
  AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
  AlgebraicCurve.RationalFunctionField.instNontrivialInftyValueGroup
  PresheafOfModules.ExteriorPower.instModulePresheafAb
  AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
  AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
  AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
  AlgebraicGeometry.isClosedImmersion_graphOver
  AlgebraicGeometry.FGSubalgebra.instIsDirectedLe
attribute [-instance]
  instQuasiSeparatedSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsCofilteredOpposite
  AlgebraicGeometry.FGSubalgebra.instIsAffineObjOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instNonempty
  AlgebraicGeometry.FGSubalgebra.instNonemptySubtypeLeSubalgebraValFG
attribute [-instance]
  instCompactSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsDirectedSubtypeLeSubalgebraValFG
  AlgebraicGeometry.FGSubalgebra.instIsAffineHomMapOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instIsFiltered
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instNeg
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulInt
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAddCommGroup
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAdd
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSub
attribute [-instance]
  instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
  AlgebraicCurve.instHasLocalResidue_of_hasCanonicalLocalResidueK
  AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
  AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
  ModularCurve.KwF4gRRTate.instAlgebraKAdicCompletionIntegers
  AlgebraicCurve.Place.kw_ffgc_continuousSMul_adicCompletionComap
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersCompletionCompletion
attribute [-instance]
  instLiesOverSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegersCompletionIdealAsIdeal
attribute [-instance]
  AlgebraicCurve.instHasCanonicalLocalResidueK
  AlgebraicCurve.Place.instAlgebra_restrictResidueField
  AlgebraicCurve.Place.instIsScalarTower_restrictResidueField
  AlgebraicCurve.instHasLocalResidue
  AlgebraicCurve.HasSeparableResidue.of_perfectField_of_isCurveOver
  AlgebraicCurve.HasSeparableResidue.of_perfectField
  AlgebraicCurve.Place.instIsLocalHom_restrictSubringHom
  AlgebraicCurve.instHasCanonicalLocalResidueKStar
  ModularCurve.KwNo6Pin.isLocalRing_completion
  SheafOfModules.isIso_ihomModelToIhom
  AlgebraicGeometry.OModulePresheaf.isScalarTower
  AlgebraicGeometry.Scheme.OrderedAffineCover.instLinearOrder
  AlgebraicGeometry.OModulePresheaf.module
  AlgebraicGeometry.Scheme.OrderedAffineCover.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCover.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.addCommGroup
  AlgebraicGeometry.Scheme.OrderedAffineCover.instDecidableEqIdx
  AlgebraicGeometry.OModulePresheaf.moduleSections
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.instSubsingletonObjZero
attribute [-instance]
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
  AlgebraicGeometry.OModulePresheaf.Leray.biC_module
  DoubleComplex.instModuleE₂I
  DoubleComplex.Bounded.modR
  DoubleComplex.instModuleE₂II
  DoubleComplex.instAddCommGroupE₂II
  DoubleComplex.Bounded.abGrp
  DoubleComplex.instAddCommGroupE₂I
  AlgebraicGeometry.ChowDatum.hι_closed
  AlgebraicGeometry.ChowDatumProj.hιN_closed
  AlgebraicGeometry.ChowDatumProj.hp_proper
  AlgebraicGeometry.ChowDatum.hp_isoU
  AlgebraicGeometry.ChowDatum.hp_proper
  AlgebraicGeometry.ProjSpace.algebraAway
  AlgebraicGeometry.ProjSpace.instIsProperProdOverπ
  AlgebraicGeometry.ChowDatumProj.hp_isoU
  AlgebraicGeometry.ProjSpace.isProper_π
  AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
  ProjSpaceCech.GradedModule.H.module
  ProjSpaceCech.GradedModule.H.addCommGroup
  ProjSpaceCech.GradedModule.sec.instAdd
  ProjSpaceCech.GradedModule.sec.instNeg
  ProjSpaceCech.GradedModule.acg
  ProjSpaceCech.GradedModule.Frac.setoid
  ProjSpaceCech.GradedModule.modR
  ProjSpaceCech.GradedModule.sec.instModule
  ProjSpaceCech.GradedModule.sec.instAddCommGroup
  ProjSpaceCech.GradedModule.sec.instZero
  ProjSpaceCech.GradedModule.Presentation.fJ
  ProjSpaceCech.GradedModule.sec.instSMul
  ProjSpaceCech.Twist.H.module
  ProjSpaceCech.Idx.instFintype
  ProjSpaceCech.Twist.H.addCommGroup
attribute [-instance]
  ProjSpaceCech.Idx.instDecidableEq
  ProjSpaceCech.Twist.Mon.instDecidableEq
  ProjSpaceCech.Twist.cochain.instAddCommGroup
  ProjSpaceCech.Twist.cochain.instModule
  AlgebraicGeometry.FGSubalgebra.tensorStage_directedSystem
  AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
  AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
  AlgebraicCurve.CurveModel.locallyOfFiniteType_gluedToBase
  AlgebraicCurve.CurveModel.isFractionRing_overlap
  AlgebraicCurve.CurveModel.isLocallyNoetherian_glued
  AlgebraicCurve.CurveModel.jacobsonSpace_glued
  AlgebraicCurve.CurveModel.isOpenImmersion_ι₀
  AlgebraicCurve.CurveModel.isIntegral_glued
  AlgebraicCurve.CurveModel.quasiSeparated_gluedToBase
  AlgebraicCurve.CurveModel.compactSpace_glued
  AlgebraicCurve.CurveModel.isIntegral_adjoin_chartRing
  AlgebraicCurve.CurveModel.isFractionRing_overlap_functionField
  AlgebraicCurve.CurveModel.isProper_gluedToBase
  AlgebraicCurve.CurveModel.isOpenImmersion_ιU
  AlgebraicCurve.CurveModel.isOpenImmersion_f₀
  AlgebraicCurve.CurveModel.isOpenImmersion_fInf
  AlgebraicCurve.CurveModel.isOpenImmersion_ιInf
  AlgebraicCurve.CurveModel.algebra_overlap_functionField
  AlgebraicCurve.CurveModel.quasiCompact_gluedToBase
  AlgebraicCurve.CurveModel.algebraAdjoin
  AlgebraicCurve.CurveModel.isDedekindDomain_chartRing
  AlgebraicCurve.CurveModel.isIntegralClosure
  AlgebraicCurve.CurveModel.finite_chartRing
  AlgebraicCurve.CurveModel.centre_isPrime
  AlgebraicCurve.CurveModel.isFractionRing_chartRing
  AlgebraicCurve.CurveModel.finiteType_chartRing
  AlgebraicCurve.CurveModel.isNoetherianRing_chartRing
  AlgebraicCurve.CurveModel.isScalarTower_base_adjoin
  AlgebraicCurve.CurveModel.isScalarTower_adjoin
  AlgebraicCurve.CurveModel.chartRing_finitePresentation
attribute [-simp]
  GoodReductionJacobian.RelativePic0Designation.mk.sizeOf_spec
  GoodReductionJacobian.AvatarSchemeBridge.mk.injEq
  GoodReductionJacobian.AvatarSchemeBridge.mk.sizeOf_spec
  GoodReductionJacobian.RelativePic0Designation.mk.injEq
  GoodReductionJacobian.schemeHomOverComp_coe
  NeronModelInfra.schemeHomOverEquivOverHom_apply
  GoodReductionJacobian.RelativeGroupLaw.mk.sizeOf_spec
  NeronModelInfra.schemeHomOverEquivOverHom_symm_apply
  NeronModelInfra.overHomToSchemeHomOver_coe
  GoodReductionJacobian.RelativeGroupLaw.mk.injEq
  NeronModelInfra.overHomToSchemeHomOver_schemeHomOverToOverHom
  NeronModelInfra.schemeHomOverToOverHom_left
  NeronModelInfra.schemeHomOverToOverHom_overHomToSchemeHomOver
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.sizeOf_spec
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
  AlgebraicCurve.CurveModel.mk.injEq
  AlgebraicCurve.CurveModel.mk.sizeOf_spec
  AlgebraicCurve.Place.mk.injEq
  AlgebraicCurve.Divisor.degree_single
  AlgebraicCurve.Divisor.smul_single
  AlgebraicCurve.Place.smul_toValuationSubring
  AlgebraicCurve.Place.heightOneSpectrum_asIdeal
  AlgebraicCurve.Place.coe_algebraMap
  AlgebraicCurve.Place.ord_one
  AlgebraicCurve.Place.coe_smulRingEquiv_apply
  AlgebraicCurve.Pic0.coe_degZeroSMulHom
  AlgebraicCurve.Place.deg_smul
  AlgebraicCurve.Pic0.mk_zero
  AlgebraicCurve.Place.mk.sizeOf_spec
  AlgebraicCurve.Divisor.degree_smul
  AlgebraicCurve.Pic0.mk_add
  AlgebraicCurve.Place.ord_zero
  AlgebraicCurve.Place.ofHeightOneSpectrum_toValuationSubring
  AlgebraicCurve.mulAdele_apply
attribute [-simp]
  AlgebraicCurve.residuePairing_apply_coe
  AlgebraicCurve.mem_adeleBdd
  AlgebraicCurve.weilSmul_one
  AlgebraicCurve.diagonalHom_apply
  AlgebraicCurve.weilSmul_apply
  AlgebraicCurve.adeleSpaceMul_coe
  AlgebraicCurve.mulAdele_one
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U1
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.injEq
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U0
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.mk.injEq
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.pullback_U1
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.pullback_U0
  TwoChartCech.Sections.mk.injEq
  TwoChartCech.Cover.mk.injEq
  TwoChartCech.GrothendieckComplex.mk.injEq
  TwoChartCech.Sections.mk.sizeOf_spec
  TwoChartCech.Cover.mk.sizeOf_spec
  TwoChartCech.Cover.lineBundle_r0_apply
  TwoChartCech.GrothendieckComplex.mk.sizeOf_spec
  TwoChartCech.Cover.lineBundle_r1_apply
  CoherentBaseChange.TwoTermComplex.mk.sizeOf_spec
  CoherentBaseChange.TwoTermComplex.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
  AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
  CategoryTheory.Functor.OverTotal.ofFibre_fst
  CategoryTheory.Functor.overTotal_map_fst
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_J
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYoneda_toGlued_uliftYonedaGluedToSheaf
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t'
attribute [-simp]
  uliftYoneda_toGlued_uliftYonedaGluedToSheaf_assoc
attribute [-simp]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_toGlued
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_openCover_map
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_comp
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_V
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_U
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_f
attribute [-simp]
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_P
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_toBase
  AlgebraicGeometry.RelPicard.rigSection_snd
  AlgebraicGeometry.RelPicard.RigidifiedLineBundle.ofInvertible_L
  AlgebraicGeometry.RelPicard.rigSection_snd_assoc
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
  GoodReductionJacobian.relativeGroupLawOfGrpObj_inv
  GoodReductionJacobian.relativeGroupLawOfGrpObj_mul
  GoodReductionJacobian.overHomEquivSchemeHomOver_apply_coe
  GoodReductionJacobian.relativeGroupLawOfGrpObj_one
  GoodReductionJacobian.overHomEquivSchemeHomOver_symm_apply_left
  PresheafOfModules.freeεIso_hom_app
  PresheafOfModules.freeμIso_hom_app
  AlgebraicCurve.coe_cechH0Equiv_apply
  AlgebraicCurve.cechH1ToH1_mk
  AlgebraicCurve.lSpaceOn_univ
  AlgebraicCurve.lSpaceOn_empty
  AlgebraicCurve.Place.congrEquiv_symm_apply
  AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
  AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
  AlgebraicCurve.Place.congrEquiv_apply
  AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
  AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
  AlgebraicCurve.Divisor.mapRestrict_single
  AlgebraicCurve.Divisor.pushforward_single
  AlgebraicCurve.Place.coe_restrictInclusion
  AlgebraicCurve.Place.mem_fiber
  AlgebraicCurve.Place.restrict_toValuationSubring
  AlgebraicCurve.Divisor.degree_pushforward
  AlgebraicCurve.Place.restrictResidueMap_residue
  AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
  AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
  AlgebraicCurve.Place.placeOfPrime_toValuationSubring
  AlgebraicCurve.Place.mem_fiberOver
  AlgebraicCurve.Place.fiberEquiv_symm_apply
  AlgebraicCurve.Place.fiberEquiv_apply
  AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
attribute [-simp]
  AlgebraicCurve.Divisor.degree_pushforwardAlong
  AlgebraicCurve.Pic0.coe_degZeroCorrespondence
  AlgebraicCurve.Place.mem_fiberAlong
  AlgebraicCurve.SemilinearAut.toRingAut_inv
  AlgebraicCurve.SemilinearAut.smul_def
  AlgebraicCurve.SemilinearAut.smul_single
  AlgebraicCurve.SemilinearAut.smul_toValuationSubring
  AlgebraicCurve.SemilinearAut.baseAut_inv
  AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_one
  AlgebraicCurve.SemilinearAut.deg_smul
  AlgebraicCurve.SemilinearAut.degree_smul
  AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
  AlgebraicCurve.SemilinearAut.baseAut_mul
  AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
  AlgebraicCurve.SemilinearAut.baseAut_one
  AlgebraicCurve.SemilinearAut.ofAlgAut_smul
  AlgebraicCurve.SemilinearAut.coe_torsion_smul
  AlgebraicCurve.SemilinearAut.toRingAut_mul
attribute [-simp]
  AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeInfty
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_some
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeOfPoint
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_none
  AlgebraicCurve.Divisor.evalFun_zero
  AlgebraicCurve.Place.evalAt_one
  AlgebraicCurve.Place.differentialCoeff_zero
  AlgebraicCurve.Place.differentialCoeff_dCoord
  AlgebraicCurve.TranscendenceTower.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
  AlgebraicCurve.TranscendenceTower.mk.injEq
  AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec
  AlgebraicCurve.PoleDivisorPackage.mk.injEq
  AlgebraicGeometry.RelPicard.thetaBundle_def
attribute [-simp]
  AlgebraicGeometry.RelPicard.picardBundle_def
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_ofRelEffDivisor
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_I
  AlgebraicGeometry.mapOnProdOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.mk.sizeOf_spec
  AlgebraicGeometry.RelEffCartierDiv.mk.injEq
  AlgebraicGeometry.mapOnProdOver_snd
  AlgebraicGeometry.mapOnProdOver_fst
  AlgebraicGeometry.mapOnProdOver_snd_assoc
  AlgebraicGeometry.mapOnProdOver_id
  AlgebraicCurve.RelEffDivisor.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_fst
  AlgebraicCurve.mapOnProd_fst_assoc
  AlgebraicCurve.mapOnProd_snd
  AlgebraicCurve.UnivDivisorPack.mk.injEq
  AlgebraicCurve.RelEffDivisor.mk.injEq
  AlgebraicCurve.UnivDivisorPack.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_snd_assoc
  AlgebraicGeometry.Scheme.Modules.exteriorPower_obj
  PresheafOfModules.exteriorPower_map_ιMulti
  PresheafOfModules.ExteriorPower.appₗ_apply
  AlgebraicGeometry.prodKerGraph_one
  AlgebraicGeometry.fibrePowOver.proj_comp
  AlgebraicGeometry.prodKerGraph_zero
  AlgebraicGeometry.RelEffCartierDiv.empty_I
  AlgebraicGeometry.fibrePowOver.proj_comp_assoc
  AlgebraicGeometry.graphOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
  AlgebraicGeometry.graphOver_fst
  AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
  AlgebraicGeometry.graphOver_snd
  AlgebraicGeometry.graphOver_snd_assoc
  AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
  AlgebraicCurve.SymmetricPowerPackage.mk.injEq
  AlgebraicGeometry.FGSubalgebra.cocone_ι_app_apply
  AlgebraicGeometry.RelPicard.fst_toProdSpec
  AlgebraicGeometry.RelPicard.toProdSpec_fst_assoc
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_cons
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_nil
attribute [-simp]
  AlgebraicGeometry.RelPicard.fst_toProdSpec_assoc
  AlgebraicGeometry.RelPicard.toProdSpec_fst
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.sizeOf_spec
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.injEq
  AlgebraicCurve.adeleSingle_coe
  AlgebraicCurve.kaehlerResidueTermKFam_apply
  AlgebraicCurve.Place.LocalResidueData.mk.injEq
  AlgebraicCurve.Place.LocalResidueData.mk.sizeOf_spec
  AlgebraicCurve.Place.kw_ffgc_adicCompletionComapIntegers_coe
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.sizeOf_spec
  AlgebraicCurve.Place.mem_simplePoleSubmodule
  AlgebraicCurve.Place.coe_uniformizerSubring
  ModularCurve.Lg37.Lg37CompletionSection.mk.injEq
  AlgebraicCurve.Place.CoefficientFieldSection.mk.injEq
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.injEq
  ModularCurve.Lg37.Lg37CompletionSection.mk.sizeOf_spec
  AlgebraicCurve.Place.CoefficientFieldSection.mk.sizeOf_spec
  AlgebraicCurve.Place.poleSubmodule_one
  AlgebraicCurve.Place.mem_poleSubmodule
  AlgebraicGeometry.Scheme.Modules.toUnitSection_ofUnitSection
  AlgebraicGeometry.Scheme.Modules.pullbackSection_def
  AlgebraicGeometry.Scheme.Modules.ofUnitSection_toUnitSection
  PresheafOfModules.InternalHom.IsSheafAux.appAt_toPresheafHom
attribute [-simp]
  SheafOfModules.ihomSectionsEquivFamily_unit
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_apply
  SheafOfModules.ihomEval_unit_app
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_right
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_left
  AlgebraicGeometry.Scheme.Modules.homOfFamily_app_apply
  SheafOfModules.unit_ihomSectionsEquivFamily
  AlgebraicGeometry.Scheme.Modules.familyOfHom_app
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_hom_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_inv_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomOfFamily_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_symm_apply
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_right
  AlgebraicGeometry.Scheme.Modules.map_unitSection
  AlgebraicGeometry.Scheme.Modules.tensorSectionsBilin_apply
  AlgebraicGeometry.Scheme.Modules.tensorPowSection_zero
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_left
  AlgebraicGeometry.Scheme.Modules.tensorPow_zero
  AlgebraicGeometry.Scheme.Modules.tensorPow_succ
  AlgebraicGeometry.Scheme.OrderedAffineCover.mk.injEq
  AlgebraicGeometry.OModulePresheaf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCover.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.mk.injEq
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_neg
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_zero
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_sub
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_add
  AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
  AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U
  AlgebraicGeometry.OModulePresheaf.Hom.mk.injEq
  AlgebraicGeometry.OModulePresheaf.Hom.id_app
  AlgebraicGeometry.OModulePresheaf.AffHom.appSections_apply
  AlgebraicGeometry.OModulePresheaf.AffHom.comp_app
  AlgebraicGeometry.OModulePresheaf.AffSES.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.AffHom.kerMap_coe
  AlgebraicGeometry.OModulePresheaf.AffHom.id_app
  AlgebraicGeometry.OModulePresheaf.Hom.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.Hom.toAffHom_app
attribute [-simp]
  AlgebraicGeometry.OModulePresheaf.SES.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.AffHom.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.Hom.comp_app
  AlgebraicGeometry.OModulePresheaf.SES.mk.injEq
  AlgebraicGeometry.OModulePresheaf.AffHom.mk.injEq
  AlgebraicGeometry.OModulePresheaf.Hom.appSections_apply
  AlgebraicGeometry.OModulePresheaf.AffSES.mk.injEq
  AlgebraicGeometry.OModulePresheaf.prod_obj
  AlgebraicGeometry.OModulePresheaf.restrOpen_obj
  AlgebraicGeometry.OModulePresheaf.DevissageStep.mk.injEq
  AlgebraicGeometry.OModulePresheaf.pushforward_obj
  AlgebraicGeometry.OModulePresheaf.im_obj
  AlgebraicGeometry.OModulePresheaf.pow_obj
  AlgebraicGeometry.OModulePresheaf.fstHom_app
  AlgebraicGeometry.OModulePresheaf.ker_obj
  AlgebraicGeometry.OModulePresheaf.coker_obj
  AlgebraicGeometry.OModulePresheaf.DevissageStep.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCover.preimage_U
  AlgebraicGeometry.OModulePresheaf.sndHom_app
  AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
  DoubleComplex.Bounded.mk.injEq
  DoubleComplex.Bounded.mk.sizeOf_spec
  DoubleComplex.Convergence.mk.injEq
  DoubleComplex.Convergence.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.injEq
  AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatumProj.mk.injEq
  AlgebraicGeometry.ChowDatum.mk.injEq
  ProjSpaceCech.GradedModule.mk.injEq
  ProjSpaceCech.GradedModule.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Presentation.mk.injEq
  ProjSpaceCech.GradedModule.Frac.mk.injEq
  ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.shift_toLinearMap
  ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.mk.injEq
  TwoChartCech.Mumford.dK_apply
attribute [-simp]
  TwoChartCech.Mumford.ι0_apply
  TwoChartCech.Mumford.ι1_apply
  TwoChartCech.KerCoprod.dK_apply
  TwoChartCech.KerCoprod.ι1_apply
  TwoChartCech.KerCoprod.ι0_apply
  AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
  AlgebraicGeometry.RelPicard.algEquivZeroGroupCut_toSubPicCondition
  AlgebraicGeometry.RelPicard.LFP.stageHom_val
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_hom_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_inv_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.restrict_P
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp
  AlgebraicGeometry.RelEffCartierDiv.functor_map_fst
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_pullbackAlong
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_symm_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp_assoc
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top
  AlgebraicGeometry.RelEffCartierDiv.mem_supportedIn_iff
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top_eq
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
  CoherentBaseChange.FibreH0Family.mk.sizeOf_spec
  CoherentBaseChange.FibreH0Family.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.sizeOf_spec
  AlgebraicCurve.CurveModel.coe_gInf
  AlgebraicCurve.CurveModel.coe_tInvChart
  AlgebraicCurve.CurveModel.ιInf_gluedToBase_assoc
  AlgebraicCurve.CurveModel.ιInf_gluedToBase
  AlgebraicCurve.CurveModel.primeOfι₀_asIdeal
  AlgebraicCurve.CurveModel.coe_tChart
  AlgebraicCurve.CurveModel.ι₀_gluedToBase_assoc
  AlgebraicCurve.CurveModel.primeOfιInf_asIdeal
attribute [-simp]
  AlgebraicCurve.CurveModel.ι₀_gluedToBase
  AlgebraicCurve.CurveModel.coe_tma
  AlgebraicCurve.CurveModel.coe_primeEquivChartPlaces
universe u
noncomputable section
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.CategoryTheory.CartesianMonoidalCategory
open _root_.AlgebraicGeometry.RelPicard
open _root_.NeronModelInfra
namespace P2mCubeAssembly
section Triv
variable {S T V : Scheme.{u}}

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.ThreeSlices
attribute [-instance]
  AlgebraicGeometry.SmoothOfRelativeDimension.fiberToSpecResidueField
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_snd
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_fst
  AlgebraicGeometry.SmoothOfRelativeDimension.smooth_one
  AlgebraicGeometry.SmoothProperCurve.isIntegral_pullback_Spec_field
  AlgebraicGeometry.IsProper.fiberToSpecResidueField
  AlgebraicCurve.CurveModel.isProper
  AlgebraicCurve.CurveModel.isIntegral
  AlgebraicCurve.CurveModel.smooth
  AlgebraicCurve.Place.instIsScalarTowerSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Divisor.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instSMulAlgEquiv
  AlgebraicCurve.Place.instIsPrincipalIdealRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instIsDiscreteValuationRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Pic0.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instAlgebraSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instMulActionAlgEquiv
  AlgebraicCurve.Pic0.instSMulAlgEquiv
  TwoChartCech.Sections.M0_moduleA
  TwoChartCech.Sections.M1_module
  TwoChartCech.Cover.A01_algebra
  TwoChartCech.Cover.A0_algebra
  TwoChartCech.Cover.A1_commRing
  TwoChartCech.Cover.A1_algebra
  TwoChartCech.Sections.M01_module
  TwoChartCech.Sections.M0_addCommGroup
  TwoChartCech.Sections.M0_tower
  TwoChartCech.Sections.M01_addCommGroup
  TwoChartCech.Cover.A0_commRing
  TwoChartCech.Sections.M1_tower
  TwoChartCech.Sections.M01_moduleA
  TwoChartCech.Sections.M0_module
  TwoChartCech.Sections.M1_moduleA
  TwoChartCech.Sections.M1_addCommGroup
  TwoChartCech.Cover.A01_commRing
  TwoChartCech.Sections.M01_tower
  CoherentBaseChange.TwoTermComplex.C0_module
  CoherentBaseChange.TwoTermComplex.C0_addCommGroup
  CoherentBaseChange.TwoTermComplex.C1_module
  CoherentBaseChange.TwoTermComplex.C1_addCommGroup
attribute [-instance]
  CoherentBaseChange.TwoTermComplex.C0_free
  CoherentBaseChange.TwoTermComplex.C1_finite
  CoherentBaseChange.TwoTermComplex.C0_finite
  CoherentBaseChange.TwoTermComplex.C1_free
  AlgebraicCurve.IsCurveOver.instNontrivialKaehler
  AlgebraicCurve.IsCurveOver.instFreeKaehler
  AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
  AlgebraicCurve.IsCurveOver.instFiniteResidue
attribute [-instance]
  instIsLocallyInjectiveFunUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsLocallySurjectiveUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsOpenImmersionToGlued
attribute [-instance]
  instIsIsoSheafZariskiTopologyTypeUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.RelPicard.isOpenImmersion_toGlued
  AlgebraicGeometry.Scheme.Modules.preservesBinaryProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback_monoidal
  AlgebraicGeometry.Scheme.Modules.sheafify_isLocalization'
  AlgebraicGeometry.Scheme.Modules.preservesTerminal_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback₀_monoidal
  AlgebraicGeometry.Scheme.Modules.preservesFiniteProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.sheafifyPullback_lifting
  PresheafOfModules.PullbackMonoidal.pullback_monoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ
  PresheafOfModules.pushforward_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_η
  PresheafOfModules.free_monoidal
  PresheafOfModules.restrictScalars_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ_gS
  PresheafOfModules.pullback_oplaxMonoidal
attribute [-instance]
  instPreservesColimitsOfSizeCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierPb
attribute [-instance]
  PresheafOfModules.pullback_monoidal'
  AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
  AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
  AlgebraicCurve.Place.instIsPrimeCenter
  AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
  instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
  AlgebraicCurve.Pic0.instModuleZModTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instSMulTorsion
  AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
  AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
  AlgebraicCurve.RationalFunctionField.instNontrivialInftyValueGroup
  PresheafOfModules.ExteriorPower.instModulePresheafAb
  AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
  AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
  AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
  AlgebraicGeometry.isClosedImmersion_graphOver
  AlgebraicGeometry.FGSubalgebra.instIsDirectedLe
attribute [-instance]
  instQuasiSeparatedSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsCofilteredOpposite
  AlgebraicGeometry.FGSubalgebra.instIsAffineObjOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instNonempty
  AlgebraicGeometry.FGSubalgebra.instNonemptySubtypeLeSubalgebraValFG
attribute [-instance]
  instCompactSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsDirectedSubtypeLeSubalgebraValFG
  AlgebraicGeometry.FGSubalgebra.instIsAffineHomMapOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instIsFiltered
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instNeg
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulInt
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAddCommGroup
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAdd
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSub
attribute [-instance]
  instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
  AlgebraicCurve.instHasLocalResidue_of_hasCanonicalLocalResidueK
  AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
  AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
  ModularCurve.KwF4gRRTate.instAlgebraKAdicCompletionIntegers
  AlgebraicCurve.Place.kw_ffgc_continuousSMul_adicCompletionComap
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersCompletionCompletion
attribute [-instance]
  instLiesOverSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegersCompletionIdealAsIdeal
attribute [-instance]
  AlgebraicCurve.instHasCanonicalLocalResidueK
  AlgebraicCurve.Place.instAlgebra_restrictResidueField
  AlgebraicCurve.Place.instIsScalarTower_restrictResidueField
  AlgebraicCurve.instHasLocalResidue
  AlgebraicCurve.HasSeparableResidue.of_perfectField_of_isCurveOver
  AlgebraicCurve.HasSeparableResidue.of_perfectField
  AlgebraicCurve.Place.instIsLocalHom_restrictSubringHom
  AlgebraicCurve.instHasCanonicalLocalResidueKStar
  ModularCurve.KwNo6Pin.isLocalRing_completion
  SheafOfModules.isIso_ihomModelToIhom
  AlgebraicGeometry.OModulePresheaf.isScalarTower
  AlgebraicGeometry.Scheme.OrderedAffineCover.instLinearOrder
  AlgebraicGeometry.OModulePresheaf.module
  AlgebraicGeometry.Scheme.OrderedAffineCover.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCover.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.addCommGroup
  AlgebraicGeometry.Scheme.OrderedAffineCover.instDecidableEqIdx
  AlgebraicGeometry.OModulePresheaf.moduleSections
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.instSubsingletonObjZero
attribute [-instance]
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
  AlgebraicGeometry.OModulePresheaf.Leray.biC_module
  DoubleComplex.instModuleE₂I
  DoubleComplex.Bounded.modR
  DoubleComplex.instModuleE₂II
  DoubleComplex.instAddCommGroupE₂II
  DoubleComplex.Bounded.abGrp
  DoubleComplex.instAddCommGroupE₂I
  AlgebraicGeometry.ChowDatum.hι_closed
  AlgebraicGeometry.ChowDatumProj.hιN_closed
  AlgebraicGeometry.ChowDatumProj.hp_proper
  AlgebraicGeometry.ChowDatum.hp_isoU
  AlgebraicGeometry.ChowDatum.hp_proper
  AlgebraicGeometry.ProjSpace.algebraAway
  AlgebraicGeometry.ProjSpace.instIsProperProdOverπ
  AlgebraicGeometry.ChowDatumProj.hp_isoU
  AlgebraicGeometry.ProjSpace.isProper_π
  AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
  ProjSpaceCech.GradedModule.H.module
  ProjSpaceCech.GradedModule.H.addCommGroup
  ProjSpaceCech.GradedModule.sec.instAdd
  ProjSpaceCech.GradedModule.sec.instNeg
  ProjSpaceCech.GradedModule.acg
  ProjSpaceCech.GradedModule.Frac.setoid
  ProjSpaceCech.GradedModule.modR
  ProjSpaceCech.GradedModule.sec.instModule
  ProjSpaceCech.GradedModule.sec.instAddCommGroup
  ProjSpaceCech.GradedModule.sec.instZero
  ProjSpaceCech.GradedModule.Presentation.fJ
  ProjSpaceCech.GradedModule.sec.instSMul
  ProjSpaceCech.Twist.H.module
  ProjSpaceCech.Idx.instFintype
  ProjSpaceCech.Twist.H.addCommGroup
attribute [-instance]
  ProjSpaceCech.Idx.instDecidableEq
  ProjSpaceCech.Twist.Mon.instDecidableEq
  ProjSpaceCech.Twist.cochain.instAddCommGroup
  ProjSpaceCech.Twist.cochain.instModule
  AlgebraicGeometry.FGSubalgebra.tensorStage_directedSystem
  AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
  AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
  AlgebraicCurve.CurveModel.locallyOfFiniteType_gluedToBase
  AlgebraicCurve.CurveModel.isFractionRing_overlap
  AlgebraicCurve.CurveModel.isLocallyNoetherian_glued
  AlgebraicCurve.CurveModel.jacobsonSpace_glued
  AlgebraicCurve.CurveModel.isOpenImmersion_ι₀
  AlgebraicCurve.CurveModel.isIntegral_glued
  AlgebraicCurve.CurveModel.quasiSeparated_gluedToBase
  AlgebraicCurve.CurveModel.compactSpace_glued
  AlgebraicCurve.CurveModel.isIntegral_adjoin_chartRing
  AlgebraicCurve.CurveModel.isFractionRing_overlap_functionField
  AlgebraicCurve.CurveModel.isProper_gluedToBase
  AlgebraicCurve.CurveModel.isOpenImmersion_ιU
  AlgebraicCurve.CurveModel.isOpenImmersion_f₀
  AlgebraicCurve.CurveModel.isOpenImmersion_fInf
  AlgebraicCurve.CurveModel.isOpenImmersion_ιInf
  AlgebraicCurve.CurveModel.algebra_overlap_functionField
  AlgebraicCurve.CurveModel.quasiCompact_gluedToBase
  AlgebraicCurve.CurveModel.algebraAdjoin
  AlgebraicCurve.CurveModel.isDedekindDomain_chartRing
  AlgebraicCurve.CurveModel.isIntegralClosure
  AlgebraicCurve.CurveModel.finite_chartRing
  AlgebraicCurve.CurveModel.centre_isPrime
  AlgebraicCurve.CurveModel.isFractionRing_chartRing
  AlgebraicCurve.CurveModel.finiteType_chartRing
  AlgebraicCurve.CurveModel.isNoetherianRing_chartRing
  AlgebraicCurve.CurveModel.isScalarTower_base_adjoin
  AlgebraicCurve.CurveModel.isScalarTower_adjoin
  AlgebraicCurve.CurveModel.chartRing_finitePresentation
attribute [-simp]
  GoodReductionJacobian.RelativePic0Designation.mk.sizeOf_spec
  GoodReductionJacobian.AvatarSchemeBridge.mk.injEq
  GoodReductionJacobian.AvatarSchemeBridge.mk.sizeOf_spec
  GoodReductionJacobian.RelativePic0Designation.mk.injEq
  GoodReductionJacobian.schemeHomOverComp_coe
  NeronModelInfra.schemeHomOverEquivOverHom_apply
  GoodReductionJacobian.RelativeGroupLaw.mk.sizeOf_spec
  NeronModelInfra.schemeHomOverEquivOverHom_symm_apply
  NeronModelInfra.overHomToSchemeHomOver_coe
  GoodReductionJacobian.RelativeGroupLaw.mk.injEq
  NeronModelInfra.overHomToSchemeHomOver_schemeHomOverToOverHom
  NeronModelInfra.schemeHomOverToOverHom_left
  NeronModelInfra.schemeHomOverToOverHom_overHomToSchemeHomOver
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.sizeOf_spec
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
  AlgebraicCurve.CurveModel.mk.injEq
  AlgebraicCurve.CurveModel.mk.sizeOf_spec
  AlgebraicCurve.Place.mk.injEq
  AlgebraicCurve.Divisor.degree_single
  AlgebraicCurve.Divisor.smul_single
  AlgebraicCurve.Place.smul_toValuationSubring
  AlgebraicCurve.Place.heightOneSpectrum_asIdeal
  AlgebraicCurve.Place.coe_algebraMap
  AlgebraicCurve.Place.ord_one
  AlgebraicCurve.Place.coe_smulRingEquiv_apply
  AlgebraicCurve.Pic0.coe_degZeroSMulHom
  AlgebraicCurve.Place.deg_smul
  AlgebraicCurve.Pic0.mk_zero
  AlgebraicCurve.Place.mk.sizeOf_spec
  AlgebraicCurve.Divisor.degree_smul
  AlgebraicCurve.Pic0.mk_add
  AlgebraicCurve.Place.ord_zero
  AlgebraicCurve.Place.ofHeightOneSpectrum_toValuationSubring
  AlgebraicCurve.mulAdele_apply
attribute [-simp]
  AlgebraicCurve.residuePairing_apply_coe
  AlgebraicCurve.mem_adeleBdd
  AlgebraicCurve.weilSmul_one
  AlgebraicCurve.diagonalHom_apply
  AlgebraicCurve.weilSmul_apply
  AlgebraicCurve.adeleSpaceMul_coe
  AlgebraicCurve.mulAdele_one
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U1
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.injEq
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U0
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.mk.injEq
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.pullback_U1
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.pullback_U0
  TwoChartCech.Sections.mk.injEq
  TwoChartCech.Cover.mk.injEq
  TwoChartCech.GrothendieckComplex.mk.injEq
  TwoChartCech.Sections.mk.sizeOf_spec
  TwoChartCech.Cover.mk.sizeOf_spec
  TwoChartCech.Cover.lineBundle_r0_apply
  TwoChartCech.GrothendieckComplex.mk.sizeOf_spec
  TwoChartCech.Cover.lineBundle_r1_apply
  CoherentBaseChange.TwoTermComplex.mk.sizeOf_spec
  CoherentBaseChange.TwoTermComplex.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
  AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
  CategoryTheory.Functor.OverTotal.ofFibre_fst
  CategoryTheory.Functor.overTotal_map_fst
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_J
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYoneda_toGlued_uliftYonedaGluedToSheaf
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t'
attribute [-simp]
  uliftYoneda_toGlued_uliftYonedaGluedToSheaf_assoc
attribute [-simp]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_toGlued
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_openCover_map
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_comp
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_V
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_U
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_f
attribute [-simp]
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_P
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_toBase
  AlgebraicGeometry.RelPicard.rigSection_snd
  AlgebraicGeometry.RelPicard.RigidifiedLineBundle.ofInvertible_L
  AlgebraicGeometry.RelPicard.rigSection_snd_assoc
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
  GoodReductionJacobian.relativeGroupLawOfGrpObj_inv
  GoodReductionJacobian.relativeGroupLawOfGrpObj_mul
  GoodReductionJacobian.overHomEquivSchemeHomOver_apply_coe
  GoodReductionJacobian.relativeGroupLawOfGrpObj_one
  GoodReductionJacobian.overHomEquivSchemeHomOver_symm_apply_left
  PresheafOfModules.freeεIso_hom_app
  PresheafOfModules.freeμIso_hom_app
  AlgebraicCurve.coe_cechH0Equiv_apply
  AlgebraicCurve.cechH1ToH1_mk
  AlgebraicCurve.lSpaceOn_univ
  AlgebraicCurve.lSpaceOn_empty
  AlgebraicCurve.Place.congrEquiv_symm_apply
  AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
  AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
  AlgebraicCurve.Place.congrEquiv_apply
  AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
  AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
  AlgebraicCurve.Divisor.mapRestrict_single
  AlgebraicCurve.Divisor.pushforward_single
  AlgebraicCurve.Place.coe_restrictInclusion
  AlgebraicCurve.Place.mem_fiber
  AlgebraicCurve.Place.restrict_toValuationSubring
  AlgebraicCurve.Divisor.degree_pushforward
  AlgebraicCurve.Place.restrictResidueMap_residue
  AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
  AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
  AlgebraicCurve.Place.placeOfPrime_toValuationSubring
  AlgebraicCurve.Place.mem_fiberOver
  AlgebraicCurve.Place.fiberEquiv_symm_apply
  AlgebraicCurve.Place.fiberEquiv_apply
  AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
attribute [-simp]
  AlgebraicCurve.Divisor.degree_pushforwardAlong
  AlgebraicCurve.Pic0.coe_degZeroCorrespondence
  AlgebraicCurve.Place.mem_fiberAlong
  AlgebraicCurve.SemilinearAut.toRingAut_inv
  AlgebraicCurve.SemilinearAut.smul_def
  AlgebraicCurve.SemilinearAut.smul_single
  AlgebraicCurve.SemilinearAut.smul_toValuationSubring
  AlgebraicCurve.SemilinearAut.baseAut_inv
  AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_one
  AlgebraicCurve.SemilinearAut.deg_smul
  AlgebraicCurve.SemilinearAut.degree_smul
  AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
  AlgebraicCurve.SemilinearAut.baseAut_mul
  AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
  AlgebraicCurve.SemilinearAut.baseAut_one
  AlgebraicCurve.SemilinearAut.ofAlgAut_smul
  AlgebraicCurve.SemilinearAut.coe_torsion_smul
  AlgebraicCurve.SemilinearAut.toRingAut_mul
attribute [-simp]
  AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeInfty
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_some
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeOfPoint
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_none
  AlgebraicCurve.Divisor.evalFun_zero
  AlgebraicCurve.Place.evalAt_one
  AlgebraicCurve.Place.differentialCoeff_zero
  AlgebraicCurve.Place.differentialCoeff_dCoord
  AlgebraicCurve.TranscendenceTower.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
  AlgebraicCurve.TranscendenceTower.mk.injEq
  AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec
  AlgebraicCurve.PoleDivisorPackage.mk.injEq
  AlgebraicGeometry.RelPicard.thetaBundle_def
attribute [-simp]
  AlgebraicGeometry.RelPicard.picardBundle_def
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_ofRelEffDivisor
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_I
  AlgebraicGeometry.mapOnProdOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.mk.sizeOf_spec
  AlgebraicGeometry.RelEffCartierDiv.mk.injEq
  AlgebraicGeometry.mapOnProdOver_snd
  AlgebraicGeometry.mapOnProdOver_fst
  AlgebraicGeometry.mapOnProdOver_snd_assoc
  AlgebraicGeometry.mapOnProdOver_id
  AlgebraicCurve.RelEffDivisor.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_fst
  AlgebraicCurve.mapOnProd_fst_assoc
  AlgebraicCurve.mapOnProd_snd
  AlgebraicCurve.UnivDivisorPack.mk.injEq
  AlgebraicCurve.RelEffDivisor.mk.injEq
  AlgebraicCurve.UnivDivisorPack.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_snd_assoc
  AlgebraicGeometry.Scheme.Modules.exteriorPower_obj
  PresheafOfModules.exteriorPower_map_ιMulti
  PresheafOfModules.ExteriorPower.appₗ_apply
  AlgebraicGeometry.prodKerGraph_one
  AlgebraicGeometry.fibrePowOver.proj_comp
  AlgebraicGeometry.prodKerGraph_zero
  AlgebraicGeometry.RelEffCartierDiv.empty_I
  AlgebraicGeometry.fibrePowOver.proj_comp_assoc
  AlgebraicGeometry.graphOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
  AlgebraicGeometry.graphOver_fst
  AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
  AlgebraicGeometry.graphOver_snd
  AlgebraicGeometry.graphOver_snd_assoc
  AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
  AlgebraicCurve.SymmetricPowerPackage.mk.injEq
  AlgebraicGeometry.FGSubalgebra.cocone_ι_app_apply
  AlgebraicGeometry.RelPicard.fst_toProdSpec
  AlgebraicGeometry.RelPicard.toProdSpec_fst_assoc
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_cons
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_nil
attribute [-simp]
  AlgebraicGeometry.RelPicard.fst_toProdSpec_assoc
  AlgebraicGeometry.RelPicard.toProdSpec_fst
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.sizeOf_spec
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.injEq
  AlgebraicCurve.adeleSingle_coe
  AlgebraicCurve.kaehlerResidueTermKFam_apply
  AlgebraicCurve.Place.LocalResidueData.mk.injEq
  AlgebraicCurve.Place.LocalResidueData.mk.sizeOf_spec
  AlgebraicCurve.Place.kw_ffgc_adicCompletionComapIntegers_coe
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.sizeOf_spec
  AlgebraicCurve.Place.mem_simplePoleSubmodule
  AlgebraicCurve.Place.coe_uniformizerSubring
  ModularCurve.Lg37.Lg37CompletionSection.mk.injEq
  AlgebraicCurve.Place.CoefficientFieldSection.mk.injEq
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.injEq
  ModularCurve.Lg37.Lg37CompletionSection.mk.sizeOf_spec
  AlgebraicCurve.Place.CoefficientFieldSection.mk.sizeOf_spec
  AlgebraicCurve.Place.poleSubmodule_one
  AlgebraicCurve.Place.mem_poleSubmodule
  AlgebraicGeometry.Scheme.Modules.toUnitSection_ofUnitSection
  AlgebraicGeometry.Scheme.Modules.pullbackSection_def
  AlgebraicGeometry.Scheme.Modules.ofUnitSection_toUnitSection
  PresheafOfModules.InternalHom.IsSheafAux.appAt_toPresheafHom
attribute [-simp]
  SheafOfModules.ihomSectionsEquivFamily_unit
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_apply
  SheafOfModules.ihomEval_unit_app
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_right
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_left
  AlgebraicGeometry.Scheme.Modules.homOfFamily_app_apply
  SheafOfModules.unit_ihomSectionsEquivFamily
  AlgebraicGeometry.Scheme.Modules.familyOfHom_app
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_hom_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_inv_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomOfFamily_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_symm_apply
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_right
  AlgebraicGeometry.Scheme.Modules.map_unitSection
  AlgebraicGeometry.Scheme.Modules.tensorSectionsBilin_apply
  AlgebraicGeometry.Scheme.Modules.tensorPowSection_zero
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_left
  AlgebraicGeometry.Scheme.Modules.tensorPow_zero
  AlgebraicGeometry.Scheme.Modules.tensorPow_succ
  AlgebraicGeometry.Scheme.OrderedAffineCover.mk.injEq
  AlgebraicGeometry.OModulePresheaf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCover.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.mk.injEq
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_neg
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_zero
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_sub
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_add
  AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
  AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U
  AlgebraicGeometry.OModulePresheaf.Hom.mk.injEq
  AlgebraicGeometry.OModulePresheaf.Hom.id_app
  AlgebraicGeometry.OModulePresheaf.AffHom.appSections_apply
  AlgebraicGeometry.OModulePresheaf.AffHom.comp_app
  AlgebraicGeometry.OModulePresheaf.AffSES.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.AffHom.kerMap_coe
  AlgebraicGeometry.OModulePresheaf.AffHom.id_app
  AlgebraicGeometry.OModulePresheaf.Hom.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.Hom.toAffHom_app
attribute [-simp]
  AlgebraicGeometry.OModulePresheaf.SES.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.AffHom.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.Hom.comp_app
  AlgebraicGeometry.OModulePresheaf.SES.mk.injEq
  AlgebraicGeometry.OModulePresheaf.AffHom.mk.injEq
  AlgebraicGeometry.OModulePresheaf.Hom.appSections_apply
  AlgebraicGeometry.OModulePresheaf.AffSES.mk.injEq
  AlgebraicGeometry.OModulePresheaf.prod_obj
  AlgebraicGeometry.OModulePresheaf.restrOpen_obj
  AlgebraicGeometry.OModulePresheaf.DevissageStep.mk.injEq
  AlgebraicGeometry.OModulePresheaf.pushforward_obj
  AlgebraicGeometry.OModulePresheaf.im_obj
  AlgebraicGeometry.OModulePresheaf.pow_obj
  AlgebraicGeometry.OModulePresheaf.fstHom_app
  AlgebraicGeometry.OModulePresheaf.ker_obj
  AlgebraicGeometry.OModulePresheaf.coker_obj
  AlgebraicGeometry.OModulePresheaf.DevissageStep.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCover.preimage_U
  AlgebraicGeometry.OModulePresheaf.sndHom_app
  AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
  DoubleComplex.Bounded.mk.injEq
  DoubleComplex.Bounded.mk.sizeOf_spec
  DoubleComplex.Convergence.mk.injEq
  DoubleComplex.Convergence.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.injEq
  AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatumProj.mk.injEq
  AlgebraicGeometry.ChowDatum.mk.injEq
  ProjSpaceCech.GradedModule.mk.injEq
  ProjSpaceCech.GradedModule.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Presentation.mk.injEq
  ProjSpaceCech.GradedModule.Frac.mk.injEq
  ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.shift_toLinearMap
  ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.mk.injEq
  TwoChartCech.Mumford.dK_apply
attribute [-simp]
  TwoChartCech.Mumford.ι0_apply
  TwoChartCech.Mumford.ι1_apply
  TwoChartCech.KerCoprod.dK_apply
  TwoChartCech.KerCoprod.ι1_apply
  TwoChartCech.KerCoprod.ι0_apply
  AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
  AlgebraicGeometry.RelPicard.algEquivZeroGroupCut_toSubPicCondition
  AlgebraicGeometry.RelPicard.LFP.stageHom_val
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_hom_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_inv_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.restrict_P
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp
  AlgebraicGeometry.RelEffCartierDiv.functor_map_fst
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_pullbackAlong
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_symm_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp_assoc
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top
  AlgebraicGeometry.RelEffCartierDiv.mem_supportedIn_iff
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top_eq
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
  CoherentBaseChange.FibreH0Family.mk.sizeOf_spec
  CoherentBaseChange.FibreH0Family.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.sizeOf_spec
  AlgebraicCurve.CurveModel.coe_gInf
  AlgebraicCurve.CurveModel.coe_tInvChart
  AlgebraicCurve.CurveModel.ιInf_gluedToBase_assoc
  AlgebraicCurve.CurveModel.ιInf_gluedToBase
  AlgebraicCurve.CurveModel.primeOfι₀_asIdeal
  AlgebraicCurve.CurveModel.coe_tChart
  AlgebraicCurve.CurveModel.ι₀_gluedToBase_assoc
  AlgebraicCurve.CurveModel.primeOfιInf_asIdeal
attribute [-simp]
  AlgebraicCurve.CurveModel.ι₀_gluedToBase
  AlgebraicCurve.CurveModel.coe_tma
  AlgebraicCurve.CurveModel.coe_primeEquivChartPlaces
universe u
noncomputable section
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.CategoryTheory.CartesianMonoidalCategory
open _root_.AlgebraicGeometry.RelPicard
open _root_.NeronModelInfra
namespace P2mCubeAssembly
section Triv
variable {S T V : Scheme.{u}}

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.ThreeSlices
attribute [-instance]
  AlgebraicGeometry.SmoothOfRelativeDimension.fiberToSpecResidueField
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_snd
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_fst
  AlgebraicGeometry.SmoothOfRelativeDimension.smooth_one
  AlgebraicGeometry.SmoothProperCurve.isIntegral_pullback_Spec_field
  AlgebraicGeometry.IsProper.fiberToSpecResidueField
  AlgebraicCurve.CurveModel.isProper
  AlgebraicCurve.CurveModel.isIntegral
  AlgebraicCurve.CurveModel.smooth
  AlgebraicCurve.Place.instIsScalarTowerSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Divisor.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instSMulAlgEquiv
  AlgebraicCurve.Place.instIsPrincipalIdealRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instIsDiscreteValuationRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Pic0.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instAlgebraSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instMulActionAlgEquiv
  AlgebraicCurve.Pic0.instSMulAlgEquiv
  TwoChartCech.Sections.M0_moduleA
  TwoChartCech.Sections.M1_module
  TwoChartCech.Cover.A01_algebra
  TwoChartCech.Cover.A0_algebra
  TwoChartCech.Cover.A1_commRing
  TwoChartCech.Cover.A1_algebra
  TwoChartCech.Sections.M01_module
  TwoChartCech.Sections.M0_addCommGroup
  TwoChartCech.Sections.M0_tower
  TwoChartCech.Sections.M01_addCommGroup
  TwoChartCech.Cover.A0_commRing
  TwoChartCech.Sections.M1_tower
  TwoChartCech.Sections.M01_moduleA
  TwoChartCech.Sections.M0_module
  TwoChartCech.Sections.M1_moduleA
  TwoChartCech.Sections.M1_addCommGroup
  TwoChartCech.Cover.A01_commRing
  TwoChartCech.Sections.M01_tower
  CoherentBaseChange.TwoTermComplex.C0_module
  CoherentBaseChange.TwoTermComplex.C0_addCommGroup
  CoherentBaseChange.TwoTermComplex.C1_module
  CoherentBaseChange.TwoTermComplex.C1_addCommGroup
attribute [-instance]
  CoherentBaseChange.TwoTermComplex.C0_free
  CoherentBaseChange.TwoTermComplex.C1_finite
  CoherentBaseChange.TwoTermComplex.C0_finite
  CoherentBaseChange.TwoTermComplex.C1_free
  AlgebraicCurve.IsCurveOver.instNontrivialKaehler
  AlgebraicCurve.IsCurveOver.instFreeKaehler
  AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
  AlgebraicCurve.IsCurveOver.instFiniteResidue
attribute [-instance]
  instIsLocallyInjectiveFunUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsLocallySurjectiveUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsOpenImmersionToGlued
attribute [-instance]
  instIsIsoSheafZariskiTopologyTypeUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.RelPicard.isOpenImmersion_toGlued
  AlgebraicGeometry.Scheme.Modules.preservesBinaryProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback_monoidal
  AlgebraicGeometry.Scheme.Modules.sheafify_isLocalization'
  AlgebraicGeometry.Scheme.Modules.preservesTerminal_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback₀_monoidal
  AlgebraicGeometry.Scheme.Modules.preservesFiniteProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.sheafifyPullback_lifting
  PresheafOfModules.PullbackMonoidal.pullback_monoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ
  PresheafOfModules.pushforward_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_η
  PresheafOfModules.free_monoidal
  PresheafOfModules.restrictScalars_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ_gS
  PresheafOfModules.pullback_oplaxMonoidal
attribute [-instance]
  instPreservesColimitsOfSizeCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierPb
attribute [-instance]
  PresheafOfModules.pullback_monoidal'
  AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
  AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
  AlgebraicCurve.Place.instIsPrimeCenter
  AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
  instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
  AlgebraicCurve.Pic0.instModuleZModTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instSMulTorsion
  AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
  AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
  AlgebraicCurve.RationalFunctionField.instNontrivialInftyValueGroup
  PresheafOfModules.ExteriorPower.instModulePresheafAb
  AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
  AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
  AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
  AlgebraicGeometry.isClosedImmersion_graphOver
  AlgebraicGeometry.FGSubalgebra.instIsDirectedLe
attribute [-instance]
  instQuasiSeparatedSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsCofilteredOpposite
  AlgebraicGeometry.FGSubalgebra.instIsAffineObjOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instNonempty
  AlgebraicGeometry.FGSubalgebra.instNonemptySubtypeLeSubalgebraValFG
attribute [-instance]
  instCompactSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsDirectedSubtypeLeSubalgebraValFG
  AlgebraicGeometry.FGSubalgebra.instIsAffineHomMapOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instIsFiltered
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instNeg
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulInt
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAddCommGroup
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAdd
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSub
attribute [-instance]
  instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
  AlgebraicCurve.instHasLocalResidue_of_hasCanonicalLocalResidueK
  AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
  AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
  ModularCurve.KwF4gRRTate.instAlgebraKAdicCompletionIntegers
  AlgebraicCurve.Place.kw_ffgc_continuousSMul_adicCompletionComap
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersCompletionCompletion
attribute [-instance]
  instLiesOverSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegersCompletionIdealAsIdeal
attribute [-instance]
  AlgebraicCurve.instHasCanonicalLocalResidueK
  AlgebraicCurve.Place.instAlgebra_restrictResidueField
  AlgebraicCurve.Place.instIsScalarTower_restrictResidueField
  AlgebraicCurve.instHasLocalResidue
  AlgebraicCurve.HasSeparableResidue.of_perfectField_of_isCurveOver
  AlgebraicCurve.HasSeparableResidue.of_perfectField
  AlgebraicCurve.Place.instIsLocalHom_restrictSubringHom
  AlgebraicCurve.instHasCanonicalLocalResidueKStar
  ModularCurve.KwNo6Pin.isLocalRing_completion
  SheafOfModules.isIso_ihomModelToIhom
  AlgebraicGeometry.OModulePresheaf.isScalarTower
  AlgebraicGeometry.Scheme.OrderedAffineCover.instLinearOrder
  AlgebraicGeometry.OModulePresheaf.module
  AlgebraicGeometry.Scheme.OrderedAffineCover.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCover.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.addCommGroup
  AlgebraicGeometry.Scheme.OrderedAffineCover.instDecidableEqIdx
  AlgebraicGeometry.OModulePresheaf.moduleSections
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.instSubsingletonObjZero
attribute [-instance]
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
  AlgebraicGeometry.OModulePresheaf.Leray.biC_module
  DoubleComplex.instModuleE₂I
  DoubleComplex.Bounded.modR
  DoubleComplex.instModuleE₂II
  DoubleComplex.instAddCommGroupE₂II
  DoubleComplex.Bounded.abGrp
  DoubleComplex.instAddCommGroupE₂I
  AlgebraicGeometry.ChowDatum.hι_closed
  AlgebraicGeometry.ChowDatumProj.hιN_closed
  AlgebraicGeometry.ChowDatumProj.hp_proper
  AlgebraicGeometry.ChowDatum.hp_isoU
  AlgebraicGeometry.ChowDatum.hp_proper
  AlgebraicGeometry.ProjSpace.algebraAway
  AlgebraicGeometry.ProjSpace.instIsProperProdOverπ
  AlgebraicGeometry.ChowDatumProj.hp_isoU
  AlgebraicGeometry.ProjSpace.isProper_π
  AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
  ProjSpaceCech.GradedModule.H.module
  ProjSpaceCech.GradedModule.H.addCommGroup
  ProjSpaceCech.GradedModule.sec.instAdd
  ProjSpaceCech.GradedModule.sec.instNeg
  ProjSpaceCech.GradedModule.acg
  ProjSpaceCech.GradedModule.Frac.setoid
  ProjSpaceCech.GradedModule.modR
  ProjSpaceCech.GradedModule.sec.instModule
  ProjSpaceCech.GradedModule.sec.instAddCommGroup
  ProjSpaceCech.GradedModule.sec.instZero
  ProjSpaceCech.GradedModule.Presentation.fJ
  ProjSpaceCech.GradedModule.sec.instSMul
  ProjSpaceCech.Twist.H.module
  ProjSpaceCech.Idx.instFintype
  ProjSpaceCech.Twist.H.addCommGroup
attribute [-instance]
  ProjSpaceCech.Idx.instDecidableEq
  ProjSpaceCech.Twist.Mon.instDecidableEq
  ProjSpaceCech.Twist.cochain.instAddCommGroup
  ProjSpaceCech.Twist.cochain.instModule
  AlgebraicGeometry.FGSubalgebra.tensorStage_directedSystem
  AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
  AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
  AlgebraicCurve.CurveModel.locallyOfFiniteType_gluedToBase
  AlgebraicCurve.CurveModel.isFractionRing_overlap
  AlgebraicCurve.CurveModel.isLocallyNoetherian_glued
  AlgebraicCurve.CurveModel.jacobsonSpace_glued
  AlgebraicCurve.CurveModel.isOpenImmersion_ι₀
  AlgebraicCurve.CurveModel.isIntegral_glued
  AlgebraicCurve.CurveModel.quasiSeparated_gluedToBase
  AlgebraicCurve.CurveModel.compactSpace_glued
  AlgebraicCurve.CurveModel.isIntegral_adjoin_chartRing
  AlgebraicCurve.CurveModel.isFractionRing_overlap_functionField
  AlgebraicCurve.CurveModel.isProper_gluedToBase
  AlgebraicCurve.CurveModel.isOpenImmersion_ιU
  AlgebraicCurve.CurveModel.isOpenImmersion_f₀
  AlgebraicCurve.CurveModel.isOpenImmersion_fInf
  AlgebraicCurve.CurveModel.isOpenImmersion_ιInf
  AlgebraicCurve.CurveModel.algebra_overlap_functionField
  AlgebraicCurve.CurveModel.quasiCompact_gluedToBase
  AlgebraicCurve.CurveModel.algebraAdjoin
  AlgebraicCurve.CurveModel.isDedekindDomain_chartRing
  AlgebraicCurve.CurveModel.isIntegralClosure
  AlgebraicCurve.CurveModel.finite_chartRing
  AlgebraicCurve.CurveModel.centre_isPrime
  AlgebraicCurve.CurveModel.isFractionRing_chartRing
  AlgebraicCurve.CurveModel.finiteType_chartRing
  AlgebraicCurve.CurveModel.isNoetherianRing_chartRing
  AlgebraicCurve.CurveModel.isScalarTower_base_adjoin
  AlgebraicCurve.CurveModel.isScalarTower_adjoin
  AlgebraicCurve.CurveModel.chartRing_finitePresentation
attribute [-simp]
  GoodReductionJacobian.RelativePic0Designation.mk.sizeOf_spec
  GoodReductionJacobian.AvatarSchemeBridge.mk.injEq
  GoodReductionJacobian.AvatarSchemeBridge.mk.sizeOf_spec
  GoodReductionJacobian.RelativePic0Designation.mk.injEq
  GoodReductionJacobian.schemeHomOverComp_coe
  NeronModelInfra.schemeHomOverEquivOverHom_apply
  GoodReductionJacobian.RelativeGroupLaw.mk.sizeOf_spec
  NeronModelInfra.schemeHomOverEquivOverHom_symm_apply
  NeronModelInfra.overHomToSchemeHomOver_coe
  GoodReductionJacobian.RelativeGroupLaw.mk.injEq
  NeronModelInfra.overHomToSchemeHomOver_schemeHomOverToOverHom
  NeronModelInfra.schemeHomOverToOverHom_left
  NeronModelInfra.schemeHomOverToOverHom_overHomToSchemeHomOver
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.sizeOf_spec
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
  AlgebraicCurve.CurveModel.mk.injEq
  AlgebraicCurve.CurveModel.mk.sizeOf_spec
  AlgebraicCurve.Place.mk.injEq
  AlgebraicCurve.Divisor.degree_single
  AlgebraicCurve.Divisor.smul_single
  AlgebraicCurve.Place.smul_toValuationSubring
  AlgebraicCurve.Place.heightOneSpectrum_asIdeal
  AlgebraicCurve.Place.coe_algebraMap
  AlgebraicCurve.Place.ord_one
  AlgebraicCurve.Place.coe_smulRingEquiv_apply
  AlgebraicCurve.Pic0.coe_degZeroSMulHom
  AlgebraicCurve.Place.deg_smul
  AlgebraicCurve.Pic0.mk_zero
  AlgebraicCurve.Place.mk.sizeOf_spec
  AlgebraicCurve.Divisor.degree_smul
  AlgebraicCurve.Pic0.mk_add
  AlgebraicCurve.Place.ord_zero
  AlgebraicCurve.Place.ofHeightOneSpectrum_toValuationSubring
  AlgebraicCurve.mulAdele_apply
attribute [-simp]
  AlgebraicCurve.residuePairing_apply_coe
  AlgebraicCurve.mem_adeleBdd
  AlgebraicCurve.weilSmul_one
  AlgebraicCurve.diagonalHom_apply
  AlgebraicCurve.weilSmul_apply
  AlgebraicCurve.adeleSpaceMul_coe
  AlgebraicCurve.mulAdele_one
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U1
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.injEq
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U0
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.mk.injEq
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.pullback_U1
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.pullback_U0
  TwoChartCech.Sections.mk.injEq
  TwoChartCech.Cover.mk.injEq
  TwoChartCech.GrothendieckComplex.mk.injEq
  TwoChartCech.Sections.mk.sizeOf_spec
  TwoChartCech.Cover.mk.sizeOf_spec
  TwoChartCech.Cover.lineBundle_r0_apply
  TwoChartCech.GrothendieckComplex.mk.sizeOf_spec
  TwoChartCech.Cover.lineBundle_r1_apply
  CoherentBaseChange.TwoTermComplex.mk.sizeOf_spec
  CoherentBaseChange.TwoTermComplex.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
  AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
  CategoryTheory.Functor.OverTotal.ofFibre_fst
  CategoryTheory.Functor.overTotal_map_fst
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_J
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYoneda_toGlued_uliftYonedaGluedToSheaf
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t'
attribute [-simp]
  uliftYoneda_toGlued_uliftYonedaGluedToSheaf_assoc
attribute [-simp]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_toGlued
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_openCover_map
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_comp
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_V
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_U
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_f
attribute [-simp]
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_P
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_toBase
  AlgebraicGeometry.RelPicard.rigSection_snd
  AlgebraicGeometry.RelPicard.RigidifiedLineBundle.ofInvertible_L
  AlgebraicGeometry.RelPicard.rigSection_snd_assoc
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
  GoodReductionJacobian.relativeGroupLawOfGrpObj_inv
  GoodReductionJacobian.relativeGroupLawOfGrpObj_mul
  GoodReductionJacobian.overHomEquivSchemeHomOver_apply_coe
  GoodReductionJacobian.relativeGroupLawOfGrpObj_one
  GoodReductionJacobian.overHomEquivSchemeHomOver_symm_apply_left
  PresheafOfModules.freeεIso_hom_app
  PresheafOfModules.freeμIso_hom_app
  AlgebraicCurve.coe_cechH0Equiv_apply
  AlgebraicCurve.cechH1ToH1_mk
  AlgebraicCurve.lSpaceOn_univ
  AlgebraicCurve.lSpaceOn_empty
  AlgebraicCurve.Place.congrEquiv_symm_apply
  AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
  AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
  AlgebraicCurve.Place.congrEquiv_apply
  AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
  AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
  AlgebraicCurve.Divisor.mapRestrict_single
  AlgebraicCurve.Divisor.pushforward_single
  AlgebraicCurve.Place.coe_restrictInclusion
  AlgebraicCurve.Place.mem_fiber
  AlgebraicCurve.Place.restrict_toValuationSubring
  AlgebraicCurve.Divisor.degree_pushforward
  AlgebraicCurve.Place.restrictResidueMap_residue
  AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
  AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
  AlgebraicCurve.Place.placeOfPrime_toValuationSubring
  AlgebraicCurve.Place.mem_fiberOver
  AlgebraicCurve.Place.fiberEquiv_symm_apply
  AlgebraicCurve.Place.fiberEquiv_apply
  AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
attribute [-simp]
  AlgebraicCurve.Divisor.degree_pushforwardAlong
  AlgebraicCurve.Pic0.coe_degZeroCorrespondence
  AlgebraicCurve.Place.mem_fiberAlong
  AlgebraicCurve.SemilinearAut.toRingAut_inv
  AlgebraicCurve.SemilinearAut.smul_def
  AlgebraicCurve.SemilinearAut.smul_single
  AlgebraicCurve.SemilinearAut.smul_toValuationSubring
  AlgebraicCurve.SemilinearAut.baseAut_inv
  AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_one
  AlgebraicCurve.SemilinearAut.deg_smul
  AlgebraicCurve.SemilinearAut.degree_smul
  AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
  AlgebraicCurve.SemilinearAut.baseAut_mul
  AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
  AlgebraicCurve.SemilinearAut.baseAut_one
  AlgebraicCurve.SemilinearAut.ofAlgAut_smul
  AlgebraicCurve.SemilinearAut.coe_torsion_smul
  AlgebraicCurve.SemilinearAut.toRingAut_mul
attribute [-simp]
  AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeInfty
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_some
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeOfPoint
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_none
  AlgebraicCurve.Divisor.evalFun_zero
  AlgebraicCurve.Place.evalAt_one
  AlgebraicCurve.Place.differentialCoeff_zero
  AlgebraicCurve.Place.differentialCoeff_dCoord
  AlgebraicCurve.TranscendenceTower.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
  AlgebraicCurve.TranscendenceTower.mk.injEq
  AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec
  AlgebraicCurve.PoleDivisorPackage.mk.injEq
  AlgebraicGeometry.RelPicard.thetaBundle_def
attribute [-simp]
  AlgebraicGeometry.RelPicard.picardBundle_def
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_ofRelEffDivisor
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_I
  AlgebraicGeometry.mapOnProdOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.mk.sizeOf_spec
  AlgebraicGeometry.RelEffCartierDiv.mk.injEq
  AlgebraicGeometry.mapOnProdOver_snd
  AlgebraicGeometry.mapOnProdOver_fst
  AlgebraicGeometry.mapOnProdOver_snd_assoc
  AlgebraicGeometry.mapOnProdOver_id
  AlgebraicCurve.RelEffDivisor.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_fst
  AlgebraicCurve.mapOnProd_fst_assoc
  AlgebraicCurve.mapOnProd_snd
  AlgebraicCurve.UnivDivisorPack.mk.injEq
  AlgebraicCurve.RelEffDivisor.mk.injEq
  AlgebraicCurve.UnivDivisorPack.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_snd_assoc
  AlgebraicGeometry.Scheme.Modules.exteriorPower_obj
  PresheafOfModules.exteriorPower_map_ιMulti
  PresheafOfModules.ExteriorPower.appₗ_apply
  AlgebraicGeometry.prodKerGraph_one
  AlgebraicGeometry.fibrePowOver.proj_comp
  AlgebraicGeometry.prodKerGraph_zero
  AlgebraicGeometry.RelEffCartierDiv.empty_I
  AlgebraicGeometry.fibrePowOver.proj_comp_assoc
  AlgebraicGeometry.graphOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
  AlgebraicGeometry.graphOver_fst
  AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
  AlgebraicGeometry.graphOver_snd
  AlgebraicGeometry.graphOver_snd_assoc
  AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
  AlgebraicCurve.SymmetricPowerPackage.mk.injEq
  AlgebraicGeometry.FGSubalgebra.cocone_ι_app_apply
  AlgebraicGeometry.RelPicard.fst_toProdSpec
  AlgebraicGeometry.RelPicard.toProdSpec_fst_assoc
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_cons
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_nil
attribute [-simp]
  AlgebraicGeometry.RelPicard.fst_toProdSpec_assoc
  AlgebraicGeometry.RelPicard.toProdSpec_fst
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.sizeOf_spec
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.injEq
  AlgebraicCurve.adeleSingle_coe
  AlgebraicCurve.kaehlerResidueTermKFam_apply
  AlgebraicCurve.Place.LocalResidueData.mk.injEq
  AlgebraicCurve.Place.LocalResidueData.mk.sizeOf_spec
  AlgebraicCurve.Place.kw_ffgc_adicCompletionComapIntegers_coe
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.sizeOf_spec
  AlgebraicCurve.Place.mem_simplePoleSubmodule
  AlgebraicCurve.Place.coe_uniformizerSubring
  ModularCurve.Lg37.Lg37CompletionSection.mk.injEq
  AlgebraicCurve.Place.CoefficientFieldSection.mk.injEq
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.injEq
  ModularCurve.Lg37.Lg37CompletionSection.mk.sizeOf_spec
  AlgebraicCurve.Place.CoefficientFieldSection.mk.sizeOf_spec
  AlgebraicCurve.Place.poleSubmodule_one
  AlgebraicCurve.Place.mem_poleSubmodule
  AlgebraicGeometry.Scheme.Modules.toUnitSection_ofUnitSection
  AlgebraicGeometry.Scheme.Modules.pullbackSection_def
  AlgebraicGeometry.Scheme.Modules.ofUnitSection_toUnitSection
  PresheafOfModules.InternalHom.IsSheafAux.appAt_toPresheafHom
attribute [-simp]
  SheafOfModules.ihomSectionsEquivFamily_unit
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_apply
  SheafOfModules.ihomEval_unit_app
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_right
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_left
  AlgebraicGeometry.Scheme.Modules.homOfFamily_app_apply
  SheafOfModules.unit_ihomSectionsEquivFamily
  AlgebraicGeometry.Scheme.Modules.familyOfHom_app
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_hom_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_inv_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomOfFamily_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_symm_apply
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_right
  AlgebraicGeometry.Scheme.Modules.map_unitSection
  AlgebraicGeometry.Scheme.Modules.tensorSectionsBilin_apply
  AlgebraicGeometry.Scheme.Modules.tensorPowSection_zero
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_left
  AlgebraicGeometry.Scheme.Modules.tensorPow_zero
  AlgebraicGeometry.Scheme.Modules.tensorPow_succ
  AlgebraicGeometry.Scheme.OrderedAffineCover.mk.injEq
  AlgebraicGeometry.OModulePresheaf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCover.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.mk.injEq
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_neg
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_zero
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_sub
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_add
  AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
  AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U
  AlgebraicGeometry.OModulePresheaf.Hom.mk.injEq
  AlgebraicGeometry.OModulePresheaf.Hom.id_app
  AlgebraicGeometry.OModulePresheaf.AffHom.appSections_apply
  AlgebraicGeometry.OModulePresheaf.AffHom.comp_app
  AlgebraicGeometry.OModulePresheaf.AffSES.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.AffHom.kerMap_coe
  AlgebraicGeometry.OModulePresheaf.AffHom.id_app
  AlgebraicGeometry.OModulePresheaf.Hom.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.Hom.toAffHom_app
attribute [-simp]
  AlgebraicGeometry.OModulePresheaf.SES.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.AffHom.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.Hom.comp_app
  AlgebraicGeometry.OModulePresheaf.SES.mk.injEq
  AlgebraicGeometry.OModulePresheaf.AffHom.mk.injEq
  AlgebraicGeometry.OModulePresheaf.Hom.appSections_apply
  AlgebraicGeometry.OModulePresheaf.AffSES.mk.injEq
  AlgebraicGeometry.OModulePresheaf.prod_obj
  AlgebraicGeometry.OModulePresheaf.restrOpen_obj
  AlgebraicGeometry.OModulePresheaf.DevissageStep.mk.injEq
  AlgebraicGeometry.OModulePresheaf.pushforward_obj
  AlgebraicGeometry.OModulePresheaf.im_obj
  AlgebraicGeometry.OModulePresheaf.pow_obj
  AlgebraicGeometry.OModulePresheaf.fstHom_app
  AlgebraicGeometry.OModulePresheaf.ker_obj
  AlgebraicGeometry.OModulePresheaf.coker_obj
  AlgebraicGeometry.OModulePresheaf.DevissageStep.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCover.preimage_U
  AlgebraicGeometry.OModulePresheaf.sndHom_app
  AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
  DoubleComplex.Bounded.mk.injEq
  DoubleComplex.Bounded.mk.sizeOf_spec
  DoubleComplex.Convergence.mk.injEq
  DoubleComplex.Convergence.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.injEq
  AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatumProj.mk.injEq
  AlgebraicGeometry.ChowDatum.mk.injEq
  ProjSpaceCech.GradedModule.mk.injEq
  ProjSpaceCech.GradedModule.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Presentation.mk.injEq
  ProjSpaceCech.GradedModule.Frac.mk.injEq
  ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.shift_toLinearMap
  ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.mk.injEq
  TwoChartCech.Mumford.dK_apply
attribute [-simp]
  TwoChartCech.Mumford.ι0_apply
  TwoChartCech.Mumford.ι1_apply
  TwoChartCech.KerCoprod.dK_apply
  TwoChartCech.KerCoprod.ι1_apply
  TwoChartCech.KerCoprod.ι0_apply
  AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
  AlgebraicGeometry.RelPicard.algEquivZeroGroupCut_toSubPicCondition
  AlgebraicGeometry.RelPicard.LFP.stageHom_val
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_hom_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_inv_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.restrict_P
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp
  AlgebraicGeometry.RelEffCartierDiv.functor_map_fst
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_pullbackAlong
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_symm_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp_assoc
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top
  AlgebraicGeometry.RelEffCartierDiv.mem_supportedIn_iff
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top_eq
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
  CoherentBaseChange.FibreH0Family.mk.sizeOf_spec
  CoherentBaseChange.FibreH0Family.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.sizeOf_spec
  AlgebraicCurve.CurveModel.coe_gInf
  AlgebraicCurve.CurveModel.coe_tInvChart
  AlgebraicCurve.CurveModel.ιInf_gluedToBase_assoc
  AlgebraicCurve.CurveModel.ιInf_gluedToBase
  AlgebraicCurve.CurveModel.primeOfι₀_asIdeal
  AlgebraicCurve.CurveModel.coe_tChart
  AlgebraicCurve.CurveModel.ι₀_gluedToBase_assoc
  AlgebraicCurve.CurveModel.primeOfιInf_asIdeal
attribute [-simp]
  AlgebraicCurve.CurveModel.ι₀_gluedToBase
  AlgebraicCurve.CurveModel.coe_tma
  AlgebraicCurve.CurveModel.coe_primeEquivChartPlaces
universe u
noncomputable section
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.CategoryTheory.CartesianMonoidalCategory
open _root_.AlgebraicGeometry.RelPicard
open _root_.NeronModelInfra
namespace P2mCubeAssembly
section Triv
variable {S T V : Scheme.{u}}

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.ThreeSlices
attribute [-instance]
  AlgebraicGeometry.SmoothOfRelativeDimension.fiberToSpecResidueField
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_snd
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_fst
  AlgebraicGeometry.SmoothOfRelativeDimension.smooth_one
  AlgebraicGeometry.SmoothProperCurve.isIntegral_pullback_Spec_field
  AlgebraicGeometry.IsProper.fiberToSpecResidueField
  AlgebraicCurve.CurveModel.isProper
  AlgebraicCurve.CurveModel.isIntegral
  AlgebraicCurve.CurveModel.smooth
  AlgebraicCurve.Place.instIsScalarTowerSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Divisor.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instSMulAlgEquiv
  AlgebraicCurve.Place.instIsPrincipalIdealRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instIsDiscreteValuationRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Pic0.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instAlgebraSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instMulActionAlgEquiv
  AlgebraicCurve.Pic0.instSMulAlgEquiv
  TwoChartCech.Sections.M0_moduleA
  TwoChartCech.Sections.M1_module
  TwoChartCech.Cover.A01_algebra
  TwoChartCech.Cover.A0_algebra
  TwoChartCech.Cover.A1_commRing
  TwoChartCech.Cover.A1_algebra
  TwoChartCech.Sections.M01_module
  TwoChartCech.Sections.M0_addCommGroup
  TwoChartCech.Sections.M0_tower
  TwoChartCech.Sections.M01_addCommGroup
  TwoChartCech.Cover.A0_commRing
  TwoChartCech.Sections.M1_tower
  TwoChartCech.Sections.M01_moduleA
  TwoChartCech.Sections.M0_module
  TwoChartCech.Sections.M1_moduleA
  TwoChartCech.Sections.M1_addCommGroup
  TwoChartCech.Cover.A01_commRing
  TwoChartCech.Sections.M01_tower
  CoherentBaseChange.TwoTermComplex.C0_module
  CoherentBaseChange.TwoTermComplex.C0_addCommGroup
  CoherentBaseChange.TwoTermComplex.C1_module
  CoherentBaseChange.TwoTermComplex.C1_addCommGroup
attribute [-instance]
  CoherentBaseChange.TwoTermComplex.C0_free
  CoherentBaseChange.TwoTermComplex.C1_finite
  CoherentBaseChange.TwoTermComplex.C0_finite
  CoherentBaseChange.TwoTermComplex.C1_free
  AlgebraicCurve.IsCurveOver.instNontrivialKaehler
  AlgebraicCurve.IsCurveOver.instFreeKaehler
  AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
  AlgebraicCurve.IsCurveOver.instFiniteResidue
attribute [-instance]
  instIsLocallyInjectiveFunUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsLocallySurjectiveUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsOpenImmersionToGlued
attribute [-instance]
  instIsIsoSheafZariskiTopologyTypeUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.RelPicard.isOpenImmersion_toGlued
  AlgebraicGeometry.Scheme.Modules.preservesBinaryProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback_monoidal
  AlgebraicGeometry.Scheme.Modules.sheafify_isLocalization'
  AlgebraicGeometry.Scheme.Modules.preservesTerminal_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback₀_monoidal
  AlgebraicGeometry.Scheme.Modules.preservesFiniteProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.sheafifyPullback_lifting
  PresheafOfModules.PullbackMonoidal.pullback_monoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ
  PresheafOfModules.pushforward_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_η
  PresheafOfModules.free_monoidal
  PresheafOfModules.restrictScalars_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ_gS
  PresheafOfModules.pullback_oplaxMonoidal
attribute [-instance]
  instPreservesColimitsOfSizeCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierPb
attribute [-instance]
  PresheafOfModules.pullback_monoidal'
  AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
  AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
  AlgebraicCurve.Place.instIsPrimeCenter
  AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
  instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
  AlgebraicCurve.Pic0.instModuleZModTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instSMulTorsion
  AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
  AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
  AlgebraicCurve.RationalFunctionField.instNontrivialInftyValueGroup
  PresheafOfModules.ExteriorPower.instModulePresheafAb
  AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
  AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
  AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
  AlgebraicGeometry.isClosedImmersion_graphOver
  AlgebraicGeometry.FGSubalgebra.instIsDirectedLe
attribute [-instance]
  instQuasiSeparatedSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsCofilteredOpposite
  AlgebraicGeometry.FGSubalgebra.instIsAffineObjOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instNonempty
  AlgebraicGeometry.FGSubalgebra.instNonemptySubtypeLeSubalgebraValFG
attribute [-instance]
  instCompactSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsDirectedSubtypeLeSubalgebraValFG
  AlgebraicGeometry.FGSubalgebra.instIsAffineHomMapOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instIsFiltered
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instNeg
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulInt
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAddCommGroup
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAdd
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSub
attribute [-instance]
  instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
  AlgebraicCurve.instHasLocalResidue_of_hasCanonicalLocalResidueK
  AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
  AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
  ModularCurve.KwF4gRRTate.instAlgebraKAdicCompletionIntegers
  AlgebraicCurve.Place.kw_ffgc_continuousSMul_adicCompletionComap
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersCompletionCompletion
attribute [-instance]
  instLiesOverSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegersCompletionIdealAsIdeal
attribute [-instance]
  AlgebraicCurve.instHasCanonicalLocalResidueK
  AlgebraicCurve.Place.instAlgebra_restrictResidueField
  AlgebraicCurve.Place.instIsScalarTower_restrictResidueField
  AlgebraicCurve.instHasLocalResidue
  AlgebraicCurve.HasSeparableResidue.of_perfectField_of_isCurveOver
  AlgebraicCurve.HasSeparableResidue.of_perfectField
  AlgebraicCurve.Place.instIsLocalHom_restrictSubringHom
  AlgebraicCurve.instHasCanonicalLocalResidueKStar
  ModularCurve.KwNo6Pin.isLocalRing_completion
  SheafOfModules.isIso_ihomModelToIhom
  AlgebraicGeometry.OModulePresheaf.isScalarTower
  AlgebraicGeometry.Scheme.OrderedAffineCover.instLinearOrder
  AlgebraicGeometry.OModulePresheaf.module
  AlgebraicGeometry.Scheme.OrderedAffineCover.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCover.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.addCommGroup
  AlgebraicGeometry.Scheme.OrderedAffineCover.instDecidableEqIdx
  AlgebraicGeometry.OModulePresheaf.moduleSections
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.instSubsingletonObjZero
attribute [-instance]
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
  AlgebraicGeometry.OModulePresheaf.Leray.biC_module
  DoubleComplex.instModuleE₂I
  DoubleComplex.Bounded.modR
  DoubleComplex.instModuleE₂II
  DoubleComplex.instAddCommGroupE₂II
  DoubleComplex.Bounded.abGrp
  DoubleComplex.instAddCommGroupE₂I
  AlgebraicGeometry.ChowDatum.hι_closed
  AlgebraicGeometry.ChowDatumProj.hιN_closed
  AlgebraicGeometry.ChowDatumProj.hp_proper
  AlgebraicGeometry.ChowDatum.hp_isoU
  AlgebraicGeometry.ChowDatum.hp_proper
  AlgebraicGeometry.ProjSpace.algebraAway
  AlgebraicGeometry.ProjSpace.instIsProperProdOverπ
  AlgebraicGeometry.ChowDatumProj.hp_isoU
  AlgebraicGeometry.ProjSpace.isProper_π
  AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
  ProjSpaceCech.GradedModule.H.module
  ProjSpaceCech.GradedModule.H.addCommGroup
  ProjSpaceCech.GradedModule.sec.instAdd
  ProjSpaceCech.GradedModule.sec.instNeg
  ProjSpaceCech.GradedModule.acg
  ProjSpaceCech.GradedModule.Frac.setoid
  ProjSpaceCech.GradedModule.modR
  ProjSpaceCech.GradedModule.sec.instModule
  ProjSpaceCech.GradedModule.sec.instAddCommGroup
  ProjSpaceCech.GradedModule.sec.instZero
  ProjSpaceCech.GradedModule.Presentation.fJ
  ProjSpaceCech.GradedModule.sec.instSMul
  ProjSpaceCech.Twist.H.module
  ProjSpaceCech.Idx.instFintype
  ProjSpaceCech.Twist.H.addCommGroup
attribute [-instance]
  ProjSpaceCech.Idx.instDecidableEq
  ProjSpaceCech.Twist.Mon.instDecidableEq
  ProjSpaceCech.Twist.cochain.instAddCommGroup
  ProjSpaceCech.Twist.cochain.instModule
  AlgebraicGeometry.FGSubalgebra.tensorStage_directedSystem
  AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
  AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
  AlgebraicCurve.CurveModel.locallyOfFiniteType_gluedToBase
  AlgebraicCurve.CurveModel.isFractionRing_overlap
  AlgebraicCurve.CurveModel.isLocallyNoetherian_glued
  AlgebraicCurve.CurveModel.jacobsonSpace_glued
  AlgebraicCurve.CurveModel.isOpenImmersion_ι₀
  AlgebraicCurve.CurveModel.isIntegral_glued
  AlgebraicCurve.CurveModel.quasiSeparated_gluedToBase
  AlgebraicCurve.CurveModel.compactSpace_glued
  AlgebraicCurve.CurveModel.isIntegral_adjoin_chartRing
  AlgebraicCurve.CurveModel.isFractionRing_overlap_functionField
  AlgebraicCurve.CurveModel.isProper_gluedToBase
  AlgebraicCurve.CurveModel.isOpenImmersion_ιU
  AlgebraicCurve.CurveModel.isOpenImmersion_f₀
  AlgebraicCurve.CurveModel.isOpenImmersion_fInf
  AlgebraicCurve.CurveModel.isOpenImmersion_ιInf
  AlgebraicCurve.CurveModel.algebra_overlap_functionField
  AlgebraicCurve.CurveModel.quasiCompact_gluedToBase
  AlgebraicCurve.CurveModel.algebraAdjoin
  AlgebraicCurve.CurveModel.isDedekindDomain_chartRing
  AlgebraicCurve.CurveModel.isIntegralClosure
  AlgebraicCurve.CurveModel.finite_chartRing
  AlgebraicCurve.CurveModel.centre_isPrime
  AlgebraicCurve.CurveModel.isFractionRing_chartRing
  AlgebraicCurve.CurveModel.finiteType_chartRing
  AlgebraicCurve.CurveModel.isNoetherianRing_chartRing
  AlgebraicCurve.CurveModel.isScalarTower_base_adjoin
  AlgebraicCurve.CurveModel.isScalarTower_adjoin
  AlgebraicCurve.CurveModel.chartRing_finitePresentation
attribute [-simp]
  GoodReductionJacobian.RelativePic0Designation.mk.sizeOf_spec
  GoodReductionJacobian.AvatarSchemeBridge.mk.injEq
  GoodReductionJacobian.AvatarSchemeBridge.mk.sizeOf_spec
  GoodReductionJacobian.RelativePic0Designation.mk.injEq
  GoodReductionJacobian.schemeHomOverComp_coe
  NeronModelInfra.schemeHomOverEquivOverHom_apply
  GoodReductionJacobian.RelativeGroupLaw.mk.sizeOf_spec
  NeronModelInfra.schemeHomOverEquivOverHom_symm_apply
  NeronModelInfra.overHomToSchemeHomOver_coe
  GoodReductionJacobian.RelativeGroupLaw.mk.injEq
  NeronModelInfra.overHomToSchemeHomOver_schemeHomOverToOverHom
  NeronModelInfra.schemeHomOverToOverHom_left
  NeronModelInfra.schemeHomOverToOverHom_overHomToSchemeHomOver
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.sizeOf_spec
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
  AlgebraicCurve.CurveModel.mk.injEq
  AlgebraicCurve.CurveModel.mk.sizeOf_spec
  AlgebraicCurve.Place.mk.injEq
  AlgebraicCurve.Divisor.degree_single
  AlgebraicCurve.Divisor.smul_single
  AlgebraicCurve.Place.smul_toValuationSubring
  AlgebraicCurve.Place.heightOneSpectrum_asIdeal
  AlgebraicCurve.Place.coe_algebraMap
  AlgebraicCurve.Place.ord_one
  AlgebraicCurve.Place.coe_smulRingEquiv_apply
  AlgebraicCurve.Pic0.coe_degZeroSMulHom
  AlgebraicCurve.Place.deg_smul
  AlgebraicCurve.Pic0.mk_zero
  AlgebraicCurve.Place.mk.sizeOf_spec
  AlgebraicCurve.Divisor.degree_smul
  AlgebraicCurve.Pic0.mk_add
  AlgebraicCurve.Place.ord_zero
  AlgebraicCurve.Place.ofHeightOneSpectrum_toValuationSubring
  AlgebraicCurve.mulAdele_apply
attribute [-simp]
  AlgebraicCurve.residuePairing_apply_coe
  AlgebraicCurve.mem_adeleBdd
  AlgebraicCurve.weilSmul_one
  AlgebraicCurve.diagonalHom_apply
  AlgebraicCurve.weilSmul_apply
  AlgebraicCurve.adeleSpaceMul_coe
  AlgebraicCurve.mulAdele_one
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U1
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.injEq
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U0
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.mk.injEq
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.pullback_U1
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.pullback_U0
  TwoChartCech.Sections.mk.injEq
  TwoChartCech.Cover.mk.injEq
  TwoChartCech.GrothendieckComplex.mk.injEq
  TwoChartCech.Sections.mk.sizeOf_spec
  TwoChartCech.Cover.mk.sizeOf_spec
  TwoChartCech.Cover.lineBundle_r0_apply
  TwoChartCech.GrothendieckComplex.mk.sizeOf_spec
  TwoChartCech.Cover.lineBundle_r1_apply
  CoherentBaseChange.TwoTermComplex.mk.sizeOf_spec
  CoherentBaseChange.TwoTermComplex.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
  AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
  CategoryTheory.Functor.OverTotal.ofFibre_fst
  CategoryTheory.Functor.overTotal_map_fst
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_J
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYoneda_toGlued_uliftYonedaGluedToSheaf
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t'
attribute [-simp]
  uliftYoneda_toGlued_uliftYonedaGluedToSheaf_assoc
attribute [-simp]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_toGlued
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_openCover_map
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_comp
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_V
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_U
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_f
attribute [-simp]
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_P
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_toBase
  AlgebraicGeometry.RelPicard.rigSection_snd
  AlgebraicGeometry.RelPicard.RigidifiedLineBundle.ofInvertible_L
  AlgebraicGeometry.RelPicard.rigSection_snd_assoc
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
  GoodReductionJacobian.relativeGroupLawOfGrpObj_inv
  GoodReductionJacobian.relativeGroupLawOfGrpObj_mul
  GoodReductionJacobian.overHomEquivSchemeHomOver_apply_coe
  GoodReductionJacobian.relativeGroupLawOfGrpObj_one
  GoodReductionJacobian.overHomEquivSchemeHomOver_symm_apply_left
  PresheafOfModules.freeεIso_hom_app
  PresheafOfModules.freeμIso_hom_app
  AlgebraicCurve.coe_cechH0Equiv_apply
  AlgebraicCurve.cechH1ToH1_mk
  AlgebraicCurve.lSpaceOn_univ
  AlgebraicCurve.lSpaceOn_empty
  AlgebraicCurve.Place.congrEquiv_symm_apply
  AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
  AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
  AlgebraicCurve.Place.congrEquiv_apply
  AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
  AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
  AlgebraicCurve.Divisor.mapRestrict_single
  AlgebraicCurve.Divisor.pushforward_single
  AlgebraicCurve.Place.coe_restrictInclusion
  AlgebraicCurve.Place.mem_fiber
  AlgebraicCurve.Place.restrict_toValuationSubring
  AlgebraicCurve.Divisor.degree_pushforward
  AlgebraicCurve.Place.restrictResidueMap_residue
  AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
  AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
  AlgebraicCurve.Place.placeOfPrime_toValuationSubring
  AlgebraicCurve.Place.mem_fiberOver
  AlgebraicCurve.Place.fiberEquiv_symm_apply
  AlgebraicCurve.Place.fiberEquiv_apply
  AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
attribute [-simp]
  AlgebraicCurve.Divisor.degree_pushforwardAlong
  AlgebraicCurve.Pic0.coe_degZeroCorrespondence
  AlgebraicCurve.Place.mem_fiberAlong
  AlgebraicCurve.SemilinearAut.toRingAut_inv
  AlgebraicCurve.SemilinearAut.smul_def
  AlgebraicCurve.SemilinearAut.smul_single
  AlgebraicCurve.SemilinearAut.smul_toValuationSubring
  AlgebraicCurve.SemilinearAut.baseAut_inv
  AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_one
  AlgebraicCurve.SemilinearAut.deg_smul
  AlgebraicCurve.SemilinearAut.degree_smul
  AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
  AlgebraicCurve.SemilinearAut.baseAut_mul
  AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
  AlgebraicCurve.SemilinearAut.baseAut_one
  AlgebraicCurve.SemilinearAut.ofAlgAut_smul
  AlgebraicCurve.SemilinearAut.coe_torsion_smul
  AlgebraicCurve.SemilinearAut.toRingAut_mul
attribute [-simp]
  AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeInfty
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_some
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeOfPoint
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_none
  AlgebraicCurve.Divisor.evalFun_zero
  AlgebraicCurve.Place.evalAt_one
  AlgebraicCurve.Place.differentialCoeff_zero
  AlgebraicCurve.Place.differentialCoeff_dCoord
  AlgebraicCurve.TranscendenceTower.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
  AlgebraicCurve.TranscendenceTower.mk.injEq
  AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec
  AlgebraicCurve.PoleDivisorPackage.mk.injEq
  AlgebraicGeometry.RelPicard.thetaBundle_def
attribute [-simp]
  AlgebraicGeometry.RelPicard.picardBundle_def
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_ofRelEffDivisor
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_I
  AlgebraicGeometry.mapOnProdOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.mk.sizeOf_spec
  AlgebraicGeometry.RelEffCartierDiv.mk.injEq
  AlgebraicGeometry.mapOnProdOver_snd
  AlgebraicGeometry.mapOnProdOver_fst
  AlgebraicGeometry.mapOnProdOver_snd_assoc
  AlgebraicGeometry.mapOnProdOver_id
  AlgebraicCurve.RelEffDivisor.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_fst
  AlgebraicCurve.mapOnProd_fst_assoc
  AlgebraicCurve.mapOnProd_snd
  AlgebraicCurve.UnivDivisorPack.mk.injEq
  AlgebraicCurve.RelEffDivisor.mk.injEq
  AlgebraicCurve.UnivDivisorPack.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_snd_assoc
  AlgebraicGeometry.Scheme.Modules.exteriorPower_obj
  PresheafOfModules.exteriorPower_map_ιMulti
  PresheafOfModules.ExteriorPower.appₗ_apply
  AlgebraicGeometry.prodKerGraph_one
  AlgebraicGeometry.fibrePowOver.proj_comp
  AlgebraicGeometry.prodKerGraph_zero
  AlgebraicGeometry.RelEffCartierDiv.empty_I
  AlgebraicGeometry.fibrePowOver.proj_comp_assoc
  AlgebraicGeometry.graphOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
  AlgebraicGeometry.graphOver_fst
  AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
  AlgebraicGeometry.graphOver_snd
  AlgebraicGeometry.graphOver_snd_assoc
  AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
  AlgebraicCurve.SymmetricPowerPackage.mk.injEq
  AlgebraicGeometry.FGSubalgebra.cocone_ι_app_apply
  AlgebraicGeometry.RelPicard.fst_toProdSpec
  AlgebraicGeometry.RelPicard.toProdSpec_fst_assoc
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_cons
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_nil
attribute [-simp]
  AlgebraicGeometry.RelPicard.fst_toProdSpec_assoc
  AlgebraicGeometry.RelPicard.toProdSpec_fst
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.sizeOf_spec
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.injEq
  AlgebraicCurve.adeleSingle_coe
  AlgebraicCurve.kaehlerResidueTermKFam_apply
  AlgebraicCurve.Place.LocalResidueData.mk.injEq
  AlgebraicCurve.Place.LocalResidueData.mk.sizeOf_spec
  AlgebraicCurve.Place.kw_ffgc_adicCompletionComapIntegers_coe
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.sizeOf_spec
  AlgebraicCurve.Place.mem_simplePoleSubmodule
  AlgebraicCurve.Place.coe_uniformizerSubring
  ModularCurve.Lg37.Lg37CompletionSection.mk.injEq
  AlgebraicCurve.Place.CoefficientFieldSection.mk.injEq
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.injEq
  ModularCurve.Lg37.Lg37CompletionSection.mk.sizeOf_spec
  AlgebraicCurve.Place.CoefficientFieldSection.mk.sizeOf_spec
  AlgebraicCurve.Place.poleSubmodule_one
  AlgebraicCurve.Place.mem_poleSubmodule
  AlgebraicGeometry.Scheme.Modules.toUnitSection_ofUnitSection
  AlgebraicGeometry.Scheme.Modules.pullbackSection_def
  AlgebraicGeometry.Scheme.Modules.ofUnitSection_toUnitSection
  PresheafOfModules.InternalHom.IsSheafAux.appAt_toPresheafHom
attribute [-simp]
  SheafOfModules.ihomSectionsEquivFamily_unit
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_apply
  SheafOfModules.ihomEval_unit_app
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_right
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_left
  AlgebraicGeometry.Scheme.Modules.homOfFamily_app_apply
  SheafOfModules.unit_ihomSectionsEquivFamily
  AlgebraicGeometry.Scheme.Modules.familyOfHom_app
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_hom_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_inv_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomOfFamily_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_symm_apply
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_right
  AlgebraicGeometry.Scheme.Modules.map_unitSection
  AlgebraicGeometry.Scheme.Modules.tensorSectionsBilin_apply
  AlgebraicGeometry.Scheme.Modules.tensorPowSection_zero
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_left
  AlgebraicGeometry.Scheme.Modules.tensorPow_zero
  AlgebraicGeometry.Scheme.Modules.tensorPow_succ
  AlgebraicGeometry.Scheme.OrderedAffineCover.mk.injEq
  AlgebraicGeometry.OModulePresheaf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCover.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.mk.injEq
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_neg
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_zero
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_sub
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_add
  AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
  AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U
  AlgebraicGeometry.OModulePresheaf.Hom.mk.injEq
  AlgebraicGeometry.OModulePresheaf.Hom.id_app
  AlgebraicGeometry.OModulePresheaf.AffHom.appSections_apply
  AlgebraicGeometry.OModulePresheaf.AffHom.comp_app
  AlgebraicGeometry.OModulePresheaf.AffSES.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.AffHom.kerMap_coe
  AlgebraicGeometry.OModulePresheaf.AffHom.id_app
  AlgebraicGeometry.OModulePresheaf.Hom.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.Hom.toAffHom_app
attribute [-simp]
  AlgebraicGeometry.OModulePresheaf.SES.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.AffHom.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.Hom.comp_app
  AlgebraicGeometry.OModulePresheaf.SES.mk.injEq
  AlgebraicGeometry.OModulePresheaf.AffHom.mk.injEq
  AlgebraicGeometry.OModulePresheaf.Hom.appSections_apply
  AlgebraicGeometry.OModulePresheaf.AffSES.mk.injEq
  AlgebraicGeometry.OModulePresheaf.prod_obj
  AlgebraicGeometry.OModulePresheaf.restrOpen_obj
  AlgebraicGeometry.OModulePresheaf.DevissageStep.mk.injEq
  AlgebraicGeometry.OModulePresheaf.pushforward_obj
  AlgebraicGeometry.OModulePresheaf.im_obj
  AlgebraicGeometry.OModulePresheaf.pow_obj
  AlgebraicGeometry.OModulePresheaf.fstHom_app
  AlgebraicGeometry.OModulePresheaf.ker_obj
  AlgebraicGeometry.OModulePresheaf.coker_obj
  AlgebraicGeometry.OModulePresheaf.DevissageStep.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCover.preimage_U
  AlgebraicGeometry.OModulePresheaf.sndHom_app
  AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
  DoubleComplex.Bounded.mk.injEq
  DoubleComplex.Bounded.mk.sizeOf_spec
  DoubleComplex.Convergence.mk.injEq
  DoubleComplex.Convergence.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.injEq
  AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatumProj.mk.injEq
  AlgebraicGeometry.ChowDatum.mk.injEq
  ProjSpaceCech.GradedModule.mk.injEq
  ProjSpaceCech.GradedModule.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Presentation.mk.injEq
  ProjSpaceCech.GradedModule.Frac.mk.injEq
  ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.shift_toLinearMap
  ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.mk.injEq
  TwoChartCech.Mumford.dK_apply
attribute [-simp]
  TwoChartCech.Mumford.ι0_apply
  TwoChartCech.Mumford.ι1_apply
  TwoChartCech.KerCoprod.dK_apply
  TwoChartCech.KerCoprod.ι1_apply
  TwoChartCech.KerCoprod.ι0_apply
  AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
  AlgebraicGeometry.RelPicard.algEquivZeroGroupCut_toSubPicCondition
  AlgebraicGeometry.RelPicard.LFP.stageHom_val
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_hom_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_inv_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.restrict_P
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp
  AlgebraicGeometry.RelEffCartierDiv.functor_map_fst
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_pullbackAlong
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_symm_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp_assoc
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top
  AlgebraicGeometry.RelEffCartierDiv.mem_supportedIn_iff
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top_eq
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
  CoherentBaseChange.FibreH0Family.mk.sizeOf_spec
  CoherentBaseChange.FibreH0Family.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.sizeOf_spec
  AlgebraicCurve.CurveModel.coe_gInf
  AlgebraicCurve.CurveModel.coe_tInvChart
  AlgebraicCurve.CurveModel.ιInf_gluedToBase_assoc
  AlgebraicCurve.CurveModel.ιInf_gluedToBase
  AlgebraicCurve.CurveModel.primeOfι₀_asIdeal
  AlgebraicCurve.CurveModel.coe_tChart
  AlgebraicCurve.CurveModel.ι₀_gluedToBase_assoc
  AlgebraicCurve.CurveModel.primeOfιInf_asIdeal
attribute [-simp]
  AlgebraicCurve.CurveModel.ι₀_gluedToBase
  AlgebraicCurve.CurveModel.coe_tma
  AlgebraicCurve.CurveModel.coe_primeEquivChartPlaces
universe u
noncomputable section
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.CategoryTheory.CartesianMonoidalCategory
open _root_.AlgebraicGeometry.RelPicard
open _root_.NeronModelInfra
namespace P2mCubeAssembly
section Slices
variable {k : Type u} [Field k]
local notation "Sk" => Spec (CommRingCat.of k)

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.ThreeSlices
attribute [-instance]
  AlgebraicGeometry.SmoothOfRelativeDimension.fiberToSpecResidueField
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_snd
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_fst
  AlgebraicGeometry.SmoothOfRelativeDimension.smooth_one
  AlgebraicGeometry.SmoothProperCurve.isIntegral_pullback_Spec_field
  AlgebraicGeometry.IsProper.fiberToSpecResidueField
  AlgebraicCurve.CurveModel.isProper
  AlgebraicCurve.CurveModel.isIntegral
  AlgebraicCurve.CurveModel.smooth
  AlgebraicCurve.Place.instIsScalarTowerSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Divisor.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instSMulAlgEquiv
  AlgebraicCurve.Place.instIsPrincipalIdealRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instIsDiscreteValuationRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Pic0.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instAlgebraSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instMulActionAlgEquiv
  AlgebraicCurve.Pic0.instSMulAlgEquiv
  TwoChartCech.Sections.M0_moduleA
  TwoChartCech.Sections.M1_module
  TwoChartCech.Cover.A01_algebra
  TwoChartCech.Cover.A0_algebra
  TwoChartCech.Cover.A1_commRing
  TwoChartCech.Cover.A1_algebra
  TwoChartCech.Sections.M01_module
  TwoChartCech.Sections.M0_addCommGroup
  TwoChartCech.Sections.M0_tower
  TwoChartCech.Sections.M01_addCommGroup
  TwoChartCech.Cover.A0_commRing
  TwoChartCech.Sections.M1_tower
  TwoChartCech.Sections.M01_moduleA
  TwoChartCech.Sections.M0_module
  TwoChartCech.Sections.M1_moduleA
  TwoChartCech.Sections.M1_addCommGroup
  TwoChartCech.Cover.A01_commRing
  TwoChartCech.Sections.M01_tower
  CoherentBaseChange.TwoTermComplex.C0_module
  CoherentBaseChange.TwoTermComplex.C0_addCommGroup
  CoherentBaseChange.TwoTermComplex.C1_module
  CoherentBaseChange.TwoTermComplex.C1_addCommGroup
attribute [-instance]
  CoherentBaseChange.TwoTermComplex.C0_free
  CoherentBaseChange.TwoTermComplex.C1_finite
  CoherentBaseChange.TwoTermComplex.C0_finite
  CoherentBaseChange.TwoTermComplex.C1_free
  AlgebraicCurve.IsCurveOver.instNontrivialKaehler
  AlgebraicCurve.IsCurveOver.instFreeKaehler
  AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
  AlgebraicCurve.IsCurveOver.instFiniteResidue
attribute [-instance]
  instIsLocallyInjectiveFunUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsLocallySurjectiveUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsOpenImmersionToGlued
attribute [-instance]
  instIsIsoSheafZariskiTopologyTypeUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.RelPicard.isOpenImmersion_toGlued
  AlgebraicGeometry.Scheme.Modules.preservesBinaryProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback_monoidal
  AlgebraicGeometry.Scheme.Modules.sheafify_isLocalization'
  AlgebraicGeometry.Scheme.Modules.preservesTerminal_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback₀_monoidal
  AlgebraicGeometry.Scheme.Modules.preservesFiniteProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.sheafifyPullback_lifting
  PresheafOfModules.PullbackMonoidal.pullback_monoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ
  PresheafOfModules.pushforward_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_η
  PresheafOfModules.free_monoidal
  PresheafOfModules.restrictScalars_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ_gS
  PresheafOfModules.pullback_oplaxMonoidal
attribute [-instance]
  instPreservesColimitsOfSizeCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierPb
attribute [-instance]
  PresheafOfModules.pullback_monoidal'
  AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
  AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
  AlgebraicCurve.Place.instIsPrimeCenter
  AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
  instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
  AlgebraicCurve.Pic0.instModuleZModTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instSMulTorsion
  AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
  AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
  AlgebraicCurve.RationalFunctionField.instNontrivialInftyValueGroup
  PresheafOfModules.ExteriorPower.instModulePresheafAb
  AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
  AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
  AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
  AlgebraicGeometry.isClosedImmersion_graphOver
  AlgebraicGeometry.FGSubalgebra.instIsDirectedLe
attribute [-instance]
  instQuasiSeparatedSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsCofilteredOpposite
  AlgebraicGeometry.FGSubalgebra.instIsAffineObjOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instNonempty
  AlgebraicGeometry.FGSubalgebra.instNonemptySubtypeLeSubalgebraValFG
attribute [-instance]
  instCompactSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsDirectedSubtypeLeSubalgebraValFG
  AlgebraicGeometry.FGSubalgebra.instIsAffineHomMapOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instIsFiltered
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instNeg
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulInt
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAddCommGroup
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAdd
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSub
attribute [-instance]
  instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
  AlgebraicCurve.instHasLocalResidue_of_hasCanonicalLocalResidueK
  AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
  AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
  ModularCurve.KwF4gRRTate.instAlgebraKAdicCompletionIntegers
  AlgebraicCurve.Place.kw_ffgc_continuousSMul_adicCompletionComap
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersCompletionCompletion
attribute [-instance]
  instLiesOverSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegersCompletionIdealAsIdeal
attribute [-instance]
  AlgebraicCurve.instHasCanonicalLocalResidueK
  AlgebraicCurve.Place.instAlgebra_restrictResidueField
  AlgebraicCurve.Place.instIsScalarTower_restrictResidueField
  AlgebraicCurve.instHasLocalResidue
  AlgebraicCurve.HasSeparableResidue.of_perfectField_of_isCurveOver
  AlgebraicCurve.HasSeparableResidue.of_perfectField
  AlgebraicCurve.Place.instIsLocalHom_restrictSubringHom
  AlgebraicCurve.instHasCanonicalLocalResidueKStar
  ModularCurve.KwNo6Pin.isLocalRing_completion
  SheafOfModules.isIso_ihomModelToIhom
  AlgebraicGeometry.OModulePresheaf.isScalarTower
  AlgebraicGeometry.Scheme.OrderedAffineCover.instLinearOrder
  AlgebraicGeometry.OModulePresheaf.module
  AlgebraicGeometry.Scheme.OrderedAffineCover.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCover.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.addCommGroup
  AlgebraicGeometry.Scheme.OrderedAffineCover.instDecidableEqIdx
  AlgebraicGeometry.OModulePresheaf.moduleSections
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.instSubsingletonObjZero
attribute [-instance]
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
  AlgebraicGeometry.OModulePresheaf.Leray.biC_module
  DoubleComplex.instModuleE₂I
  DoubleComplex.Bounded.modR
  DoubleComplex.instModuleE₂II
  DoubleComplex.instAddCommGroupE₂II
  DoubleComplex.Bounded.abGrp
  DoubleComplex.instAddCommGroupE₂I
  AlgebraicGeometry.ChowDatum.hι_closed
  AlgebraicGeometry.ChowDatumProj.hιN_closed
  AlgebraicGeometry.ChowDatumProj.hp_proper
  AlgebraicGeometry.ChowDatum.hp_isoU
  AlgebraicGeometry.ChowDatum.hp_proper
  AlgebraicGeometry.ProjSpace.algebraAway
  AlgebraicGeometry.ProjSpace.instIsProperProdOverπ
  AlgebraicGeometry.ChowDatumProj.hp_isoU
  AlgebraicGeometry.ProjSpace.isProper_π
  AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
  ProjSpaceCech.GradedModule.H.module
  ProjSpaceCech.GradedModule.H.addCommGroup
  ProjSpaceCech.GradedModule.sec.instAdd
  ProjSpaceCech.GradedModule.sec.instNeg
  ProjSpaceCech.GradedModule.acg
  ProjSpaceCech.GradedModule.Frac.setoid
  ProjSpaceCech.GradedModule.modR
  ProjSpaceCech.GradedModule.sec.instModule
  ProjSpaceCech.GradedModule.sec.instAddCommGroup
  ProjSpaceCech.GradedModule.sec.instZero
  ProjSpaceCech.GradedModule.Presentation.fJ
  ProjSpaceCech.GradedModule.sec.instSMul
  ProjSpaceCech.Twist.H.module
  ProjSpaceCech.Idx.instFintype
  ProjSpaceCech.Twist.H.addCommGroup
attribute [-instance]
  ProjSpaceCech.Idx.instDecidableEq
  ProjSpaceCech.Twist.Mon.instDecidableEq
  ProjSpaceCech.Twist.cochain.instAddCommGroup
  ProjSpaceCech.Twist.cochain.instModule
  AlgebraicGeometry.FGSubalgebra.tensorStage_directedSystem
  AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
  AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
  AlgebraicCurve.CurveModel.locallyOfFiniteType_gluedToBase
  AlgebraicCurve.CurveModel.isFractionRing_overlap
  AlgebraicCurve.CurveModel.isLocallyNoetherian_glued
  AlgebraicCurve.CurveModel.jacobsonSpace_glued
  AlgebraicCurve.CurveModel.isOpenImmersion_ι₀
  AlgebraicCurve.CurveModel.isIntegral_glued
  AlgebraicCurve.CurveModel.quasiSeparated_gluedToBase
  AlgebraicCurve.CurveModel.compactSpace_glued
  AlgebraicCurve.CurveModel.isIntegral_adjoin_chartRing
  AlgebraicCurve.CurveModel.isFractionRing_overlap_functionField
  AlgebraicCurve.CurveModel.isProper_gluedToBase
  AlgebraicCurve.CurveModel.isOpenImmersion_ιU
  AlgebraicCurve.CurveModel.isOpenImmersion_f₀
  AlgebraicCurve.CurveModel.isOpenImmersion_fInf
  AlgebraicCurve.CurveModel.isOpenImmersion_ιInf
  AlgebraicCurve.CurveModel.algebra_overlap_functionField
  AlgebraicCurve.CurveModel.quasiCompact_gluedToBase
  AlgebraicCurve.CurveModel.algebraAdjoin
  AlgebraicCurve.CurveModel.isDedekindDomain_chartRing
  AlgebraicCurve.CurveModel.isIntegralClosure
  AlgebraicCurve.CurveModel.finite_chartRing
  AlgebraicCurve.CurveModel.centre_isPrime
  AlgebraicCurve.CurveModel.isFractionRing_chartRing
  AlgebraicCurve.CurveModel.finiteType_chartRing
  AlgebraicCurve.CurveModel.isNoetherianRing_chartRing
  AlgebraicCurve.CurveModel.isScalarTower_base_adjoin
  AlgebraicCurve.CurveModel.isScalarTower_adjoin
  AlgebraicCurve.CurveModel.chartRing_finitePresentation
attribute [-simp]
  GoodReductionJacobian.RelativePic0Designation.mk.sizeOf_spec
  GoodReductionJacobian.AvatarSchemeBridge.mk.injEq
  GoodReductionJacobian.AvatarSchemeBridge.mk.sizeOf_spec
  GoodReductionJacobian.RelativePic0Designation.mk.injEq
  GoodReductionJacobian.schemeHomOverComp_coe
  NeronModelInfra.schemeHomOverEquivOverHom_apply
  GoodReductionJacobian.RelativeGroupLaw.mk.sizeOf_spec
  NeronModelInfra.schemeHomOverEquivOverHom_symm_apply
  NeronModelInfra.overHomToSchemeHomOver_coe
  GoodReductionJacobian.RelativeGroupLaw.mk.injEq
  NeronModelInfra.overHomToSchemeHomOver_schemeHomOverToOverHom
  NeronModelInfra.schemeHomOverToOverHom_left
  NeronModelInfra.schemeHomOverToOverHom_overHomToSchemeHomOver
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.sizeOf_spec
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
  AlgebraicCurve.CurveModel.mk.injEq
  AlgebraicCurve.CurveModel.mk.sizeOf_spec
  AlgebraicCurve.Place.mk.injEq
  AlgebraicCurve.Divisor.degree_single
  AlgebraicCurve.Divisor.smul_single
  AlgebraicCurve.Place.smul_toValuationSubring
  AlgebraicCurve.Place.heightOneSpectrum_asIdeal
  AlgebraicCurve.Place.coe_algebraMap
  AlgebraicCurve.Place.ord_one
  AlgebraicCurve.Place.coe_smulRingEquiv_apply
  AlgebraicCurve.Pic0.coe_degZeroSMulHom
  AlgebraicCurve.Place.deg_smul
  AlgebraicCurve.Pic0.mk_zero
  AlgebraicCurve.Place.mk.sizeOf_spec
  AlgebraicCurve.Divisor.degree_smul
  AlgebraicCurve.Pic0.mk_add
  AlgebraicCurve.Place.ord_zero
  AlgebraicCurve.Place.ofHeightOneSpectrum_toValuationSubring
  AlgebraicCurve.mulAdele_apply
attribute [-simp]
  AlgebraicCurve.residuePairing_apply_coe
  AlgebraicCurve.mem_adeleBdd
  AlgebraicCurve.weilSmul_one
  AlgebraicCurve.diagonalHom_apply
  AlgebraicCurve.weilSmul_apply
  AlgebraicCurve.adeleSpaceMul_coe
  AlgebraicCurve.mulAdele_one
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U1
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.injEq
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U0
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.mk.injEq
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.pullback_U1
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.pullback_U0
  TwoChartCech.Sections.mk.injEq
  TwoChartCech.Cover.mk.injEq
  TwoChartCech.GrothendieckComplex.mk.injEq
  TwoChartCech.Sections.mk.sizeOf_spec
  TwoChartCech.Cover.mk.sizeOf_spec
  TwoChartCech.Cover.lineBundle_r0_apply
  TwoChartCech.GrothendieckComplex.mk.sizeOf_spec
  TwoChartCech.Cover.lineBundle_r1_apply
  CoherentBaseChange.TwoTermComplex.mk.sizeOf_spec
  CoherentBaseChange.TwoTermComplex.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
  AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
  CategoryTheory.Functor.OverTotal.ofFibre_fst
  CategoryTheory.Functor.overTotal_map_fst
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_J
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYoneda_toGlued_uliftYonedaGluedToSheaf
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t'
attribute [-simp]
  uliftYoneda_toGlued_uliftYonedaGluedToSheaf_assoc
attribute [-simp]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_toGlued
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_openCover_map
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_comp
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_V
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_U
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_f
attribute [-simp]
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_P
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_toBase
  AlgebraicGeometry.RelPicard.rigSection_snd
  AlgebraicGeometry.RelPicard.RigidifiedLineBundle.ofInvertible_L
  AlgebraicGeometry.RelPicard.rigSection_snd_assoc
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
  GoodReductionJacobian.relativeGroupLawOfGrpObj_inv
  GoodReductionJacobian.relativeGroupLawOfGrpObj_mul
  GoodReductionJacobian.overHomEquivSchemeHomOver_apply_coe
  GoodReductionJacobian.relativeGroupLawOfGrpObj_one
  GoodReductionJacobian.overHomEquivSchemeHomOver_symm_apply_left
  PresheafOfModules.freeεIso_hom_app
  PresheafOfModules.freeμIso_hom_app
  AlgebraicCurve.coe_cechH0Equiv_apply
  AlgebraicCurve.cechH1ToH1_mk
  AlgebraicCurve.lSpaceOn_univ
  AlgebraicCurve.lSpaceOn_empty
  AlgebraicCurve.Place.congrEquiv_symm_apply
  AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
  AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
  AlgebraicCurve.Place.congrEquiv_apply
  AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
  AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
  AlgebraicCurve.Divisor.mapRestrict_single
  AlgebraicCurve.Divisor.pushforward_single
  AlgebraicCurve.Place.coe_restrictInclusion
  AlgebraicCurve.Place.mem_fiber
  AlgebraicCurve.Place.restrict_toValuationSubring
  AlgebraicCurve.Divisor.degree_pushforward
  AlgebraicCurve.Place.restrictResidueMap_residue
  AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
  AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
  AlgebraicCurve.Place.placeOfPrime_toValuationSubring
  AlgebraicCurve.Place.mem_fiberOver
  AlgebraicCurve.Place.fiberEquiv_symm_apply
  AlgebraicCurve.Place.fiberEquiv_apply
  AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
attribute [-simp]
  AlgebraicCurve.Divisor.degree_pushforwardAlong
  AlgebraicCurve.Pic0.coe_degZeroCorrespondence
  AlgebraicCurve.Place.mem_fiberAlong
  AlgebraicCurve.SemilinearAut.toRingAut_inv
  AlgebraicCurve.SemilinearAut.smul_def
  AlgebraicCurve.SemilinearAut.smul_single
  AlgebraicCurve.SemilinearAut.smul_toValuationSubring
  AlgebraicCurve.SemilinearAut.baseAut_inv
  AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_one
  AlgebraicCurve.SemilinearAut.deg_smul
  AlgebraicCurve.SemilinearAut.degree_smul
  AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
  AlgebraicCurve.SemilinearAut.baseAut_mul
  AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
  AlgebraicCurve.SemilinearAut.baseAut_one
  AlgebraicCurve.SemilinearAut.ofAlgAut_smul
  AlgebraicCurve.SemilinearAut.coe_torsion_smul
  AlgebraicCurve.SemilinearAut.toRingAut_mul
attribute [-simp]
  AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeInfty
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_some
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeOfPoint
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_none
  AlgebraicCurve.Divisor.evalFun_zero
  AlgebraicCurve.Place.evalAt_one
  AlgebraicCurve.Place.differentialCoeff_zero
  AlgebraicCurve.Place.differentialCoeff_dCoord
  AlgebraicCurve.TranscendenceTower.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
  AlgebraicCurve.TranscendenceTower.mk.injEq
  AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec
  AlgebraicCurve.PoleDivisorPackage.mk.injEq
  AlgebraicGeometry.RelPicard.thetaBundle_def
attribute [-simp]
  AlgebraicGeometry.RelPicard.picardBundle_def
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_ofRelEffDivisor
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_I
  AlgebraicGeometry.mapOnProdOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.mk.sizeOf_spec
  AlgebraicGeometry.RelEffCartierDiv.mk.injEq
  AlgebraicGeometry.mapOnProdOver_snd
  AlgebraicGeometry.mapOnProdOver_fst
  AlgebraicGeometry.mapOnProdOver_snd_assoc
  AlgebraicGeometry.mapOnProdOver_id
  AlgebraicCurve.RelEffDivisor.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_fst
  AlgebraicCurve.mapOnProd_fst_assoc
  AlgebraicCurve.mapOnProd_snd
  AlgebraicCurve.UnivDivisorPack.mk.injEq
  AlgebraicCurve.RelEffDivisor.mk.injEq
  AlgebraicCurve.UnivDivisorPack.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_snd_assoc
  AlgebraicGeometry.Scheme.Modules.exteriorPower_obj
  PresheafOfModules.exteriorPower_map_ιMulti
  PresheafOfModules.ExteriorPower.appₗ_apply
  AlgebraicGeometry.prodKerGraph_one
  AlgebraicGeometry.fibrePowOver.proj_comp
  AlgebraicGeometry.prodKerGraph_zero
  AlgebraicGeometry.RelEffCartierDiv.empty_I
  AlgebraicGeometry.fibrePowOver.proj_comp_assoc
  AlgebraicGeometry.graphOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
  AlgebraicGeometry.graphOver_fst
  AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
  AlgebraicGeometry.graphOver_snd
  AlgebraicGeometry.graphOver_snd_assoc
  AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
  AlgebraicCurve.SymmetricPowerPackage.mk.injEq
  AlgebraicGeometry.FGSubalgebra.cocone_ι_app_apply
  AlgebraicGeometry.RelPicard.fst_toProdSpec
  AlgebraicGeometry.RelPicard.toProdSpec_fst_assoc
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_cons
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_nil
attribute [-simp]
  AlgebraicGeometry.RelPicard.fst_toProdSpec_assoc
  AlgebraicGeometry.RelPicard.toProdSpec_fst
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.sizeOf_spec
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.injEq
  AlgebraicCurve.adeleSingle_coe
  AlgebraicCurve.kaehlerResidueTermKFam_apply
  AlgebraicCurve.Place.LocalResidueData.mk.injEq
  AlgebraicCurve.Place.LocalResidueData.mk.sizeOf_spec
  AlgebraicCurve.Place.kw_ffgc_adicCompletionComapIntegers_coe
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.sizeOf_spec
  AlgebraicCurve.Place.mem_simplePoleSubmodule
  AlgebraicCurve.Place.coe_uniformizerSubring
  ModularCurve.Lg37.Lg37CompletionSection.mk.injEq
  AlgebraicCurve.Place.CoefficientFieldSection.mk.injEq
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.injEq
  ModularCurve.Lg37.Lg37CompletionSection.mk.sizeOf_spec
  AlgebraicCurve.Place.CoefficientFieldSection.mk.sizeOf_spec
  AlgebraicCurve.Place.poleSubmodule_one
  AlgebraicCurve.Place.mem_poleSubmodule
  AlgebraicGeometry.Scheme.Modules.toUnitSection_ofUnitSection
  AlgebraicGeometry.Scheme.Modules.pullbackSection_def
  AlgebraicGeometry.Scheme.Modules.ofUnitSection_toUnitSection
  PresheafOfModules.InternalHom.IsSheafAux.appAt_toPresheafHom
attribute [-simp]
  SheafOfModules.ihomSectionsEquivFamily_unit
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_apply
  SheafOfModules.ihomEval_unit_app
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_right
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_left
  AlgebraicGeometry.Scheme.Modules.homOfFamily_app_apply
  SheafOfModules.unit_ihomSectionsEquivFamily
  AlgebraicGeometry.Scheme.Modules.familyOfHom_app
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_hom_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_inv_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomOfFamily_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_symm_apply
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_right
  AlgebraicGeometry.Scheme.Modules.map_unitSection
  AlgebraicGeometry.Scheme.Modules.tensorSectionsBilin_apply
  AlgebraicGeometry.Scheme.Modules.tensorPowSection_zero
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_left
  AlgebraicGeometry.Scheme.Modules.tensorPow_zero
  AlgebraicGeometry.Scheme.Modules.tensorPow_succ
  AlgebraicGeometry.Scheme.OrderedAffineCover.mk.injEq
  AlgebraicGeometry.OModulePresheaf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCover.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.mk.injEq
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_neg
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_zero
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_sub
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_add
  AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
  AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U
  AlgebraicGeometry.OModulePresheaf.Hom.mk.injEq
  AlgebraicGeometry.OModulePresheaf.Hom.id_app
  AlgebraicGeometry.OModulePresheaf.AffHom.appSections_apply
  AlgebraicGeometry.OModulePresheaf.AffHom.comp_app
  AlgebraicGeometry.OModulePresheaf.AffSES.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.AffHom.kerMap_coe
  AlgebraicGeometry.OModulePresheaf.AffHom.id_app
  AlgebraicGeometry.OModulePresheaf.Hom.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.Hom.toAffHom_app
attribute [-simp]
  AlgebraicGeometry.OModulePresheaf.SES.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.AffHom.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.Hom.comp_app
  AlgebraicGeometry.OModulePresheaf.SES.mk.injEq
  AlgebraicGeometry.OModulePresheaf.AffHom.mk.injEq
  AlgebraicGeometry.OModulePresheaf.Hom.appSections_apply
  AlgebraicGeometry.OModulePresheaf.AffSES.mk.injEq
  AlgebraicGeometry.OModulePresheaf.prod_obj
  AlgebraicGeometry.OModulePresheaf.restrOpen_obj
  AlgebraicGeometry.OModulePresheaf.DevissageStep.mk.injEq
  AlgebraicGeometry.OModulePresheaf.pushforward_obj
  AlgebraicGeometry.OModulePresheaf.im_obj
  AlgebraicGeometry.OModulePresheaf.pow_obj
  AlgebraicGeometry.OModulePresheaf.fstHom_app
  AlgebraicGeometry.OModulePresheaf.ker_obj
  AlgebraicGeometry.OModulePresheaf.coker_obj
  AlgebraicGeometry.OModulePresheaf.DevissageStep.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCover.preimage_U
  AlgebraicGeometry.OModulePresheaf.sndHom_app
  AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
  DoubleComplex.Bounded.mk.injEq
  DoubleComplex.Bounded.mk.sizeOf_spec
  DoubleComplex.Convergence.mk.injEq
  DoubleComplex.Convergence.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.injEq
  AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatumProj.mk.injEq
  AlgebraicGeometry.ChowDatum.mk.injEq
  ProjSpaceCech.GradedModule.mk.injEq
  ProjSpaceCech.GradedModule.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Presentation.mk.injEq
  ProjSpaceCech.GradedModule.Frac.mk.injEq
  ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.shift_toLinearMap
  ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.mk.injEq
  TwoChartCech.Mumford.dK_apply
attribute [-simp]
  TwoChartCech.Mumford.ι0_apply
  TwoChartCech.Mumford.ι1_apply
  TwoChartCech.KerCoprod.dK_apply
  TwoChartCech.KerCoprod.ι1_apply
  TwoChartCech.KerCoprod.ι0_apply
  AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
  AlgebraicGeometry.RelPicard.algEquivZeroGroupCut_toSubPicCondition
  AlgebraicGeometry.RelPicard.LFP.stageHom_val
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_hom_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_inv_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.restrict_P
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp
  AlgebraicGeometry.RelEffCartierDiv.functor_map_fst
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_pullbackAlong
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_symm_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp_assoc
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top
  AlgebraicGeometry.RelEffCartierDiv.mem_supportedIn_iff
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top_eq
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
  CoherentBaseChange.FibreH0Family.mk.sizeOf_spec
  CoherentBaseChange.FibreH0Family.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.sizeOf_spec
  AlgebraicCurve.CurveModel.coe_gInf
  AlgebraicCurve.CurveModel.coe_tInvChart
  AlgebraicCurve.CurveModel.ιInf_gluedToBase_assoc
  AlgebraicCurve.CurveModel.ιInf_gluedToBase
  AlgebraicCurve.CurveModel.primeOfι₀_asIdeal
  AlgebraicCurve.CurveModel.coe_tChart
  AlgebraicCurve.CurveModel.ι₀_gluedToBase_assoc
  AlgebraicCurve.CurveModel.primeOfιInf_asIdeal
attribute [-simp]
  AlgebraicCurve.CurveModel.ι₀_gluedToBase
  AlgebraicCurve.CurveModel.coe_tma
  AlgebraicCurve.CurveModel.coe_primeEquivChartPlaces
universe u
noncomputable section
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.CategoryTheory.CartesianMonoidalCategory
open _root_.AlgebraicGeometry.RelPicard
open _root_.NeronModelInfra
namespace P2mCubeAssembly
section Slices
variable {k : Type u} [Field k]
local notation "Sk" => Spec (CommRingCat.of k)

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.ThreeSlices
attribute [-instance]
  AlgebraicGeometry.SmoothOfRelativeDimension.fiberToSpecResidueField
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_snd
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_fst
  AlgebraicGeometry.SmoothOfRelativeDimension.smooth_one
  AlgebraicGeometry.SmoothProperCurve.isIntegral_pullback_Spec_field
  AlgebraicGeometry.IsProper.fiberToSpecResidueField
  AlgebraicCurve.CurveModel.isProper
  AlgebraicCurve.CurveModel.isIntegral
  AlgebraicCurve.CurveModel.smooth
  AlgebraicCurve.Place.instIsScalarTowerSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Divisor.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instSMulAlgEquiv
  AlgebraicCurve.Place.instIsPrincipalIdealRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instIsDiscreteValuationRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Pic0.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instAlgebraSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instMulActionAlgEquiv
  AlgebraicCurve.Pic0.instSMulAlgEquiv
  TwoChartCech.Sections.M0_moduleA
  TwoChartCech.Sections.M1_module
  TwoChartCech.Cover.A01_algebra
  TwoChartCech.Cover.A0_algebra
  TwoChartCech.Cover.A1_commRing
  TwoChartCech.Cover.A1_algebra
  TwoChartCech.Sections.M01_module
  TwoChartCech.Sections.M0_addCommGroup
  TwoChartCech.Sections.M0_tower
  TwoChartCech.Sections.M01_addCommGroup
  TwoChartCech.Cover.A0_commRing
  TwoChartCech.Sections.M1_tower
  TwoChartCech.Sections.M01_moduleA
  TwoChartCech.Sections.M0_module
  TwoChartCech.Sections.M1_moduleA
  TwoChartCech.Sections.M1_addCommGroup
  TwoChartCech.Cover.A01_commRing
  TwoChartCech.Sections.M01_tower
  CoherentBaseChange.TwoTermComplex.C0_module
  CoherentBaseChange.TwoTermComplex.C0_addCommGroup
  CoherentBaseChange.TwoTermComplex.C1_module
  CoherentBaseChange.TwoTermComplex.C1_addCommGroup
attribute [-instance]
  CoherentBaseChange.TwoTermComplex.C0_free
  CoherentBaseChange.TwoTermComplex.C1_finite
  CoherentBaseChange.TwoTermComplex.C0_finite
  CoherentBaseChange.TwoTermComplex.C1_free
  AlgebraicCurve.IsCurveOver.instNontrivialKaehler
  AlgebraicCurve.IsCurveOver.instFreeKaehler
  AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
  AlgebraicCurve.IsCurveOver.instFiniteResidue
attribute [-instance]
  instIsLocallyInjectiveFunUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsLocallySurjectiveUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsOpenImmersionToGlued
attribute [-instance]
  instIsIsoSheafZariskiTopologyTypeUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.RelPicard.isOpenImmersion_toGlued
  AlgebraicGeometry.Scheme.Modules.preservesBinaryProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback_monoidal
  AlgebraicGeometry.Scheme.Modules.sheafify_isLocalization'
  AlgebraicGeometry.Scheme.Modules.preservesTerminal_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback₀_monoidal
  AlgebraicGeometry.Scheme.Modules.preservesFiniteProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.sheafifyPullback_lifting
  PresheafOfModules.PullbackMonoidal.pullback_monoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ
  PresheafOfModules.pushforward_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_η
  PresheafOfModules.free_monoidal
  PresheafOfModules.restrictScalars_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ_gS
  PresheafOfModules.pullback_oplaxMonoidal
attribute [-instance]
  instPreservesColimitsOfSizeCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierPb
attribute [-instance]
  PresheafOfModules.pullback_monoidal'
  AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
  AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
  AlgebraicCurve.Place.instIsPrimeCenter
  AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
  instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
  AlgebraicCurve.Pic0.instModuleZModTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instSMulTorsion
  AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
  AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
  AlgebraicCurve.RationalFunctionField.instNontrivialInftyValueGroup
  PresheafOfModules.ExteriorPower.instModulePresheafAb
  AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
  AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
  AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
  AlgebraicGeometry.isClosedImmersion_graphOver
  AlgebraicGeometry.FGSubalgebra.instIsDirectedLe
attribute [-instance]
  instQuasiSeparatedSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsCofilteredOpposite
  AlgebraicGeometry.FGSubalgebra.instIsAffineObjOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instNonempty
  AlgebraicGeometry.FGSubalgebra.instNonemptySubtypeLeSubalgebraValFG
attribute [-instance]
  instCompactSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsDirectedSubtypeLeSubalgebraValFG
  AlgebraicGeometry.FGSubalgebra.instIsAffineHomMapOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instIsFiltered
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instNeg
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulInt
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAddCommGroup
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAdd
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSub
attribute [-instance]
  instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
  AlgebraicCurve.instHasLocalResidue_of_hasCanonicalLocalResidueK
  AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
  AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
  ModularCurve.KwF4gRRTate.instAlgebraKAdicCompletionIntegers
  AlgebraicCurve.Place.kw_ffgc_continuousSMul_adicCompletionComap
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersCompletionCompletion
attribute [-instance]
  instLiesOverSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegersCompletionIdealAsIdeal
attribute [-instance]
  AlgebraicCurve.instHasCanonicalLocalResidueK
  AlgebraicCurve.Place.instAlgebra_restrictResidueField
  AlgebraicCurve.Place.instIsScalarTower_restrictResidueField
  AlgebraicCurve.instHasLocalResidue
  AlgebraicCurve.HasSeparableResidue.of_perfectField_of_isCurveOver
  AlgebraicCurve.HasSeparableResidue.of_perfectField
  AlgebraicCurve.Place.instIsLocalHom_restrictSubringHom
  AlgebraicCurve.instHasCanonicalLocalResidueKStar
  ModularCurve.KwNo6Pin.isLocalRing_completion
  SheafOfModules.isIso_ihomModelToIhom
  AlgebraicGeometry.OModulePresheaf.isScalarTower
  AlgebraicGeometry.Scheme.OrderedAffineCover.instLinearOrder
  AlgebraicGeometry.OModulePresheaf.module
  AlgebraicGeometry.Scheme.OrderedAffineCover.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCover.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.addCommGroup
  AlgebraicGeometry.Scheme.OrderedAffineCover.instDecidableEqIdx
  AlgebraicGeometry.OModulePresheaf.moduleSections
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.instSubsingletonObjZero
attribute [-instance]
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
  AlgebraicGeometry.OModulePresheaf.Leray.biC_module
  DoubleComplex.instModuleE₂I
  DoubleComplex.Bounded.modR
  DoubleComplex.instModuleE₂II
  DoubleComplex.instAddCommGroupE₂II
  DoubleComplex.Bounded.abGrp
  DoubleComplex.instAddCommGroupE₂I
  AlgebraicGeometry.ChowDatum.hι_closed
  AlgebraicGeometry.ChowDatumProj.hιN_closed
  AlgebraicGeometry.ChowDatumProj.hp_proper
  AlgebraicGeometry.ChowDatum.hp_isoU
  AlgebraicGeometry.ChowDatum.hp_proper
  AlgebraicGeometry.ProjSpace.algebraAway
  AlgebraicGeometry.ProjSpace.instIsProperProdOverπ
  AlgebraicGeometry.ChowDatumProj.hp_isoU
  AlgebraicGeometry.ProjSpace.isProper_π
  AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
  ProjSpaceCech.GradedModule.H.module
  ProjSpaceCech.GradedModule.H.addCommGroup
  ProjSpaceCech.GradedModule.sec.instAdd
  ProjSpaceCech.GradedModule.sec.instNeg
  ProjSpaceCech.GradedModule.acg
  ProjSpaceCech.GradedModule.Frac.setoid
  ProjSpaceCech.GradedModule.modR
  ProjSpaceCech.GradedModule.sec.instModule
  ProjSpaceCech.GradedModule.sec.instAddCommGroup
  ProjSpaceCech.GradedModule.sec.instZero
  ProjSpaceCech.GradedModule.Presentation.fJ
  ProjSpaceCech.GradedModule.sec.instSMul
  ProjSpaceCech.Twist.H.module
  ProjSpaceCech.Idx.instFintype
  ProjSpaceCech.Twist.H.addCommGroup
attribute [-instance]
  ProjSpaceCech.Idx.instDecidableEq
  ProjSpaceCech.Twist.Mon.instDecidableEq
  ProjSpaceCech.Twist.cochain.instAddCommGroup
  ProjSpaceCech.Twist.cochain.instModule
  AlgebraicGeometry.FGSubalgebra.tensorStage_directedSystem
  AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
  AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
  AlgebraicCurve.CurveModel.locallyOfFiniteType_gluedToBase
  AlgebraicCurve.CurveModel.isFractionRing_overlap
  AlgebraicCurve.CurveModel.isLocallyNoetherian_glued
  AlgebraicCurve.CurveModel.jacobsonSpace_glued
  AlgebraicCurve.CurveModel.isOpenImmersion_ι₀
  AlgebraicCurve.CurveModel.isIntegral_glued
  AlgebraicCurve.CurveModel.quasiSeparated_gluedToBase
  AlgebraicCurve.CurveModel.compactSpace_glued
  AlgebraicCurve.CurveModel.isIntegral_adjoin_chartRing
  AlgebraicCurve.CurveModel.isFractionRing_overlap_functionField
  AlgebraicCurve.CurveModel.isProper_gluedToBase
  AlgebraicCurve.CurveModel.isOpenImmersion_ιU
  AlgebraicCurve.CurveModel.isOpenImmersion_f₀
  AlgebraicCurve.CurveModel.isOpenImmersion_fInf
  AlgebraicCurve.CurveModel.isOpenImmersion_ιInf
  AlgebraicCurve.CurveModel.algebra_overlap_functionField
  AlgebraicCurve.CurveModel.quasiCompact_gluedToBase
  AlgebraicCurve.CurveModel.algebraAdjoin
  AlgebraicCurve.CurveModel.isDedekindDomain_chartRing
  AlgebraicCurve.CurveModel.isIntegralClosure
  AlgebraicCurve.CurveModel.finite_chartRing
  AlgebraicCurve.CurveModel.centre_isPrime
  AlgebraicCurve.CurveModel.isFractionRing_chartRing
  AlgebraicCurve.CurveModel.finiteType_chartRing
  AlgebraicCurve.CurveModel.isNoetherianRing_chartRing
  AlgebraicCurve.CurveModel.isScalarTower_base_adjoin
  AlgebraicCurve.CurveModel.isScalarTower_adjoin
  AlgebraicCurve.CurveModel.chartRing_finitePresentation
attribute [-simp]
  GoodReductionJacobian.RelativePic0Designation.mk.sizeOf_spec
  GoodReductionJacobian.AvatarSchemeBridge.mk.injEq
  GoodReductionJacobian.AvatarSchemeBridge.mk.sizeOf_spec
  GoodReductionJacobian.RelativePic0Designation.mk.injEq
  GoodReductionJacobian.schemeHomOverComp_coe
  NeronModelInfra.schemeHomOverEquivOverHom_apply
  GoodReductionJacobian.RelativeGroupLaw.mk.sizeOf_spec
  NeronModelInfra.schemeHomOverEquivOverHom_symm_apply
  NeronModelInfra.overHomToSchemeHomOver_coe
  GoodReductionJacobian.RelativeGroupLaw.mk.injEq
  NeronModelInfra.overHomToSchemeHomOver_schemeHomOverToOverHom
  NeronModelInfra.schemeHomOverToOverHom_left
  NeronModelInfra.schemeHomOverToOverHom_overHomToSchemeHomOver
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.sizeOf_spec
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
  AlgebraicCurve.CurveModel.mk.injEq
  AlgebraicCurve.CurveModel.mk.sizeOf_spec
  AlgebraicCurve.Place.mk.injEq
  AlgebraicCurve.Divisor.degree_single
  AlgebraicCurve.Divisor.smul_single
  AlgebraicCurve.Place.smul_toValuationSubring
  AlgebraicCurve.Place.heightOneSpectrum_asIdeal
  AlgebraicCurve.Place.coe_algebraMap
  AlgebraicCurve.Place.ord_one
  AlgebraicCurve.Place.coe_smulRingEquiv_apply
  AlgebraicCurve.Pic0.coe_degZeroSMulHom
  AlgebraicCurve.Place.deg_smul
  AlgebraicCurve.Pic0.mk_zero
  AlgebraicCurve.Place.mk.sizeOf_spec
  AlgebraicCurve.Divisor.degree_smul
  AlgebraicCurve.Pic0.mk_add
  AlgebraicCurve.Place.ord_zero
  AlgebraicCurve.Place.ofHeightOneSpectrum_toValuationSubring
  AlgebraicCurve.mulAdele_apply
attribute [-simp]
  AlgebraicCurve.residuePairing_apply_coe
  AlgebraicCurve.mem_adeleBdd
  AlgebraicCurve.weilSmul_one
  AlgebraicCurve.diagonalHom_apply
  AlgebraicCurve.weilSmul_apply
  AlgebraicCurve.adeleSpaceMul_coe
  AlgebraicCurve.mulAdele_one
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U1
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.injEq
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U0
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.mk.injEq
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.pullback_U1
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.pullback_U0
  TwoChartCech.Sections.mk.injEq
  TwoChartCech.Cover.mk.injEq
  TwoChartCech.GrothendieckComplex.mk.injEq
  TwoChartCech.Sections.mk.sizeOf_spec
  TwoChartCech.Cover.mk.sizeOf_spec
  TwoChartCech.Cover.lineBundle_r0_apply
  TwoChartCech.GrothendieckComplex.mk.sizeOf_spec
  TwoChartCech.Cover.lineBundle_r1_apply
  CoherentBaseChange.TwoTermComplex.mk.sizeOf_spec
  CoherentBaseChange.TwoTermComplex.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
  AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
  CategoryTheory.Functor.OverTotal.ofFibre_fst
  CategoryTheory.Functor.overTotal_map_fst
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_J
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYoneda_toGlued_uliftYonedaGluedToSheaf
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t'
attribute [-simp]
  uliftYoneda_toGlued_uliftYonedaGluedToSheaf_assoc
attribute [-simp]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_toGlued
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_openCover_map
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_comp
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_V
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_U
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_f
attribute [-simp]
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_P
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_toBase
  AlgebraicGeometry.RelPicard.rigSection_snd
  AlgebraicGeometry.RelPicard.RigidifiedLineBundle.ofInvertible_L
  AlgebraicGeometry.RelPicard.rigSection_snd_assoc
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
  GoodReductionJacobian.relativeGroupLawOfGrpObj_inv
  GoodReductionJacobian.relativeGroupLawOfGrpObj_mul
  GoodReductionJacobian.overHomEquivSchemeHomOver_apply_coe
  GoodReductionJacobian.relativeGroupLawOfGrpObj_one
  GoodReductionJacobian.overHomEquivSchemeHomOver_symm_apply_left
  PresheafOfModules.freeεIso_hom_app
  PresheafOfModules.freeμIso_hom_app
  AlgebraicCurve.coe_cechH0Equiv_apply
  AlgebraicCurve.cechH1ToH1_mk
  AlgebraicCurve.lSpaceOn_univ
  AlgebraicCurve.lSpaceOn_empty
  AlgebraicCurve.Place.congrEquiv_symm_apply
  AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
  AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
  AlgebraicCurve.Place.congrEquiv_apply
  AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
  AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
  AlgebraicCurve.Divisor.mapRestrict_single
  AlgebraicCurve.Divisor.pushforward_single
  AlgebraicCurve.Place.coe_restrictInclusion
  AlgebraicCurve.Place.mem_fiber
  AlgebraicCurve.Place.restrict_toValuationSubring
  AlgebraicCurve.Divisor.degree_pushforward
  AlgebraicCurve.Place.restrictResidueMap_residue
  AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
  AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
  AlgebraicCurve.Place.placeOfPrime_toValuationSubring
  AlgebraicCurve.Place.mem_fiberOver
  AlgebraicCurve.Place.fiberEquiv_symm_apply
  AlgebraicCurve.Place.fiberEquiv_apply
  AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
attribute [-simp]
  AlgebraicCurve.Divisor.degree_pushforwardAlong
  AlgebraicCurve.Pic0.coe_degZeroCorrespondence
  AlgebraicCurve.Place.mem_fiberAlong
  AlgebraicCurve.SemilinearAut.toRingAut_inv
  AlgebraicCurve.SemilinearAut.smul_def
  AlgebraicCurve.SemilinearAut.smul_single
  AlgebraicCurve.SemilinearAut.smul_toValuationSubring
  AlgebraicCurve.SemilinearAut.baseAut_inv
  AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_one
  AlgebraicCurve.SemilinearAut.deg_smul
  AlgebraicCurve.SemilinearAut.degree_smul
  AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
  AlgebraicCurve.SemilinearAut.baseAut_mul
  AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
  AlgebraicCurve.SemilinearAut.baseAut_one
  AlgebraicCurve.SemilinearAut.ofAlgAut_smul
  AlgebraicCurve.SemilinearAut.coe_torsion_smul
  AlgebraicCurve.SemilinearAut.toRingAut_mul
attribute [-simp]
  AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeInfty
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_some
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeOfPoint
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_none
  AlgebraicCurve.Divisor.evalFun_zero
  AlgebraicCurve.Place.evalAt_one
  AlgebraicCurve.Place.differentialCoeff_zero
  AlgebraicCurve.Place.differentialCoeff_dCoord
  AlgebraicCurve.TranscendenceTower.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
  AlgebraicCurve.TranscendenceTower.mk.injEq
  AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec
  AlgebraicCurve.PoleDivisorPackage.mk.injEq
  AlgebraicGeometry.RelPicard.thetaBundle_def
attribute [-simp]
  AlgebraicGeometry.RelPicard.picardBundle_def
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_ofRelEffDivisor
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_I
  AlgebraicGeometry.mapOnProdOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.mk.sizeOf_spec
  AlgebraicGeometry.RelEffCartierDiv.mk.injEq
  AlgebraicGeometry.mapOnProdOver_snd
  AlgebraicGeometry.mapOnProdOver_fst
  AlgebraicGeometry.mapOnProdOver_snd_assoc
  AlgebraicGeometry.mapOnProdOver_id
  AlgebraicCurve.RelEffDivisor.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_fst
  AlgebraicCurve.mapOnProd_fst_assoc
  AlgebraicCurve.mapOnProd_snd
  AlgebraicCurve.UnivDivisorPack.mk.injEq
  AlgebraicCurve.RelEffDivisor.mk.injEq
  AlgebraicCurve.UnivDivisorPack.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_snd_assoc
  AlgebraicGeometry.Scheme.Modules.exteriorPower_obj
  PresheafOfModules.exteriorPower_map_ιMulti
  PresheafOfModules.ExteriorPower.appₗ_apply
  AlgebraicGeometry.prodKerGraph_one
  AlgebraicGeometry.fibrePowOver.proj_comp
  AlgebraicGeometry.prodKerGraph_zero
  AlgebraicGeometry.RelEffCartierDiv.empty_I
  AlgebraicGeometry.fibrePowOver.proj_comp_assoc
  AlgebraicGeometry.graphOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
  AlgebraicGeometry.graphOver_fst
  AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
  AlgebraicGeometry.graphOver_snd
  AlgebraicGeometry.graphOver_snd_assoc
  AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
  AlgebraicCurve.SymmetricPowerPackage.mk.injEq
  AlgebraicGeometry.FGSubalgebra.cocone_ι_app_apply
  AlgebraicGeometry.RelPicard.fst_toProdSpec
  AlgebraicGeometry.RelPicard.toProdSpec_fst_assoc
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_cons
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_nil
attribute [-simp]
  AlgebraicGeometry.RelPicard.fst_toProdSpec_assoc
  AlgebraicGeometry.RelPicard.toProdSpec_fst
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.sizeOf_spec
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.injEq
  AlgebraicCurve.adeleSingle_coe
  AlgebraicCurve.kaehlerResidueTermKFam_apply
  AlgebraicCurve.Place.LocalResidueData.mk.injEq
  AlgebraicCurve.Place.LocalResidueData.mk.sizeOf_spec
  AlgebraicCurve.Place.kw_ffgc_adicCompletionComapIntegers_coe
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.sizeOf_spec
  AlgebraicCurve.Place.mem_simplePoleSubmodule
  AlgebraicCurve.Place.coe_uniformizerSubring
  ModularCurve.Lg37.Lg37CompletionSection.mk.injEq
  AlgebraicCurve.Place.CoefficientFieldSection.mk.injEq
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.injEq
  ModularCurve.Lg37.Lg37CompletionSection.mk.sizeOf_spec
  AlgebraicCurve.Place.CoefficientFieldSection.mk.sizeOf_spec
  AlgebraicCurve.Place.poleSubmodule_one
  AlgebraicCurve.Place.mem_poleSubmodule
  AlgebraicGeometry.Scheme.Modules.toUnitSection_ofUnitSection
  AlgebraicGeometry.Scheme.Modules.pullbackSection_def
  AlgebraicGeometry.Scheme.Modules.ofUnitSection_toUnitSection
  PresheafOfModules.InternalHom.IsSheafAux.appAt_toPresheafHom
attribute [-simp]
  SheafOfModules.ihomSectionsEquivFamily_unit
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_apply
  SheafOfModules.ihomEval_unit_app
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_right
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_left
  AlgebraicGeometry.Scheme.Modules.homOfFamily_app_apply
  SheafOfModules.unit_ihomSectionsEquivFamily
  AlgebraicGeometry.Scheme.Modules.familyOfHom_app
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_hom_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_inv_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomOfFamily_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_symm_apply
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_right
  AlgebraicGeometry.Scheme.Modules.map_unitSection
  AlgebraicGeometry.Scheme.Modules.tensorSectionsBilin_apply
  AlgebraicGeometry.Scheme.Modules.tensorPowSection_zero
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_left
  AlgebraicGeometry.Scheme.Modules.tensorPow_zero
  AlgebraicGeometry.Scheme.Modules.tensorPow_succ
  AlgebraicGeometry.Scheme.OrderedAffineCover.mk.injEq
  AlgebraicGeometry.OModulePresheaf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCover.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.mk.injEq
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_neg
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_zero
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_sub
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_add
  AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
  AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U
  AlgebraicGeometry.OModulePresheaf.Hom.mk.injEq
  AlgebraicGeometry.OModulePresheaf.Hom.id_app
  AlgebraicGeometry.OModulePresheaf.AffHom.appSections_apply
  AlgebraicGeometry.OModulePresheaf.AffHom.comp_app
  AlgebraicGeometry.OModulePresheaf.AffSES.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.AffHom.kerMap_coe
  AlgebraicGeometry.OModulePresheaf.AffHom.id_app
  AlgebraicGeometry.OModulePresheaf.Hom.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.Hom.toAffHom_app
attribute [-simp]
  AlgebraicGeometry.OModulePresheaf.SES.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.AffHom.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.Hom.comp_app
  AlgebraicGeometry.OModulePresheaf.SES.mk.injEq
  AlgebraicGeometry.OModulePresheaf.AffHom.mk.injEq
  AlgebraicGeometry.OModulePresheaf.Hom.appSections_apply
  AlgebraicGeometry.OModulePresheaf.AffSES.mk.injEq
  AlgebraicGeometry.OModulePresheaf.prod_obj
  AlgebraicGeometry.OModulePresheaf.restrOpen_obj
  AlgebraicGeometry.OModulePresheaf.DevissageStep.mk.injEq
  AlgebraicGeometry.OModulePresheaf.pushforward_obj
  AlgebraicGeometry.OModulePresheaf.im_obj
  AlgebraicGeometry.OModulePresheaf.pow_obj
  AlgebraicGeometry.OModulePresheaf.fstHom_app
  AlgebraicGeometry.OModulePresheaf.ker_obj
  AlgebraicGeometry.OModulePresheaf.coker_obj
  AlgebraicGeometry.OModulePresheaf.DevissageStep.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCover.preimage_U
  AlgebraicGeometry.OModulePresheaf.sndHom_app
  AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
  DoubleComplex.Bounded.mk.injEq
  DoubleComplex.Bounded.mk.sizeOf_spec
  DoubleComplex.Convergence.mk.injEq
  DoubleComplex.Convergence.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.injEq
  AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatumProj.mk.injEq
  AlgebraicGeometry.ChowDatum.mk.injEq
  ProjSpaceCech.GradedModule.mk.injEq
  ProjSpaceCech.GradedModule.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Presentation.mk.injEq
  ProjSpaceCech.GradedModule.Frac.mk.injEq
  ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.shift_toLinearMap
  ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.mk.injEq
  TwoChartCech.Mumford.dK_apply
attribute [-simp]
  TwoChartCech.Mumford.ι0_apply
  TwoChartCech.Mumford.ι1_apply
  TwoChartCech.KerCoprod.dK_apply
  TwoChartCech.KerCoprod.ι1_apply
  TwoChartCech.KerCoprod.ι0_apply
  AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
  AlgebraicGeometry.RelPicard.algEquivZeroGroupCut_toSubPicCondition
  AlgebraicGeometry.RelPicard.LFP.stageHom_val
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_hom_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_inv_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.restrict_P
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp
  AlgebraicGeometry.RelEffCartierDiv.functor_map_fst
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_pullbackAlong
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_symm_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp_assoc
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top
  AlgebraicGeometry.RelEffCartierDiv.mem_supportedIn_iff
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top_eq
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
  CoherentBaseChange.FibreH0Family.mk.sizeOf_spec
  CoherentBaseChange.FibreH0Family.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.sizeOf_spec
  AlgebraicCurve.CurveModel.coe_gInf
  AlgebraicCurve.CurveModel.coe_tInvChart
  AlgebraicCurve.CurveModel.ιInf_gluedToBase_assoc
  AlgebraicCurve.CurveModel.ιInf_gluedToBase
  AlgebraicCurve.CurveModel.primeOfι₀_asIdeal
  AlgebraicCurve.CurveModel.coe_tChart
  AlgebraicCurve.CurveModel.ι₀_gluedToBase_assoc
  AlgebraicCurve.CurveModel.primeOfιInf_asIdeal
attribute [-simp]
  AlgebraicCurve.CurveModel.ι₀_gluedToBase
  AlgebraicCurve.CurveModel.coe_tma
  AlgebraicCurve.CurveModel.coe_primeEquivChartPlaces
universe u
noncomputable section
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.CategoryTheory.CartesianMonoidalCategory
open _root_.AlgebraicGeometry.RelPicard
open _root_.NeronModelInfra
namespace P2mCubeAssembly
section Slices
variable {k : Type u} [Field k]
local notation "Sk" => Spec (CommRingCat.of k)

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.ThreeSlices
attribute [-instance]
  AlgebraicGeometry.SmoothOfRelativeDimension.fiberToSpecResidueField
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_snd
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_fst
  AlgebraicGeometry.SmoothOfRelativeDimension.smooth_one
  AlgebraicGeometry.SmoothProperCurve.isIntegral_pullback_Spec_field
  AlgebraicGeometry.IsProper.fiberToSpecResidueField
  AlgebraicCurve.CurveModel.isProper
  AlgebraicCurve.CurveModel.isIntegral
  AlgebraicCurve.CurveModel.smooth
  AlgebraicCurve.Place.instIsScalarTowerSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Divisor.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instSMulAlgEquiv
  AlgebraicCurve.Place.instIsPrincipalIdealRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instIsDiscreteValuationRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Pic0.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instAlgebraSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instMulActionAlgEquiv
  AlgebraicCurve.Pic0.instSMulAlgEquiv
  TwoChartCech.Sections.M0_moduleA
  TwoChartCech.Sections.M1_module
  TwoChartCech.Cover.A01_algebra
  TwoChartCech.Cover.A0_algebra
  TwoChartCech.Cover.A1_commRing
  TwoChartCech.Cover.A1_algebra
  TwoChartCech.Sections.M01_module
  TwoChartCech.Sections.M0_addCommGroup
  TwoChartCech.Sections.M0_tower
  TwoChartCech.Sections.M01_addCommGroup
  TwoChartCech.Cover.A0_commRing
  TwoChartCech.Sections.M1_tower
  TwoChartCech.Sections.M01_moduleA
  TwoChartCech.Sections.M0_module
  TwoChartCech.Sections.M1_moduleA
  TwoChartCech.Sections.M1_addCommGroup
  TwoChartCech.Cover.A01_commRing
  TwoChartCech.Sections.M01_tower
  CoherentBaseChange.TwoTermComplex.C0_module
  CoherentBaseChange.TwoTermComplex.C0_addCommGroup
  CoherentBaseChange.TwoTermComplex.C1_module
  CoherentBaseChange.TwoTermComplex.C1_addCommGroup
attribute [-instance]
  CoherentBaseChange.TwoTermComplex.C0_free
  CoherentBaseChange.TwoTermComplex.C1_finite
  CoherentBaseChange.TwoTermComplex.C0_finite
  CoherentBaseChange.TwoTermComplex.C1_free
  AlgebraicCurve.IsCurveOver.instNontrivialKaehler
  AlgebraicCurve.IsCurveOver.instFreeKaehler
  AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
  AlgebraicCurve.IsCurveOver.instFiniteResidue
attribute [-instance]
  instIsLocallyInjectiveFunUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsLocallySurjectiveUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsOpenImmersionToGlued
attribute [-instance]
  instIsIsoSheafZariskiTopologyTypeUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.RelPicard.isOpenImmersion_toGlued
  AlgebraicGeometry.Scheme.Modules.preservesBinaryProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback_monoidal
  AlgebraicGeometry.Scheme.Modules.sheafify_isLocalization'
  AlgebraicGeometry.Scheme.Modules.preservesTerminal_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback₀_monoidal
  AlgebraicGeometry.Scheme.Modules.preservesFiniteProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.sheafifyPullback_lifting
  PresheafOfModules.PullbackMonoidal.pullback_monoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ
  PresheafOfModules.pushforward_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_η
  PresheafOfModules.free_monoidal
  PresheafOfModules.restrictScalars_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ_gS
  PresheafOfModules.pullback_oplaxMonoidal
attribute [-instance]
  instPreservesColimitsOfSizeCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierPb
attribute [-instance]
  PresheafOfModules.pullback_monoidal'
  AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
  AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
  AlgebraicCurve.Place.instIsPrimeCenter
  AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
  instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
  AlgebraicCurve.Pic0.instModuleZModTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instSMulTorsion
  AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
  AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
  AlgebraicCurve.RationalFunctionField.instNontrivialInftyValueGroup
  PresheafOfModules.ExteriorPower.instModulePresheafAb
  AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
  AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
  AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
  AlgebraicGeometry.isClosedImmersion_graphOver
  AlgebraicGeometry.FGSubalgebra.instIsDirectedLe
attribute [-instance]
  instQuasiSeparatedSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsCofilteredOpposite
  AlgebraicGeometry.FGSubalgebra.instIsAffineObjOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instNonempty
  AlgebraicGeometry.FGSubalgebra.instNonemptySubtypeLeSubalgebraValFG
attribute [-instance]
  instCompactSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsDirectedSubtypeLeSubalgebraValFG
  AlgebraicGeometry.FGSubalgebra.instIsAffineHomMapOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instIsFiltered
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instNeg
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulInt
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAddCommGroup
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAdd
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSub
attribute [-instance]
  instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
  AlgebraicCurve.instHasLocalResidue_of_hasCanonicalLocalResidueK
  AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
  AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
  ModularCurve.KwF4gRRTate.instAlgebraKAdicCompletionIntegers
  AlgebraicCurve.Place.kw_ffgc_continuousSMul_adicCompletionComap
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersCompletionCompletion
attribute [-instance]
  instLiesOverSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegersCompletionIdealAsIdeal
attribute [-instance]
  AlgebraicCurve.instHasCanonicalLocalResidueK
  AlgebraicCurve.Place.instAlgebra_restrictResidueField
  AlgebraicCurve.Place.instIsScalarTower_restrictResidueField
  AlgebraicCurve.instHasLocalResidue
  AlgebraicCurve.HasSeparableResidue.of_perfectField_of_isCurveOver
  AlgebraicCurve.HasSeparableResidue.of_perfectField
  AlgebraicCurve.Place.instIsLocalHom_restrictSubringHom
  AlgebraicCurve.instHasCanonicalLocalResidueKStar
  ModularCurve.KwNo6Pin.isLocalRing_completion
  SheafOfModules.isIso_ihomModelToIhom
  AlgebraicGeometry.OModulePresheaf.isScalarTower
  AlgebraicGeometry.Scheme.OrderedAffineCover.instLinearOrder
  AlgebraicGeometry.OModulePresheaf.module
  AlgebraicGeometry.Scheme.OrderedAffineCover.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCover.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.addCommGroup
  AlgebraicGeometry.Scheme.OrderedAffineCover.instDecidableEqIdx
  AlgebraicGeometry.OModulePresheaf.moduleSections
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.instSubsingletonObjZero
attribute [-instance]
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
  AlgebraicGeometry.OModulePresheaf.Leray.biC_module
  DoubleComplex.instModuleE₂I
  DoubleComplex.Bounded.modR
  DoubleComplex.instModuleE₂II
  DoubleComplex.instAddCommGroupE₂II
  DoubleComplex.Bounded.abGrp
  DoubleComplex.instAddCommGroupE₂I
  AlgebraicGeometry.ChowDatum.hι_closed
  AlgebraicGeometry.ChowDatumProj.hιN_closed
  AlgebraicGeometry.ChowDatumProj.hp_proper
  AlgebraicGeometry.ChowDatum.hp_isoU
  AlgebraicGeometry.ChowDatum.hp_proper
  AlgebraicGeometry.ProjSpace.algebraAway
  AlgebraicGeometry.ProjSpace.instIsProperProdOverπ
  AlgebraicGeometry.ChowDatumProj.hp_isoU
  AlgebraicGeometry.ProjSpace.isProper_π
  AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
  ProjSpaceCech.GradedModule.H.module
  ProjSpaceCech.GradedModule.H.addCommGroup
  ProjSpaceCech.GradedModule.sec.instAdd
  ProjSpaceCech.GradedModule.sec.instNeg
  ProjSpaceCech.GradedModule.acg
  ProjSpaceCech.GradedModule.Frac.setoid
  ProjSpaceCech.GradedModule.modR
  ProjSpaceCech.GradedModule.sec.instModule
  ProjSpaceCech.GradedModule.sec.instAddCommGroup
  ProjSpaceCech.GradedModule.sec.instZero
  ProjSpaceCech.GradedModule.Presentation.fJ
  ProjSpaceCech.GradedModule.sec.instSMul
  ProjSpaceCech.Twist.H.module
  ProjSpaceCech.Idx.instFintype
  ProjSpaceCech.Twist.H.addCommGroup
attribute [-instance]
  ProjSpaceCech.Idx.instDecidableEq
  ProjSpaceCech.Twist.Mon.instDecidableEq
  ProjSpaceCech.Twist.cochain.instAddCommGroup
  ProjSpaceCech.Twist.cochain.instModule
  AlgebraicGeometry.FGSubalgebra.tensorStage_directedSystem
  AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
  AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
  AlgebraicCurve.CurveModel.locallyOfFiniteType_gluedToBase
  AlgebraicCurve.CurveModel.isFractionRing_overlap
  AlgebraicCurve.CurveModel.isLocallyNoetherian_glued
  AlgebraicCurve.CurveModel.jacobsonSpace_glued
  AlgebraicCurve.CurveModel.isOpenImmersion_ι₀
  AlgebraicCurve.CurveModel.isIntegral_glued
  AlgebraicCurve.CurveModel.quasiSeparated_gluedToBase
  AlgebraicCurve.CurveModel.compactSpace_glued
  AlgebraicCurve.CurveModel.isIntegral_adjoin_chartRing
  AlgebraicCurve.CurveModel.isFractionRing_overlap_functionField
  AlgebraicCurve.CurveModel.isProper_gluedToBase
  AlgebraicCurve.CurveModel.isOpenImmersion_ιU
  AlgebraicCurve.CurveModel.isOpenImmersion_f₀
  AlgebraicCurve.CurveModel.isOpenImmersion_fInf
  AlgebraicCurve.CurveModel.isOpenImmersion_ιInf
  AlgebraicCurve.CurveModel.algebra_overlap_functionField
  AlgebraicCurve.CurveModel.quasiCompact_gluedToBase
  AlgebraicCurve.CurveModel.algebraAdjoin
  AlgebraicCurve.CurveModel.isDedekindDomain_chartRing
  AlgebraicCurve.CurveModel.isIntegralClosure
  AlgebraicCurve.CurveModel.finite_chartRing
  AlgebraicCurve.CurveModel.centre_isPrime
  AlgebraicCurve.CurveModel.isFractionRing_chartRing
  AlgebraicCurve.CurveModel.finiteType_chartRing
  AlgebraicCurve.CurveModel.isNoetherianRing_chartRing
  AlgebraicCurve.CurveModel.isScalarTower_base_adjoin
  AlgebraicCurve.CurveModel.isScalarTower_adjoin
  AlgebraicCurve.CurveModel.chartRing_finitePresentation
attribute [-simp]
  GoodReductionJacobian.RelativePic0Designation.mk.sizeOf_spec
  GoodReductionJacobian.AvatarSchemeBridge.mk.injEq
  GoodReductionJacobian.AvatarSchemeBridge.mk.sizeOf_spec
  GoodReductionJacobian.RelativePic0Designation.mk.injEq
  GoodReductionJacobian.schemeHomOverComp_coe
  NeronModelInfra.schemeHomOverEquivOverHom_apply
  GoodReductionJacobian.RelativeGroupLaw.mk.sizeOf_spec
  NeronModelInfra.schemeHomOverEquivOverHom_symm_apply
  NeronModelInfra.overHomToSchemeHomOver_coe
  GoodReductionJacobian.RelativeGroupLaw.mk.injEq
  NeronModelInfra.overHomToSchemeHomOver_schemeHomOverToOverHom
  NeronModelInfra.schemeHomOverToOverHom_left
  NeronModelInfra.schemeHomOverToOverHom_overHomToSchemeHomOver
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.sizeOf_spec
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
  AlgebraicCurve.CurveModel.mk.injEq
  AlgebraicCurve.CurveModel.mk.sizeOf_spec
  AlgebraicCurve.Place.mk.injEq
  AlgebraicCurve.Divisor.degree_single
  AlgebraicCurve.Divisor.smul_single
  AlgebraicCurve.Place.smul_toValuationSubring
  AlgebraicCurve.Place.heightOneSpectrum_asIdeal
  AlgebraicCurve.Place.coe_algebraMap
  AlgebraicCurve.Place.ord_one
  AlgebraicCurve.Place.coe_smulRingEquiv_apply
  AlgebraicCurve.Pic0.coe_degZeroSMulHom
  AlgebraicCurve.Place.deg_smul
  AlgebraicCurve.Pic0.mk_zero
  AlgebraicCurve.Place.mk.sizeOf_spec
  AlgebraicCurve.Divisor.degree_smul
  AlgebraicCurve.Pic0.mk_add
  AlgebraicCurve.Place.ord_zero
  AlgebraicCurve.Place.ofHeightOneSpectrum_toValuationSubring
  AlgebraicCurve.mulAdele_apply
attribute [-simp]
  AlgebraicCurve.residuePairing_apply_coe
  AlgebraicCurve.mem_adeleBdd
  AlgebraicCurve.weilSmul_one
  AlgebraicCurve.diagonalHom_apply
  AlgebraicCurve.weilSmul_apply
  AlgebraicCurve.adeleSpaceMul_coe
  AlgebraicCurve.mulAdele_one
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U1
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.injEq
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U0
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.mk.injEq
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.pullback_U1
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.pullback_U0
  TwoChartCech.Sections.mk.injEq
  TwoChartCech.Cover.mk.injEq
  TwoChartCech.GrothendieckComplex.mk.injEq
  TwoChartCech.Sections.mk.sizeOf_spec
  TwoChartCech.Cover.mk.sizeOf_spec
  TwoChartCech.Cover.lineBundle_r0_apply
  TwoChartCech.GrothendieckComplex.mk.sizeOf_spec
  TwoChartCech.Cover.lineBundle_r1_apply
  CoherentBaseChange.TwoTermComplex.mk.sizeOf_spec
  CoherentBaseChange.TwoTermComplex.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
  AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
  CategoryTheory.Functor.OverTotal.ofFibre_fst
  CategoryTheory.Functor.overTotal_map_fst
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_J
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYoneda_toGlued_uliftYonedaGluedToSheaf
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t'
attribute [-simp]
  uliftYoneda_toGlued_uliftYonedaGluedToSheaf_assoc
attribute [-simp]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_toGlued
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_openCover_map
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_comp
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_V
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_U
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_f
attribute [-simp]
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_P
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_toBase
  AlgebraicGeometry.RelPicard.rigSection_snd
  AlgebraicGeometry.RelPicard.RigidifiedLineBundle.ofInvertible_L
  AlgebraicGeometry.RelPicard.rigSection_snd_assoc
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
  GoodReductionJacobian.relativeGroupLawOfGrpObj_inv
  GoodReductionJacobian.relativeGroupLawOfGrpObj_mul
  GoodReductionJacobian.overHomEquivSchemeHomOver_apply_coe
  GoodReductionJacobian.relativeGroupLawOfGrpObj_one
  GoodReductionJacobian.overHomEquivSchemeHomOver_symm_apply_left
  PresheafOfModules.freeεIso_hom_app
  PresheafOfModules.freeμIso_hom_app
  AlgebraicCurve.coe_cechH0Equiv_apply
  AlgebraicCurve.cechH1ToH1_mk
  AlgebraicCurve.lSpaceOn_univ
  AlgebraicCurve.lSpaceOn_empty
  AlgebraicCurve.Place.congrEquiv_symm_apply
  AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
  AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
  AlgebraicCurve.Place.congrEquiv_apply
  AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
  AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
  AlgebraicCurve.Divisor.mapRestrict_single
  AlgebraicCurve.Divisor.pushforward_single
  AlgebraicCurve.Place.coe_restrictInclusion
  AlgebraicCurve.Place.mem_fiber
  AlgebraicCurve.Place.restrict_toValuationSubring
  AlgebraicCurve.Divisor.degree_pushforward
  AlgebraicCurve.Place.restrictResidueMap_residue
  AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
  AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
  AlgebraicCurve.Place.placeOfPrime_toValuationSubring
  AlgebraicCurve.Place.mem_fiberOver
  AlgebraicCurve.Place.fiberEquiv_symm_apply
  AlgebraicCurve.Place.fiberEquiv_apply
  AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
attribute [-simp]
  AlgebraicCurve.Divisor.degree_pushforwardAlong
  AlgebraicCurve.Pic0.coe_degZeroCorrespondence
  AlgebraicCurve.Place.mem_fiberAlong
  AlgebraicCurve.SemilinearAut.toRingAut_inv
  AlgebraicCurve.SemilinearAut.smul_def
  AlgebraicCurve.SemilinearAut.smul_single
  AlgebraicCurve.SemilinearAut.smul_toValuationSubring
  AlgebraicCurve.SemilinearAut.baseAut_inv
  AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_one
  AlgebraicCurve.SemilinearAut.deg_smul
  AlgebraicCurve.SemilinearAut.degree_smul
  AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
  AlgebraicCurve.SemilinearAut.baseAut_mul
  AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
  AlgebraicCurve.SemilinearAut.baseAut_one
  AlgebraicCurve.SemilinearAut.ofAlgAut_smul
  AlgebraicCurve.SemilinearAut.coe_torsion_smul
  AlgebraicCurve.SemilinearAut.toRingAut_mul
attribute [-simp]
  AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeInfty
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_some
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeOfPoint
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_none
  AlgebraicCurve.Divisor.evalFun_zero
  AlgebraicCurve.Place.evalAt_one
  AlgebraicCurve.Place.differentialCoeff_zero
  AlgebraicCurve.Place.differentialCoeff_dCoord
  AlgebraicCurve.TranscendenceTower.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
  AlgebraicCurve.TranscendenceTower.mk.injEq
  AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec
  AlgebraicCurve.PoleDivisorPackage.mk.injEq
  AlgebraicGeometry.RelPicard.thetaBundle_def
attribute [-simp]
  AlgebraicGeometry.RelPicard.picardBundle_def
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_ofRelEffDivisor
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_I
  AlgebraicGeometry.mapOnProdOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.mk.sizeOf_spec
  AlgebraicGeometry.RelEffCartierDiv.mk.injEq
  AlgebraicGeometry.mapOnProdOver_snd
  AlgebraicGeometry.mapOnProdOver_fst
  AlgebraicGeometry.mapOnProdOver_snd_assoc
  AlgebraicGeometry.mapOnProdOver_id
  AlgebraicCurve.RelEffDivisor.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_fst
  AlgebraicCurve.mapOnProd_fst_assoc
  AlgebraicCurve.mapOnProd_snd
  AlgebraicCurve.UnivDivisorPack.mk.injEq
  AlgebraicCurve.RelEffDivisor.mk.injEq
  AlgebraicCurve.UnivDivisorPack.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_snd_assoc
  AlgebraicGeometry.Scheme.Modules.exteriorPower_obj
  PresheafOfModules.exteriorPower_map_ιMulti
  PresheafOfModules.ExteriorPower.appₗ_apply
  AlgebraicGeometry.prodKerGraph_one
  AlgebraicGeometry.fibrePowOver.proj_comp
  AlgebraicGeometry.prodKerGraph_zero
  AlgebraicGeometry.RelEffCartierDiv.empty_I
  AlgebraicGeometry.fibrePowOver.proj_comp_assoc
  AlgebraicGeometry.graphOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
  AlgebraicGeometry.graphOver_fst
  AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
  AlgebraicGeometry.graphOver_snd
  AlgebraicGeometry.graphOver_snd_assoc
  AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
  AlgebraicCurve.SymmetricPowerPackage.mk.injEq
  AlgebraicGeometry.FGSubalgebra.cocone_ι_app_apply
  AlgebraicGeometry.RelPicard.fst_toProdSpec
  AlgebraicGeometry.RelPicard.toProdSpec_fst_assoc
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_cons
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_nil
attribute [-simp]
  AlgebraicGeometry.RelPicard.fst_toProdSpec_assoc
  AlgebraicGeometry.RelPicard.toProdSpec_fst
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.sizeOf_spec
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.injEq
  AlgebraicCurve.adeleSingle_coe
  AlgebraicCurve.kaehlerResidueTermKFam_apply
  AlgebraicCurve.Place.LocalResidueData.mk.injEq
  AlgebraicCurve.Place.LocalResidueData.mk.sizeOf_spec
  AlgebraicCurve.Place.kw_ffgc_adicCompletionComapIntegers_coe
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.sizeOf_spec
  AlgebraicCurve.Place.mem_simplePoleSubmodule
  AlgebraicCurve.Place.coe_uniformizerSubring
  ModularCurve.Lg37.Lg37CompletionSection.mk.injEq
  AlgebraicCurve.Place.CoefficientFieldSection.mk.injEq
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.injEq
  ModularCurve.Lg37.Lg37CompletionSection.mk.sizeOf_spec
  AlgebraicCurve.Place.CoefficientFieldSection.mk.sizeOf_spec
  AlgebraicCurve.Place.poleSubmodule_one
  AlgebraicCurve.Place.mem_poleSubmodule
  AlgebraicGeometry.Scheme.Modules.toUnitSection_ofUnitSection
  AlgebraicGeometry.Scheme.Modules.pullbackSection_def
  AlgebraicGeometry.Scheme.Modules.ofUnitSection_toUnitSection
  PresheafOfModules.InternalHom.IsSheafAux.appAt_toPresheafHom
attribute [-simp]
  SheafOfModules.ihomSectionsEquivFamily_unit
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_apply
  SheafOfModules.ihomEval_unit_app
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_right
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_left
  AlgebraicGeometry.Scheme.Modules.homOfFamily_app_apply
  SheafOfModules.unit_ihomSectionsEquivFamily
  AlgebraicGeometry.Scheme.Modules.familyOfHom_app
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_hom_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_inv_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomOfFamily_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_symm_apply
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_right
  AlgebraicGeometry.Scheme.Modules.map_unitSection
  AlgebraicGeometry.Scheme.Modules.tensorSectionsBilin_apply
  AlgebraicGeometry.Scheme.Modules.tensorPowSection_zero
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_left
  AlgebraicGeometry.Scheme.Modules.tensorPow_zero
  AlgebraicGeometry.Scheme.Modules.tensorPow_succ
  AlgebraicGeometry.Scheme.OrderedAffineCover.mk.injEq
  AlgebraicGeometry.OModulePresheaf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCover.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.mk.injEq
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_neg
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_zero
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_sub
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_add
  AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
  AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U
  AlgebraicGeometry.OModulePresheaf.Hom.mk.injEq
  AlgebraicGeometry.OModulePresheaf.Hom.id_app
  AlgebraicGeometry.OModulePresheaf.AffHom.appSections_apply
  AlgebraicGeometry.OModulePresheaf.AffHom.comp_app
  AlgebraicGeometry.OModulePresheaf.AffSES.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.AffHom.kerMap_coe
  AlgebraicGeometry.OModulePresheaf.AffHom.id_app
  AlgebraicGeometry.OModulePresheaf.Hom.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.Hom.toAffHom_app
attribute [-simp]
  AlgebraicGeometry.OModulePresheaf.SES.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.AffHom.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.Hom.comp_app
  AlgebraicGeometry.OModulePresheaf.SES.mk.injEq
  AlgebraicGeometry.OModulePresheaf.AffHom.mk.injEq
  AlgebraicGeometry.OModulePresheaf.Hom.appSections_apply
  AlgebraicGeometry.OModulePresheaf.AffSES.mk.injEq
  AlgebraicGeometry.OModulePresheaf.prod_obj
  AlgebraicGeometry.OModulePresheaf.restrOpen_obj
  AlgebraicGeometry.OModulePresheaf.DevissageStep.mk.injEq
  AlgebraicGeometry.OModulePresheaf.pushforward_obj
  AlgebraicGeometry.OModulePresheaf.im_obj
  AlgebraicGeometry.OModulePresheaf.pow_obj
  AlgebraicGeometry.OModulePresheaf.fstHom_app
  AlgebraicGeometry.OModulePresheaf.ker_obj
  AlgebraicGeometry.OModulePresheaf.coker_obj
  AlgebraicGeometry.OModulePresheaf.DevissageStep.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCover.preimage_U
  AlgebraicGeometry.OModulePresheaf.sndHom_app
  AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
  DoubleComplex.Bounded.mk.injEq
  DoubleComplex.Bounded.mk.sizeOf_spec
  DoubleComplex.Convergence.mk.injEq
  DoubleComplex.Convergence.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.injEq
  AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatumProj.mk.injEq
  AlgebraicGeometry.ChowDatum.mk.injEq
  ProjSpaceCech.GradedModule.mk.injEq
  ProjSpaceCech.GradedModule.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Presentation.mk.injEq
  ProjSpaceCech.GradedModule.Frac.mk.injEq
  ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.shift_toLinearMap
  ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.mk.injEq
  TwoChartCech.Mumford.dK_apply
attribute [-simp]
  TwoChartCech.Mumford.ι0_apply
  TwoChartCech.Mumford.ι1_apply
  TwoChartCech.KerCoprod.dK_apply
  TwoChartCech.KerCoprod.ι1_apply
  TwoChartCech.KerCoprod.ι0_apply
  AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
  AlgebraicGeometry.RelPicard.algEquivZeroGroupCut_toSubPicCondition
  AlgebraicGeometry.RelPicard.LFP.stageHom_val
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_hom_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_inv_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.restrict_P
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp
  AlgebraicGeometry.RelEffCartierDiv.functor_map_fst
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_pullbackAlong
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_symm_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp_assoc
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top
  AlgebraicGeometry.RelEffCartierDiv.mem_supportedIn_iff
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top_eq
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
  CoherentBaseChange.FibreH0Family.mk.sizeOf_spec
  CoherentBaseChange.FibreH0Family.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.sizeOf_spec
  AlgebraicCurve.CurveModel.coe_gInf
  AlgebraicCurve.CurveModel.coe_tInvChart
  AlgebraicCurve.CurveModel.ιInf_gluedToBase_assoc
  AlgebraicCurve.CurveModel.ιInf_gluedToBase
  AlgebraicCurve.CurveModel.primeOfι₀_asIdeal
  AlgebraicCurve.CurveModel.coe_tChart
  AlgebraicCurve.CurveModel.ι₀_gluedToBase_assoc
  AlgebraicCurve.CurveModel.primeOfιInf_asIdeal
attribute [-simp]
  AlgebraicCurve.CurveModel.ι₀_gluedToBase
  AlgebraicCurve.CurveModel.coe_tma
  AlgebraicCurve.CurveModel.coe_primeEquivChartPlaces
universe u
noncomputable section
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.CategoryTheory.CartesianMonoidalCategory
open _root_.AlgebraicGeometry.RelPicard
open _root_.NeronModelInfra
namespace P2mCubeAssembly
section Slices
variable {k : Type u} [Field k]
local notation "Sk" => Spec (CommRingCat.of k)

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.ThreeSlices
attribute [-instance]
  AlgebraicGeometry.SmoothOfRelativeDimension.fiberToSpecResidueField
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_snd
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_fst
  AlgebraicGeometry.SmoothOfRelativeDimension.smooth_one
  AlgebraicGeometry.SmoothProperCurve.isIntegral_pullback_Spec_field
  AlgebraicGeometry.IsProper.fiberToSpecResidueField
  AlgebraicCurve.CurveModel.isProper
  AlgebraicCurve.CurveModel.isIntegral
  AlgebraicCurve.CurveModel.smooth
  AlgebraicCurve.Place.instIsScalarTowerSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Divisor.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instSMulAlgEquiv
  AlgebraicCurve.Place.instIsPrincipalIdealRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instIsDiscreteValuationRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Pic0.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instAlgebraSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instMulActionAlgEquiv
  AlgebraicCurve.Pic0.instSMulAlgEquiv
  TwoChartCech.Sections.M0_moduleA
  TwoChartCech.Sections.M1_module
  TwoChartCech.Cover.A01_algebra
  TwoChartCech.Cover.A0_algebra
  TwoChartCech.Cover.A1_commRing
  TwoChartCech.Cover.A1_algebra
  TwoChartCech.Sections.M01_module
  TwoChartCech.Sections.M0_addCommGroup
  TwoChartCech.Sections.M0_tower
  TwoChartCech.Sections.M01_addCommGroup
  TwoChartCech.Cover.A0_commRing
  TwoChartCech.Sections.M1_tower
  TwoChartCech.Sections.M01_moduleA
  TwoChartCech.Sections.M0_module
  TwoChartCech.Sections.M1_moduleA
  TwoChartCech.Sections.M1_addCommGroup
  TwoChartCech.Cover.A01_commRing
  TwoChartCech.Sections.M01_tower
  CoherentBaseChange.TwoTermComplex.C0_module
  CoherentBaseChange.TwoTermComplex.C0_addCommGroup
  CoherentBaseChange.TwoTermComplex.C1_module
  CoherentBaseChange.TwoTermComplex.C1_addCommGroup
attribute [-instance]
  CoherentBaseChange.TwoTermComplex.C0_free
  CoherentBaseChange.TwoTermComplex.C1_finite
  CoherentBaseChange.TwoTermComplex.C0_finite
  CoherentBaseChange.TwoTermComplex.C1_free
  AlgebraicCurve.IsCurveOver.instNontrivialKaehler
  AlgebraicCurve.IsCurveOver.instFreeKaehler
  AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
  AlgebraicCurve.IsCurveOver.instFiniteResidue
attribute [-instance]
  instIsLocallyInjectiveFunUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsLocallySurjectiveUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsOpenImmersionToGlued
attribute [-instance]
  instIsIsoSheafZariskiTopologyTypeUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.RelPicard.isOpenImmersion_toGlued
  AlgebraicGeometry.Scheme.Modules.preservesBinaryProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback_monoidal
  AlgebraicGeometry.Scheme.Modules.sheafify_isLocalization'
  AlgebraicGeometry.Scheme.Modules.preservesTerminal_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback₀_monoidal
  AlgebraicGeometry.Scheme.Modules.preservesFiniteProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.sheafifyPullback_lifting
  PresheafOfModules.PullbackMonoidal.pullback_monoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ
  PresheafOfModules.pushforward_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_η
  PresheafOfModules.free_monoidal
  PresheafOfModules.restrictScalars_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ_gS
  PresheafOfModules.pullback_oplaxMonoidal
attribute [-instance]
  instPreservesColimitsOfSizeCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierPb
attribute [-instance]
  PresheafOfModules.pullback_monoidal'
  AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
  AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
  AlgebraicCurve.Place.instIsPrimeCenter
  AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
  instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
  AlgebraicCurve.Pic0.instModuleZModTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instSMulTorsion
  AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
  AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
  AlgebraicCurve.RationalFunctionField.instNontrivialInftyValueGroup
  PresheafOfModules.ExteriorPower.instModulePresheafAb
  AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
  AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
  AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
  AlgebraicGeometry.isClosedImmersion_graphOver
  AlgebraicGeometry.FGSubalgebra.instIsDirectedLe
attribute [-instance]
  instQuasiSeparatedSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsCofilteredOpposite
  AlgebraicGeometry.FGSubalgebra.instIsAffineObjOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instNonempty
  AlgebraicGeometry.FGSubalgebra.instNonemptySubtypeLeSubalgebraValFG
attribute [-instance]
  instCompactSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsDirectedSubtypeLeSubalgebraValFG
  AlgebraicGeometry.FGSubalgebra.instIsAffineHomMapOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instIsFiltered
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instNeg
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulInt
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAddCommGroup
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAdd
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSub
attribute [-instance]
  instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
  AlgebraicCurve.instHasLocalResidue_of_hasCanonicalLocalResidueK
  AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
  AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
  ModularCurve.KwF4gRRTate.instAlgebraKAdicCompletionIntegers
  AlgebraicCurve.Place.kw_ffgc_continuousSMul_adicCompletionComap
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersCompletionCompletion
attribute [-instance]
  instLiesOverSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegersCompletionIdealAsIdeal
attribute [-instance]
  AlgebraicCurve.instHasCanonicalLocalResidueK
  AlgebraicCurve.Place.instAlgebra_restrictResidueField
  AlgebraicCurve.Place.instIsScalarTower_restrictResidueField
  AlgebraicCurve.instHasLocalResidue
  AlgebraicCurve.HasSeparableResidue.of_perfectField_of_isCurveOver
  AlgebraicCurve.HasSeparableResidue.of_perfectField
  AlgebraicCurve.Place.instIsLocalHom_restrictSubringHom
  AlgebraicCurve.instHasCanonicalLocalResidueKStar
  ModularCurve.KwNo6Pin.isLocalRing_completion
  SheafOfModules.isIso_ihomModelToIhom
  AlgebraicGeometry.OModulePresheaf.isScalarTower
  AlgebraicGeometry.Scheme.OrderedAffineCover.instLinearOrder
  AlgebraicGeometry.OModulePresheaf.module
  AlgebraicGeometry.Scheme.OrderedAffineCover.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCover.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.addCommGroup
  AlgebraicGeometry.Scheme.OrderedAffineCover.instDecidableEqIdx
  AlgebraicGeometry.OModulePresheaf.moduleSections
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.instSubsingletonObjZero
attribute [-instance]
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
  AlgebraicGeometry.OModulePresheaf.Leray.biC_module
  DoubleComplex.instModuleE₂I
  DoubleComplex.Bounded.modR
  DoubleComplex.instModuleE₂II
  DoubleComplex.instAddCommGroupE₂II
  DoubleComplex.Bounded.abGrp
  DoubleComplex.instAddCommGroupE₂I
  AlgebraicGeometry.ChowDatum.hι_closed
  AlgebraicGeometry.ChowDatumProj.hιN_closed
  AlgebraicGeometry.ChowDatumProj.hp_proper
  AlgebraicGeometry.ChowDatum.hp_isoU
  AlgebraicGeometry.ChowDatum.hp_proper
  AlgebraicGeometry.ProjSpace.algebraAway
  AlgebraicGeometry.ProjSpace.instIsProperProdOverπ
  AlgebraicGeometry.ChowDatumProj.hp_isoU
  AlgebraicGeometry.ProjSpace.isProper_π
  AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
  ProjSpaceCech.GradedModule.H.module
  ProjSpaceCech.GradedModule.H.addCommGroup
  ProjSpaceCech.GradedModule.sec.instAdd
  ProjSpaceCech.GradedModule.sec.instNeg
  ProjSpaceCech.GradedModule.acg
  ProjSpaceCech.GradedModule.Frac.setoid
  ProjSpaceCech.GradedModule.modR
  ProjSpaceCech.GradedModule.sec.instModule
  ProjSpaceCech.GradedModule.sec.instAddCommGroup
  ProjSpaceCech.GradedModule.sec.instZero
  ProjSpaceCech.GradedModule.Presentation.fJ
  ProjSpaceCech.GradedModule.sec.instSMul
  ProjSpaceCech.Twist.H.module
  ProjSpaceCech.Idx.instFintype
  ProjSpaceCech.Twist.H.addCommGroup
attribute [-instance]
  ProjSpaceCech.Idx.instDecidableEq
  ProjSpaceCech.Twist.Mon.instDecidableEq
  ProjSpaceCech.Twist.cochain.instAddCommGroup
  ProjSpaceCech.Twist.cochain.instModule
  AlgebraicGeometry.FGSubalgebra.tensorStage_directedSystem
  AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
  AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
  AlgebraicCurve.CurveModel.locallyOfFiniteType_gluedToBase
  AlgebraicCurve.CurveModel.isFractionRing_overlap
  AlgebraicCurve.CurveModel.isLocallyNoetherian_glued
  AlgebraicCurve.CurveModel.jacobsonSpace_glued
  AlgebraicCurve.CurveModel.isOpenImmersion_ι₀
  AlgebraicCurve.CurveModel.isIntegral_glued
  AlgebraicCurve.CurveModel.quasiSeparated_gluedToBase
  AlgebraicCurve.CurveModel.compactSpace_glued
  AlgebraicCurve.CurveModel.isIntegral_adjoin_chartRing
  AlgebraicCurve.CurveModel.isFractionRing_overlap_functionField
  AlgebraicCurve.CurveModel.isProper_gluedToBase
  AlgebraicCurve.CurveModel.isOpenImmersion_ιU
  AlgebraicCurve.CurveModel.isOpenImmersion_f₀
  AlgebraicCurve.CurveModel.isOpenImmersion_fInf
  AlgebraicCurve.CurveModel.isOpenImmersion_ιInf
  AlgebraicCurve.CurveModel.algebra_overlap_functionField
  AlgebraicCurve.CurveModel.quasiCompact_gluedToBase
  AlgebraicCurve.CurveModel.algebraAdjoin
  AlgebraicCurve.CurveModel.isDedekindDomain_chartRing
  AlgebraicCurve.CurveModel.isIntegralClosure
  AlgebraicCurve.CurveModel.finite_chartRing
  AlgebraicCurve.CurveModel.centre_isPrime
  AlgebraicCurve.CurveModel.isFractionRing_chartRing
  AlgebraicCurve.CurveModel.finiteType_chartRing
  AlgebraicCurve.CurveModel.isNoetherianRing_chartRing
  AlgebraicCurve.CurveModel.isScalarTower_base_adjoin
  AlgebraicCurve.CurveModel.isScalarTower_adjoin
  AlgebraicCurve.CurveModel.chartRing_finitePresentation
attribute [-simp]
  GoodReductionJacobian.RelativePic0Designation.mk.sizeOf_spec
  GoodReductionJacobian.AvatarSchemeBridge.mk.injEq
  GoodReductionJacobian.AvatarSchemeBridge.mk.sizeOf_spec
  GoodReductionJacobian.RelativePic0Designation.mk.injEq
  GoodReductionJacobian.schemeHomOverComp_coe
  NeronModelInfra.schemeHomOverEquivOverHom_apply
  GoodReductionJacobian.RelativeGroupLaw.mk.sizeOf_spec
  NeronModelInfra.schemeHomOverEquivOverHom_symm_apply
  NeronModelInfra.overHomToSchemeHomOver_coe
  GoodReductionJacobian.RelativeGroupLaw.mk.injEq
  NeronModelInfra.overHomToSchemeHomOver_schemeHomOverToOverHom
  NeronModelInfra.schemeHomOverToOverHom_left
  NeronModelInfra.schemeHomOverToOverHom_overHomToSchemeHomOver
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.sizeOf_spec
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
  AlgebraicCurve.CurveModel.mk.injEq
  AlgebraicCurve.CurveModel.mk.sizeOf_spec
  AlgebraicCurve.Place.mk.injEq
  AlgebraicCurve.Divisor.degree_single
  AlgebraicCurve.Divisor.smul_single
  AlgebraicCurve.Place.smul_toValuationSubring
  AlgebraicCurve.Place.heightOneSpectrum_asIdeal
  AlgebraicCurve.Place.coe_algebraMap
  AlgebraicCurve.Place.ord_one
  AlgebraicCurve.Place.coe_smulRingEquiv_apply
  AlgebraicCurve.Pic0.coe_degZeroSMulHom
  AlgebraicCurve.Place.deg_smul
  AlgebraicCurve.Pic0.mk_zero
  AlgebraicCurve.Place.mk.sizeOf_spec
  AlgebraicCurve.Divisor.degree_smul
  AlgebraicCurve.Pic0.mk_add
  AlgebraicCurve.Place.ord_zero
  AlgebraicCurve.Place.ofHeightOneSpectrum_toValuationSubring
  AlgebraicCurve.mulAdele_apply
attribute [-simp]
  AlgebraicCurve.residuePairing_apply_coe
  AlgebraicCurve.mem_adeleBdd
  AlgebraicCurve.weilSmul_one
  AlgebraicCurve.diagonalHom_apply
  AlgebraicCurve.weilSmul_apply
  AlgebraicCurve.adeleSpaceMul_coe
  AlgebraicCurve.mulAdele_one
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U1
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.injEq
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U0
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.mk.injEq
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.pullback_U1
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.pullback_U0
  TwoChartCech.Sections.mk.injEq
  TwoChartCech.Cover.mk.injEq
  TwoChartCech.GrothendieckComplex.mk.injEq
  TwoChartCech.Sections.mk.sizeOf_spec
  TwoChartCech.Cover.mk.sizeOf_spec
  TwoChartCech.Cover.lineBundle_r0_apply
  TwoChartCech.GrothendieckComplex.mk.sizeOf_spec
  TwoChartCech.Cover.lineBundle_r1_apply
  CoherentBaseChange.TwoTermComplex.mk.sizeOf_spec
  CoherentBaseChange.TwoTermComplex.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
  AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
  CategoryTheory.Functor.OverTotal.ofFibre_fst
  CategoryTheory.Functor.overTotal_map_fst
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_J
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYoneda_toGlued_uliftYonedaGluedToSheaf
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t'
attribute [-simp]
  uliftYoneda_toGlued_uliftYonedaGluedToSheaf_assoc
attribute [-simp]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_toGlued
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_openCover_map
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_comp
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_V
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_U
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_f
attribute [-simp]
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_P
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_toBase
  AlgebraicGeometry.RelPicard.rigSection_snd
  AlgebraicGeometry.RelPicard.RigidifiedLineBundle.ofInvertible_L
  AlgebraicGeometry.RelPicard.rigSection_snd_assoc
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
  GoodReductionJacobian.relativeGroupLawOfGrpObj_inv
  GoodReductionJacobian.relativeGroupLawOfGrpObj_mul
  GoodReductionJacobian.overHomEquivSchemeHomOver_apply_coe
  GoodReductionJacobian.relativeGroupLawOfGrpObj_one
  GoodReductionJacobian.overHomEquivSchemeHomOver_symm_apply_left
  PresheafOfModules.freeεIso_hom_app
  PresheafOfModules.freeμIso_hom_app
  AlgebraicCurve.coe_cechH0Equiv_apply
  AlgebraicCurve.cechH1ToH1_mk
  AlgebraicCurve.lSpaceOn_univ
  AlgebraicCurve.lSpaceOn_empty
  AlgebraicCurve.Place.congrEquiv_symm_apply
  AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
  AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
  AlgebraicCurve.Place.congrEquiv_apply
  AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
  AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
  AlgebraicCurve.Divisor.mapRestrict_single
  AlgebraicCurve.Divisor.pushforward_single
  AlgebraicCurve.Place.coe_restrictInclusion
  AlgebraicCurve.Place.mem_fiber
  AlgebraicCurve.Place.restrict_toValuationSubring
  AlgebraicCurve.Divisor.degree_pushforward
  AlgebraicCurve.Place.restrictResidueMap_residue
  AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
  AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
  AlgebraicCurve.Place.placeOfPrime_toValuationSubring
  AlgebraicCurve.Place.mem_fiberOver
  AlgebraicCurve.Place.fiberEquiv_symm_apply
  AlgebraicCurve.Place.fiberEquiv_apply
  AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
attribute [-simp]
  AlgebraicCurve.Divisor.degree_pushforwardAlong
  AlgebraicCurve.Pic0.coe_degZeroCorrespondence
  AlgebraicCurve.Place.mem_fiberAlong
  AlgebraicCurve.SemilinearAut.toRingAut_inv
  AlgebraicCurve.SemilinearAut.smul_def
  AlgebraicCurve.SemilinearAut.smul_single
  AlgebraicCurve.SemilinearAut.smul_toValuationSubring
  AlgebraicCurve.SemilinearAut.baseAut_inv
  AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_one
  AlgebraicCurve.SemilinearAut.deg_smul
  AlgebraicCurve.SemilinearAut.degree_smul
  AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
  AlgebraicCurve.SemilinearAut.baseAut_mul
  AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
  AlgebraicCurve.SemilinearAut.baseAut_one
  AlgebraicCurve.SemilinearAut.ofAlgAut_smul
  AlgebraicCurve.SemilinearAut.coe_torsion_smul
  AlgebraicCurve.SemilinearAut.toRingAut_mul
attribute [-simp]
  AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeInfty
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_some
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeOfPoint
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_none
  AlgebraicCurve.Divisor.evalFun_zero
  AlgebraicCurve.Place.evalAt_one
  AlgebraicCurve.Place.differentialCoeff_zero
  AlgebraicCurve.Place.differentialCoeff_dCoord
  AlgebraicCurve.TranscendenceTower.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
  AlgebraicCurve.TranscendenceTower.mk.injEq
  AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec
  AlgebraicCurve.PoleDivisorPackage.mk.injEq
  AlgebraicGeometry.RelPicard.thetaBundle_def
attribute [-simp]
  AlgebraicGeometry.RelPicard.picardBundle_def
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_ofRelEffDivisor
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_I
  AlgebraicGeometry.mapOnProdOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.mk.sizeOf_spec
  AlgebraicGeometry.RelEffCartierDiv.mk.injEq
  AlgebraicGeometry.mapOnProdOver_snd
  AlgebraicGeometry.mapOnProdOver_fst
  AlgebraicGeometry.mapOnProdOver_snd_assoc
  AlgebraicGeometry.mapOnProdOver_id
  AlgebraicCurve.RelEffDivisor.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_fst
  AlgebraicCurve.mapOnProd_fst_assoc
  AlgebraicCurve.mapOnProd_snd
  AlgebraicCurve.UnivDivisorPack.mk.injEq
  AlgebraicCurve.RelEffDivisor.mk.injEq
  AlgebraicCurve.UnivDivisorPack.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_snd_assoc
  AlgebraicGeometry.Scheme.Modules.exteriorPower_obj
  PresheafOfModules.exteriorPower_map_ιMulti
  PresheafOfModules.ExteriorPower.appₗ_apply
  AlgebraicGeometry.prodKerGraph_one
  AlgebraicGeometry.fibrePowOver.proj_comp
  AlgebraicGeometry.prodKerGraph_zero
  AlgebraicGeometry.RelEffCartierDiv.empty_I
  AlgebraicGeometry.fibrePowOver.proj_comp_assoc
  AlgebraicGeometry.graphOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
  AlgebraicGeometry.graphOver_fst
  AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
  AlgebraicGeometry.graphOver_snd
  AlgebraicGeometry.graphOver_snd_assoc
  AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
  AlgebraicCurve.SymmetricPowerPackage.mk.injEq
  AlgebraicGeometry.FGSubalgebra.cocone_ι_app_apply
  AlgebraicGeometry.RelPicard.fst_toProdSpec
  AlgebraicGeometry.RelPicard.toProdSpec_fst_assoc
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_cons
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_nil
attribute [-simp]
  AlgebraicGeometry.RelPicard.fst_toProdSpec_assoc
  AlgebraicGeometry.RelPicard.toProdSpec_fst
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.sizeOf_spec
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.injEq
  AlgebraicCurve.adeleSingle_coe
  AlgebraicCurve.kaehlerResidueTermKFam_apply
  AlgebraicCurve.Place.LocalResidueData.mk.injEq
  AlgebraicCurve.Place.LocalResidueData.mk.sizeOf_spec
  AlgebraicCurve.Place.kw_ffgc_adicCompletionComapIntegers_coe
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.sizeOf_spec
  AlgebraicCurve.Place.mem_simplePoleSubmodule
  AlgebraicCurve.Place.coe_uniformizerSubring
  ModularCurve.Lg37.Lg37CompletionSection.mk.injEq
  AlgebraicCurve.Place.CoefficientFieldSection.mk.injEq
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.injEq
  ModularCurve.Lg37.Lg37CompletionSection.mk.sizeOf_spec
  AlgebraicCurve.Place.CoefficientFieldSection.mk.sizeOf_spec
  AlgebraicCurve.Place.poleSubmodule_one
  AlgebraicCurve.Place.mem_poleSubmodule
  AlgebraicGeometry.Scheme.Modules.toUnitSection_ofUnitSection
  AlgebraicGeometry.Scheme.Modules.pullbackSection_def
  AlgebraicGeometry.Scheme.Modules.ofUnitSection_toUnitSection
  PresheafOfModules.InternalHom.IsSheafAux.appAt_toPresheafHom
attribute [-simp]
  SheafOfModules.ihomSectionsEquivFamily_unit
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_apply
  SheafOfModules.ihomEval_unit_app
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_right
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_left
  AlgebraicGeometry.Scheme.Modules.homOfFamily_app_apply
  SheafOfModules.unit_ihomSectionsEquivFamily
  AlgebraicGeometry.Scheme.Modules.familyOfHom_app
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_hom_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_inv_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomOfFamily_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_symm_apply
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_right
  AlgebraicGeometry.Scheme.Modules.map_unitSection
  AlgebraicGeometry.Scheme.Modules.tensorSectionsBilin_apply
  AlgebraicGeometry.Scheme.Modules.tensorPowSection_zero
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_left
  AlgebraicGeometry.Scheme.Modules.tensorPow_zero
  AlgebraicGeometry.Scheme.Modules.tensorPow_succ
  AlgebraicGeometry.Scheme.OrderedAffineCover.mk.injEq
  AlgebraicGeometry.OModulePresheaf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCover.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.mk.injEq
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_neg
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_zero
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_sub
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_add
  AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
  AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U
  AlgebraicGeometry.OModulePresheaf.Hom.mk.injEq
  AlgebraicGeometry.OModulePresheaf.Hom.id_app
  AlgebraicGeometry.OModulePresheaf.AffHom.appSections_apply
  AlgebraicGeometry.OModulePresheaf.AffHom.comp_app
  AlgebraicGeometry.OModulePresheaf.AffSES.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.AffHom.kerMap_coe
  AlgebraicGeometry.OModulePresheaf.AffHom.id_app
  AlgebraicGeometry.OModulePresheaf.Hom.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.Hom.toAffHom_app
attribute [-simp]
  AlgebraicGeometry.OModulePresheaf.SES.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.AffHom.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.Hom.comp_app
  AlgebraicGeometry.OModulePresheaf.SES.mk.injEq
  AlgebraicGeometry.OModulePresheaf.AffHom.mk.injEq
  AlgebraicGeometry.OModulePresheaf.Hom.appSections_apply
  AlgebraicGeometry.OModulePresheaf.AffSES.mk.injEq
  AlgebraicGeometry.OModulePresheaf.prod_obj
  AlgebraicGeometry.OModulePresheaf.restrOpen_obj
  AlgebraicGeometry.OModulePresheaf.DevissageStep.mk.injEq
  AlgebraicGeometry.OModulePresheaf.pushforward_obj
  AlgebraicGeometry.OModulePresheaf.im_obj
  AlgebraicGeometry.OModulePresheaf.pow_obj
  AlgebraicGeometry.OModulePresheaf.fstHom_app
  AlgebraicGeometry.OModulePresheaf.ker_obj
  AlgebraicGeometry.OModulePresheaf.coker_obj
  AlgebraicGeometry.OModulePresheaf.DevissageStep.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCover.preimage_U
  AlgebraicGeometry.OModulePresheaf.sndHom_app
  AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
  DoubleComplex.Bounded.mk.injEq
  DoubleComplex.Bounded.mk.sizeOf_spec
  DoubleComplex.Convergence.mk.injEq
  DoubleComplex.Convergence.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.injEq
  AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatumProj.mk.injEq
  AlgebraicGeometry.ChowDatum.mk.injEq
  ProjSpaceCech.GradedModule.mk.injEq
  ProjSpaceCech.GradedModule.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Presentation.mk.injEq
  ProjSpaceCech.GradedModule.Frac.mk.injEq
  ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.shift_toLinearMap
  ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.mk.injEq
  TwoChartCech.Mumford.dK_apply
attribute [-simp]
  TwoChartCech.Mumford.ι0_apply
  TwoChartCech.Mumford.ι1_apply
  TwoChartCech.KerCoprod.dK_apply
  TwoChartCech.KerCoprod.ι1_apply
  TwoChartCech.KerCoprod.ι0_apply
  AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
  AlgebraicGeometry.RelPicard.algEquivZeroGroupCut_toSubPicCondition
  AlgebraicGeometry.RelPicard.LFP.stageHom_val
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_hom_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_inv_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.restrict_P
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp
  AlgebraicGeometry.RelEffCartierDiv.functor_map_fst
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_pullbackAlong
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_symm_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp_assoc
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top
  AlgebraicGeometry.RelEffCartierDiv.mem_supportedIn_iff
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top_eq
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
  CoherentBaseChange.FibreH0Family.mk.sizeOf_spec
  CoherentBaseChange.FibreH0Family.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.sizeOf_spec
  AlgebraicCurve.CurveModel.coe_gInf
  AlgebraicCurve.CurveModel.coe_tInvChart
  AlgebraicCurve.CurveModel.ιInf_gluedToBase_assoc
  AlgebraicCurve.CurveModel.ιInf_gluedToBase
  AlgebraicCurve.CurveModel.primeOfι₀_asIdeal
  AlgebraicCurve.CurveModel.coe_tChart
  AlgebraicCurve.CurveModel.ι₀_gluedToBase_assoc
  AlgebraicCurve.CurveModel.primeOfιInf_asIdeal
attribute [-simp]
  AlgebraicCurve.CurveModel.ι₀_gluedToBase
  AlgebraicCurve.CurveModel.coe_tma
  AlgebraicCurve.CurveModel.coe_primeEquivChartPlaces
universe u
noncomputable section
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.CategoryTheory.CartesianMonoidalCategory
open _root_.AlgebraicGeometry.RelPicard
open _root_.NeronModelInfra
namespace P2mCubeAssembly
section Slices
variable {k : Type u} [Field k]
local notation "Sk" => Spec (CommRingCat.of k)

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.ThreeSlices
attribute [-instance]
  AlgebraicGeometry.SmoothOfRelativeDimension.fiberToSpecResidueField
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_snd
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_fst
  AlgebraicGeometry.SmoothOfRelativeDimension.smooth_one
  AlgebraicGeometry.SmoothProperCurve.isIntegral_pullback_Spec_field
  AlgebraicGeometry.IsProper.fiberToSpecResidueField
  AlgebraicCurve.CurveModel.isProper
  AlgebraicCurve.CurveModel.isIntegral
  AlgebraicCurve.CurveModel.smooth
  AlgebraicCurve.Place.instIsScalarTowerSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Divisor.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instSMulAlgEquiv
  AlgebraicCurve.Place.instIsPrincipalIdealRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instIsDiscreteValuationRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Pic0.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instAlgebraSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instMulActionAlgEquiv
  AlgebraicCurve.Pic0.instSMulAlgEquiv
  TwoChartCech.Sections.M0_moduleA
  TwoChartCech.Sections.M1_module
  TwoChartCech.Cover.A01_algebra
  TwoChartCech.Cover.A0_algebra
  TwoChartCech.Cover.A1_commRing
  TwoChartCech.Cover.A1_algebra
  TwoChartCech.Sections.M01_module
  TwoChartCech.Sections.M0_addCommGroup
  TwoChartCech.Sections.M0_tower
  TwoChartCech.Sections.M01_addCommGroup
  TwoChartCech.Cover.A0_commRing
  TwoChartCech.Sections.M1_tower
  TwoChartCech.Sections.M01_moduleA
  TwoChartCech.Sections.M0_module
  TwoChartCech.Sections.M1_moduleA
  TwoChartCech.Sections.M1_addCommGroup
  TwoChartCech.Cover.A01_commRing
  TwoChartCech.Sections.M01_tower
  CoherentBaseChange.TwoTermComplex.C0_module
  CoherentBaseChange.TwoTermComplex.C0_addCommGroup
  CoherentBaseChange.TwoTermComplex.C1_module
  CoherentBaseChange.TwoTermComplex.C1_addCommGroup
attribute [-instance]
  CoherentBaseChange.TwoTermComplex.C0_free
  CoherentBaseChange.TwoTermComplex.C1_finite
  CoherentBaseChange.TwoTermComplex.C0_finite
  CoherentBaseChange.TwoTermComplex.C1_free
  AlgebraicCurve.IsCurveOver.instNontrivialKaehler
  AlgebraicCurve.IsCurveOver.instFreeKaehler
  AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
  AlgebraicCurve.IsCurveOver.instFiniteResidue
attribute [-instance]
  instIsLocallyInjectiveFunUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsLocallySurjectiveUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsOpenImmersionToGlued
attribute [-instance]
  instIsIsoSheafZariskiTopologyTypeUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.RelPicard.isOpenImmersion_toGlued
  AlgebraicGeometry.Scheme.Modules.preservesBinaryProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback_monoidal
  AlgebraicGeometry.Scheme.Modules.sheafify_isLocalization'
  AlgebraicGeometry.Scheme.Modules.preservesTerminal_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback₀_monoidal
  AlgebraicGeometry.Scheme.Modules.preservesFiniteProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.sheafifyPullback_lifting
  PresheafOfModules.PullbackMonoidal.pullback_monoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ
  PresheafOfModules.pushforward_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_η
  PresheafOfModules.free_monoidal
  PresheafOfModules.restrictScalars_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ_gS
  PresheafOfModules.pullback_oplaxMonoidal
attribute [-instance]
  instPreservesColimitsOfSizeCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierPb
attribute [-instance]
  PresheafOfModules.pullback_monoidal'
  AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
  AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
  AlgebraicCurve.Place.instIsPrimeCenter
  AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
  instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
  AlgebraicCurve.Pic0.instModuleZModTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instSMulTorsion
  AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
  AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
  AlgebraicCurve.RationalFunctionField.instNontrivialInftyValueGroup
  PresheafOfModules.ExteriorPower.instModulePresheafAb
  AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
  AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
  AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
  AlgebraicGeometry.isClosedImmersion_graphOver
  AlgebraicGeometry.FGSubalgebra.instIsDirectedLe
attribute [-instance]
  instQuasiSeparatedSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsCofilteredOpposite
  AlgebraicGeometry.FGSubalgebra.instIsAffineObjOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instNonempty
  AlgebraicGeometry.FGSubalgebra.instNonemptySubtypeLeSubalgebraValFG
attribute [-instance]
  instCompactSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsDirectedSubtypeLeSubalgebraValFG
  AlgebraicGeometry.FGSubalgebra.instIsAffineHomMapOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instIsFiltered
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instNeg
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulInt
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAddCommGroup
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAdd
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSub
attribute [-instance]
  instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
  AlgebraicCurve.instHasLocalResidue_of_hasCanonicalLocalResidueK
  AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
  AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
  ModularCurve.KwF4gRRTate.instAlgebraKAdicCompletionIntegers
  AlgebraicCurve.Place.kw_ffgc_continuousSMul_adicCompletionComap
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersCompletionCompletion
attribute [-instance]
  instLiesOverSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegersCompletionIdealAsIdeal
attribute [-instance]
  AlgebraicCurve.instHasCanonicalLocalResidueK
  AlgebraicCurve.Place.instAlgebra_restrictResidueField
  AlgebraicCurve.Place.instIsScalarTower_restrictResidueField
  AlgebraicCurve.instHasLocalResidue
  AlgebraicCurve.HasSeparableResidue.of_perfectField_of_isCurveOver
  AlgebraicCurve.HasSeparableResidue.of_perfectField
  AlgebraicCurve.Place.instIsLocalHom_restrictSubringHom
  AlgebraicCurve.instHasCanonicalLocalResidueKStar
  ModularCurve.KwNo6Pin.isLocalRing_completion
  SheafOfModules.isIso_ihomModelToIhom
  AlgebraicGeometry.OModulePresheaf.isScalarTower
  AlgebraicGeometry.Scheme.OrderedAffineCover.instLinearOrder
  AlgebraicGeometry.OModulePresheaf.module
  AlgebraicGeometry.Scheme.OrderedAffineCover.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCover.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.addCommGroup
  AlgebraicGeometry.Scheme.OrderedAffineCover.instDecidableEqIdx
  AlgebraicGeometry.OModulePresheaf.moduleSections
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.instSubsingletonObjZero
attribute [-instance]
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
  AlgebraicGeometry.OModulePresheaf.Leray.biC_module
  DoubleComplex.instModuleE₂I
  DoubleComplex.Bounded.modR
  DoubleComplex.instModuleE₂II
  DoubleComplex.instAddCommGroupE₂II
  DoubleComplex.Bounded.abGrp
  DoubleComplex.instAddCommGroupE₂I
  AlgebraicGeometry.ChowDatum.hι_closed
  AlgebraicGeometry.ChowDatumProj.hιN_closed
  AlgebraicGeometry.ChowDatumProj.hp_proper
  AlgebraicGeometry.ChowDatum.hp_isoU
  AlgebraicGeometry.ChowDatum.hp_proper
  AlgebraicGeometry.ProjSpace.algebraAway
  AlgebraicGeometry.ProjSpace.instIsProperProdOverπ
  AlgebraicGeometry.ChowDatumProj.hp_isoU
  AlgebraicGeometry.ProjSpace.isProper_π
  AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
  ProjSpaceCech.GradedModule.H.module
  ProjSpaceCech.GradedModule.H.addCommGroup
  ProjSpaceCech.GradedModule.sec.instAdd
  ProjSpaceCech.GradedModule.sec.instNeg
  ProjSpaceCech.GradedModule.acg
  ProjSpaceCech.GradedModule.Frac.setoid
  ProjSpaceCech.GradedModule.modR
  ProjSpaceCech.GradedModule.sec.instModule
  ProjSpaceCech.GradedModule.sec.instAddCommGroup
  ProjSpaceCech.GradedModule.sec.instZero
  ProjSpaceCech.GradedModule.Presentation.fJ
  ProjSpaceCech.GradedModule.sec.instSMul
  ProjSpaceCech.Twist.H.module
  ProjSpaceCech.Idx.instFintype
  ProjSpaceCech.Twist.H.addCommGroup
attribute [-instance]
  ProjSpaceCech.Idx.instDecidableEq
  ProjSpaceCech.Twist.Mon.instDecidableEq
  ProjSpaceCech.Twist.cochain.instAddCommGroup
  ProjSpaceCech.Twist.cochain.instModule
  AlgebraicGeometry.FGSubalgebra.tensorStage_directedSystem
  AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
  AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
  AlgebraicCurve.CurveModel.locallyOfFiniteType_gluedToBase
  AlgebraicCurve.CurveModel.isFractionRing_overlap
  AlgebraicCurve.CurveModel.isLocallyNoetherian_glued
  AlgebraicCurve.CurveModel.jacobsonSpace_glued
  AlgebraicCurve.CurveModel.isOpenImmersion_ι₀
  AlgebraicCurve.CurveModel.isIntegral_glued
  AlgebraicCurve.CurveModel.quasiSeparated_gluedToBase
  AlgebraicCurve.CurveModel.compactSpace_glued
  AlgebraicCurve.CurveModel.isIntegral_adjoin_chartRing
  AlgebraicCurve.CurveModel.isFractionRing_overlap_functionField
  AlgebraicCurve.CurveModel.isProper_gluedToBase
  AlgebraicCurve.CurveModel.isOpenImmersion_ιU
  AlgebraicCurve.CurveModel.isOpenImmersion_f₀
  AlgebraicCurve.CurveModel.isOpenImmersion_fInf
  AlgebraicCurve.CurveModel.isOpenImmersion_ιInf
  AlgebraicCurve.CurveModel.algebra_overlap_functionField
  AlgebraicCurve.CurveModel.quasiCompact_gluedToBase
  AlgebraicCurve.CurveModel.algebraAdjoin
  AlgebraicCurve.CurveModel.isDedekindDomain_chartRing
  AlgebraicCurve.CurveModel.isIntegralClosure
  AlgebraicCurve.CurveModel.finite_chartRing
  AlgebraicCurve.CurveModel.centre_isPrime
  AlgebraicCurve.CurveModel.isFractionRing_chartRing
  AlgebraicCurve.CurveModel.finiteType_chartRing
  AlgebraicCurve.CurveModel.isNoetherianRing_chartRing
  AlgebraicCurve.CurveModel.isScalarTower_base_adjoin
  AlgebraicCurve.CurveModel.isScalarTower_adjoin
  AlgebraicCurve.CurveModel.chartRing_finitePresentation
attribute [-simp]
  GoodReductionJacobian.RelativePic0Designation.mk.sizeOf_spec
  GoodReductionJacobian.AvatarSchemeBridge.mk.injEq
  GoodReductionJacobian.AvatarSchemeBridge.mk.sizeOf_spec
  GoodReductionJacobian.RelativePic0Designation.mk.injEq
  GoodReductionJacobian.schemeHomOverComp_coe
  NeronModelInfra.schemeHomOverEquivOverHom_apply
  GoodReductionJacobian.RelativeGroupLaw.mk.sizeOf_spec
  NeronModelInfra.schemeHomOverEquivOverHom_symm_apply
  NeronModelInfra.overHomToSchemeHomOver_coe
  GoodReductionJacobian.RelativeGroupLaw.mk.injEq
  NeronModelInfra.overHomToSchemeHomOver_schemeHomOverToOverHom
  NeronModelInfra.schemeHomOverToOverHom_left
  NeronModelInfra.schemeHomOverToOverHom_overHomToSchemeHomOver
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.sizeOf_spec
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
  AlgebraicCurve.CurveModel.mk.injEq
  AlgebraicCurve.CurveModel.mk.sizeOf_spec
  AlgebraicCurve.Place.mk.injEq
  AlgebraicCurve.Divisor.degree_single
  AlgebraicCurve.Divisor.smul_single
  AlgebraicCurve.Place.smul_toValuationSubring
  AlgebraicCurve.Place.heightOneSpectrum_asIdeal
  AlgebraicCurve.Place.coe_algebraMap
  AlgebraicCurve.Place.ord_one
  AlgebraicCurve.Place.coe_smulRingEquiv_apply
  AlgebraicCurve.Pic0.coe_degZeroSMulHom
  AlgebraicCurve.Place.deg_smul
  AlgebraicCurve.Pic0.mk_zero
  AlgebraicCurve.Place.mk.sizeOf_spec
  AlgebraicCurve.Divisor.degree_smul
  AlgebraicCurve.Pic0.mk_add
  AlgebraicCurve.Place.ord_zero
  AlgebraicCurve.Place.ofHeightOneSpectrum_toValuationSubring
  AlgebraicCurve.mulAdele_apply
attribute [-simp]
  AlgebraicCurve.residuePairing_apply_coe
  AlgebraicCurve.mem_adeleBdd
  AlgebraicCurve.weilSmul_one
  AlgebraicCurve.diagonalHom_apply
  AlgebraicCurve.weilSmul_apply
  AlgebraicCurve.adeleSpaceMul_coe
  AlgebraicCurve.mulAdele_one
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U1
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.injEq
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U0
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.mk.injEq
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.pullback_U1
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.pullback_U0
  TwoChartCech.Sections.mk.injEq
  TwoChartCech.Cover.mk.injEq
  TwoChartCech.GrothendieckComplex.mk.injEq
  TwoChartCech.Sections.mk.sizeOf_spec
  TwoChartCech.Cover.mk.sizeOf_spec
  TwoChartCech.Cover.lineBundle_r0_apply
  TwoChartCech.GrothendieckComplex.mk.sizeOf_spec
  TwoChartCech.Cover.lineBundle_r1_apply
  CoherentBaseChange.TwoTermComplex.mk.sizeOf_spec
  CoherentBaseChange.TwoTermComplex.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
  AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
  CategoryTheory.Functor.OverTotal.ofFibre_fst
  CategoryTheory.Functor.overTotal_map_fst
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_J
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYoneda_toGlued_uliftYonedaGluedToSheaf
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t'
attribute [-simp]
  uliftYoneda_toGlued_uliftYonedaGluedToSheaf_assoc
attribute [-simp]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_toGlued
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_openCover_map
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_comp
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_V
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_U
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_f
attribute [-simp]
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_P
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_toBase
  AlgebraicGeometry.RelPicard.rigSection_snd
  AlgebraicGeometry.RelPicard.RigidifiedLineBundle.ofInvertible_L
  AlgebraicGeometry.RelPicard.rigSection_snd_assoc
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
  GoodReductionJacobian.relativeGroupLawOfGrpObj_inv
  GoodReductionJacobian.relativeGroupLawOfGrpObj_mul
  GoodReductionJacobian.overHomEquivSchemeHomOver_apply_coe
  GoodReductionJacobian.relativeGroupLawOfGrpObj_one
  GoodReductionJacobian.overHomEquivSchemeHomOver_symm_apply_left
  PresheafOfModules.freeεIso_hom_app
  PresheafOfModules.freeμIso_hom_app
  AlgebraicCurve.coe_cechH0Equiv_apply
  AlgebraicCurve.cechH1ToH1_mk
  AlgebraicCurve.lSpaceOn_univ
  AlgebraicCurve.lSpaceOn_empty
  AlgebraicCurve.Place.congrEquiv_symm_apply
  AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
  AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
  AlgebraicCurve.Place.congrEquiv_apply
  AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
  AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
  AlgebraicCurve.Divisor.mapRestrict_single
  AlgebraicCurve.Divisor.pushforward_single
  AlgebraicCurve.Place.coe_restrictInclusion
  AlgebraicCurve.Place.mem_fiber
  AlgebraicCurve.Place.restrict_toValuationSubring
  AlgebraicCurve.Divisor.degree_pushforward
  AlgebraicCurve.Place.restrictResidueMap_residue
  AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
  AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
  AlgebraicCurve.Place.placeOfPrime_toValuationSubring
  AlgebraicCurve.Place.mem_fiberOver
  AlgebraicCurve.Place.fiberEquiv_symm_apply
  AlgebraicCurve.Place.fiberEquiv_apply
  AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
attribute [-simp]
  AlgebraicCurve.Divisor.degree_pushforwardAlong
  AlgebraicCurve.Pic0.coe_degZeroCorrespondence
  AlgebraicCurve.Place.mem_fiberAlong
  AlgebraicCurve.SemilinearAut.toRingAut_inv
  AlgebraicCurve.SemilinearAut.smul_def
  AlgebraicCurve.SemilinearAut.smul_single
  AlgebraicCurve.SemilinearAut.smul_toValuationSubring
  AlgebraicCurve.SemilinearAut.baseAut_inv
  AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_one
  AlgebraicCurve.SemilinearAut.deg_smul
  AlgebraicCurve.SemilinearAut.degree_smul
  AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
  AlgebraicCurve.SemilinearAut.baseAut_mul
  AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
  AlgebraicCurve.SemilinearAut.baseAut_one
  AlgebraicCurve.SemilinearAut.ofAlgAut_smul
  AlgebraicCurve.SemilinearAut.coe_torsion_smul
  AlgebraicCurve.SemilinearAut.toRingAut_mul
attribute [-simp]
  AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeInfty
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_some
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeOfPoint
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_none
  AlgebraicCurve.Divisor.evalFun_zero
  AlgebraicCurve.Place.evalAt_one
  AlgebraicCurve.Place.differentialCoeff_zero
  AlgebraicCurve.Place.differentialCoeff_dCoord
  AlgebraicCurve.TranscendenceTower.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
  AlgebraicCurve.TranscendenceTower.mk.injEq
  AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec
  AlgebraicCurve.PoleDivisorPackage.mk.injEq
  AlgebraicGeometry.RelPicard.thetaBundle_def
attribute [-simp]
  AlgebraicGeometry.RelPicard.picardBundle_def
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_ofRelEffDivisor
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_I
  AlgebraicGeometry.mapOnProdOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.mk.sizeOf_spec
  AlgebraicGeometry.RelEffCartierDiv.mk.injEq
  AlgebraicGeometry.mapOnProdOver_snd
  AlgebraicGeometry.mapOnProdOver_fst
  AlgebraicGeometry.mapOnProdOver_snd_assoc
  AlgebraicGeometry.mapOnProdOver_id
  AlgebraicCurve.RelEffDivisor.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_fst
  AlgebraicCurve.mapOnProd_fst_assoc
  AlgebraicCurve.mapOnProd_snd
  AlgebraicCurve.UnivDivisorPack.mk.injEq
  AlgebraicCurve.RelEffDivisor.mk.injEq
  AlgebraicCurve.UnivDivisorPack.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_snd_assoc
  AlgebraicGeometry.Scheme.Modules.exteriorPower_obj
  PresheafOfModules.exteriorPower_map_ιMulti
  PresheafOfModules.ExteriorPower.appₗ_apply
  AlgebraicGeometry.prodKerGraph_one
  AlgebraicGeometry.fibrePowOver.proj_comp
  AlgebraicGeometry.prodKerGraph_zero
  AlgebraicGeometry.RelEffCartierDiv.empty_I
  AlgebraicGeometry.fibrePowOver.proj_comp_assoc
  AlgebraicGeometry.graphOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
  AlgebraicGeometry.graphOver_fst
  AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
  AlgebraicGeometry.graphOver_snd
  AlgebraicGeometry.graphOver_snd_assoc
  AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
  AlgebraicCurve.SymmetricPowerPackage.mk.injEq
  AlgebraicGeometry.FGSubalgebra.cocone_ι_app_apply
  AlgebraicGeometry.RelPicard.fst_toProdSpec
  AlgebraicGeometry.RelPicard.toProdSpec_fst_assoc
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_cons
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_nil
attribute [-simp]
  AlgebraicGeometry.RelPicard.fst_toProdSpec_assoc
  AlgebraicGeometry.RelPicard.toProdSpec_fst
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.sizeOf_spec
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.injEq
  AlgebraicCurve.adeleSingle_coe
  AlgebraicCurve.kaehlerResidueTermKFam_apply
  AlgebraicCurve.Place.LocalResidueData.mk.injEq
  AlgebraicCurve.Place.LocalResidueData.mk.sizeOf_spec
  AlgebraicCurve.Place.kw_ffgc_adicCompletionComapIntegers_coe
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.sizeOf_spec
  AlgebraicCurve.Place.mem_simplePoleSubmodule
  AlgebraicCurve.Place.coe_uniformizerSubring
  ModularCurve.Lg37.Lg37CompletionSection.mk.injEq
  AlgebraicCurve.Place.CoefficientFieldSection.mk.injEq
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.injEq
  ModularCurve.Lg37.Lg37CompletionSection.mk.sizeOf_spec
  AlgebraicCurve.Place.CoefficientFieldSection.mk.sizeOf_spec
  AlgebraicCurve.Place.poleSubmodule_one
  AlgebraicCurve.Place.mem_poleSubmodule
  AlgebraicGeometry.Scheme.Modules.toUnitSection_ofUnitSection
  AlgebraicGeometry.Scheme.Modules.pullbackSection_def
  AlgebraicGeometry.Scheme.Modules.ofUnitSection_toUnitSection
  PresheafOfModules.InternalHom.IsSheafAux.appAt_toPresheafHom
attribute [-simp]
  SheafOfModules.ihomSectionsEquivFamily_unit
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_apply
  SheafOfModules.ihomEval_unit_app
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_right
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_left
  AlgebraicGeometry.Scheme.Modules.homOfFamily_app_apply
  SheafOfModules.unit_ihomSectionsEquivFamily
  AlgebraicGeometry.Scheme.Modules.familyOfHom_app
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_hom_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_inv_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomOfFamily_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_symm_apply
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_right
  AlgebraicGeometry.Scheme.Modules.map_unitSection
  AlgebraicGeometry.Scheme.Modules.tensorSectionsBilin_apply
  AlgebraicGeometry.Scheme.Modules.tensorPowSection_zero
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_left
  AlgebraicGeometry.Scheme.Modules.tensorPow_zero
  AlgebraicGeometry.Scheme.Modules.tensorPow_succ
  AlgebraicGeometry.Scheme.OrderedAffineCover.mk.injEq
  AlgebraicGeometry.OModulePresheaf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCover.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.mk.injEq
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_neg
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_zero
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_sub
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_add
  AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
  AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U
  AlgebraicGeometry.OModulePresheaf.Hom.mk.injEq
  AlgebraicGeometry.OModulePresheaf.Hom.id_app
  AlgebraicGeometry.OModulePresheaf.AffHom.appSections_apply
  AlgebraicGeometry.OModulePresheaf.AffHom.comp_app
  AlgebraicGeometry.OModulePresheaf.AffSES.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.AffHom.kerMap_coe
  AlgebraicGeometry.OModulePresheaf.AffHom.id_app
  AlgebraicGeometry.OModulePresheaf.Hom.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.Hom.toAffHom_app
attribute [-simp]
  AlgebraicGeometry.OModulePresheaf.SES.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.AffHom.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.Hom.comp_app
  AlgebraicGeometry.OModulePresheaf.SES.mk.injEq
  AlgebraicGeometry.OModulePresheaf.AffHom.mk.injEq
  AlgebraicGeometry.OModulePresheaf.Hom.appSections_apply
  AlgebraicGeometry.OModulePresheaf.AffSES.mk.injEq
  AlgebraicGeometry.OModulePresheaf.prod_obj
  AlgebraicGeometry.OModulePresheaf.restrOpen_obj
  AlgebraicGeometry.OModulePresheaf.DevissageStep.mk.injEq
  AlgebraicGeometry.OModulePresheaf.pushforward_obj
  AlgebraicGeometry.OModulePresheaf.im_obj
  AlgebraicGeometry.OModulePresheaf.pow_obj
  AlgebraicGeometry.OModulePresheaf.fstHom_app
  AlgebraicGeometry.OModulePresheaf.ker_obj
  AlgebraicGeometry.OModulePresheaf.coker_obj
  AlgebraicGeometry.OModulePresheaf.DevissageStep.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCover.preimage_U
  AlgebraicGeometry.OModulePresheaf.sndHom_app
  AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
  DoubleComplex.Bounded.mk.injEq
  DoubleComplex.Bounded.mk.sizeOf_spec
  DoubleComplex.Convergence.mk.injEq
  DoubleComplex.Convergence.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.injEq
  AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatumProj.mk.injEq
  AlgebraicGeometry.ChowDatum.mk.injEq
  ProjSpaceCech.GradedModule.mk.injEq
  ProjSpaceCech.GradedModule.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Presentation.mk.injEq
  ProjSpaceCech.GradedModule.Frac.mk.injEq
  ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.shift_toLinearMap
  ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.mk.injEq
  TwoChartCech.Mumford.dK_apply
attribute [-simp]
  TwoChartCech.Mumford.ι0_apply
  TwoChartCech.Mumford.ι1_apply
  TwoChartCech.KerCoprod.dK_apply
  TwoChartCech.KerCoprod.ι1_apply
  TwoChartCech.KerCoprod.ι0_apply
  AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
  AlgebraicGeometry.RelPicard.algEquivZeroGroupCut_toSubPicCondition
  AlgebraicGeometry.RelPicard.LFP.stageHom_val
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_hom_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_inv_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.restrict_P
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp
  AlgebraicGeometry.RelEffCartierDiv.functor_map_fst
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_pullbackAlong
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_symm_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp_assoc
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top
  AlgebraicGeometry.RelEffCartierDiv.mem_supportedIn_iff
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top_eq
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
  CoherentBaseChange.FibreH0Family.mk.sizeOf_spec
  CoherentBaseChange.FibreH0Family.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.sizeOf_spec
  AlgebraicCurve.CurveModel.coe_gInf
  AlgebraicCurve.CurveModel.coe_tInvChart
  AlgebraicCurve.CurveModel.ιInf_gluedToBase_assoc
  AlgebraicCurve.CurveModel.ιInf_gluedToBase
  AlgebraicCurve.CurveModel.primeOfι₀_asIdeal
  AlgebraicCurve.CurveModel.coe_tChart
  AlgebraicCurve.CurveModel.ι₀_gluedToBase_assoc
  AlgebraicCurve.CurveModel.primeOfιInf_asIdeal
attribute [-simp]
  AlgebraicCurve.CurveModel.ι₀_gluedToBase
  AlgebraicCurve.CurveModel.coe_tma
  AlgebraicCurve.CurveModel.coe_primeEquivChartPlaces
universe u
noncomputable section
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.CategoryTheory.CartesianMonoidalCategory
open _root_.AlgebraicGeometry.RelPicard
open _root_.NeronModelInfra
namespace P2mCubeAssembly
section Slices
variable {k : Type u} [Field k]
local notation "Sk" => Spec (CommRingCat.of k)

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.ThreeSlices
attribute [-instance]
  AlgebraicGeometry.SmoothOfRelativeDimension.fiberToSpecResidueField
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_snd
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_fst
  AlgebraicGeometry.SmoothOfRelativeDimension.smooth_one
  AlgebraicGeometry.SmoothProperCurve.isIntegral_pullback_Spec_field
  AlgebraicGeometry.IsProper.fiberToSpecResidueField
  AlgebraicCurve.CurveModel.isProper
  AlgebraicCurve.CurveModel.isIntegral
  AlgebraicCurve.CurveModel.smooth
  AlgebraicCurve.Place.instIsScalarTowerSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Divisor.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instSMulAlgEquiv
  AlgebraicCurve.Place.instIsPrincipalIdealRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instIsDiscreteValuationRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Pic0.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instAlgebraSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instMulActionAlgEquiv
  AlgebraicCurve.Pic0.instSMulAlgEquiv
  TwoChartCech.Sections.M0_moduleA
  TwoChartCech.Sections.M1_module
  TwoChartCech.Cover.A01_algebra
  TwoChartCech.Cover.A0_algebra
  TwoChartCech.Cover.A1_commRing
  TwoChartCech.Cover.A1_algebra
  TwoChartCech.Sections.M01_module
  TwoChartCech.Sections.M0_addCommGroup
  TwoChartCech.Sections.M0_tower
  TwoChartCech.Sections.M01_addCommGroup
  TwoChartCech.Cover.A0_commRing
  TwoChartCech.Sections.M1_tower
  TwoChartCech.Sections.M01_moduleA
  TwoChartCech.Sections.M0_module
  TwoChartCech.Sections.M1_moduleA
  TwoChartCech.Sections.M1_addCommGroup
  TwoChartCech.Cover.A01_commRing
  TwoChartCech.Sections.M01_tower
  CoherentBaseChange.TwoTermComplex.C0_module
  CoherentBaseChange.TwoTermComplex.C0_addCommGroup
  CoherentBaseChange.TwoTermComplex.C1_module
  CoherentBaseChange.TwoTermComplex.C1_addCommGroup
attribute [-instance]
  CoherentBaseChange.TwoTermComplex.C0_free
  CoherentBaseChange.TwoTermComplex.C1_finite
  CoherentBaseChange.TwoTermComplex.C0_finite
  CoherentBaseChange.TwoTermComplex.C1_free
  AlgebraicCurve.IsCurveOver.instNontrivialKaehler
  AlgebraicCurve.IsCurveOver.instFreeKaehler
  AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
  AlgebraicCurve.IsCurveOver.instFiniteResidue
attribute [-instance]
  instIsLocallyInjectiveFunUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsLocallySurjectiveUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsOpenImmersionToGlued
attribute [-instance]
  instIsIsoSheafZariskiTopologyTypeUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.RelPicard.isOpenImmersion_toGlued
  AlgebraicGeometry.Scheme.Modules.preservesBinaryProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback_monoidal
  AlgebraicGeometry.Scheme.Modules.sheafify_isLocalization'
  AlgebraicGeometry.Scheme.Modules.preservesTerminal_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback₀_monoidal
  AlgebraicGeometry.Scheme.Modules.preservesFiniteProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.sheafifyPullback_lifting
  PresheafOfModules.PullbackMonoidal.pullback_monoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ
  PresheafOfModules.pushforward_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_η
  PresheafOfModules.free_monoidal
  PresheafOfModules.restrictScalars_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ_gS
  PresheafOfModules.pullback_oplaxMonoidal
attribute [-instance]
  instPreservesColimitsOfSizeCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierPb
attribute [-instance]
  PresheafOfModules.pullback_monoidal'
  AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
  AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
  AlgebraicCurve.Place.instIsPrimeCenter
  AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
  instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
  AlgebraicCurve.Pic0.instModuleZModTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instSMulTorsion
  AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
  AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
  AlgebraicCurve.RationalFunctionField.instNontrivialInftyValueGroup
  PresheafOfModules.ExteriorPower.instModulePresheafAb
  AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
  AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
  AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
  AlgebraicGeometry.isClosedImmersion_graphOver
  AlgebraicGeometry.FGSubalgebra.instIsDirectedLe
attribute [-instance]
  instQuasiSeparatedSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsCofilteredOpposite
  AlgebraicGeometry.FGSubalgebra.instIsAffineObjOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instNonempty
  AlgebraicGeometry.FGSubalgebra.instNonemptySubtypeLeSubalgebraValFG
attribute [-instance]
  instCompactSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsDirectedSubtypeLeSubalgebraValFG
  AlgebraicGeometry.FGSubalgebra.instIsAffineHomMapOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instIsFiltered
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instNeg
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulInt
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAddCommGroup
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAdd
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSub
attribute [-instance]
  instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
  AlgebraicCurve.instHasLocalResidue_of_hasCanonicalLocalResidueK
  AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
  AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
  ModularCurve.KwF4gRRTate.instAlgebraKAdicCompletionIntegers
  AlgebraicCurve.Place.kw_ffgc_continuousSMul_adicCompletionComap
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersCompletionCompletion
attribute [-instance]
  instLiesOverSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegersCompletionIdealAsIdeal
attribute [-instance]
  AlgebraicCurve.instHasCanonicalLocalResidueK
  AlgebraicCurve.Place.instAlgebra_restrictResidueField
  AlgebraicCurve.Place.instIsScalarTower_restrictResidueField
  AlgebraicCurve.instHasLocalResidue
  AlgebraicCurve.HasSeparableResidue.of_perfectField_of_isCurveOver
  AlgebraicCurve.HasSeparableResidue.of_perfectField
  AlgebraicCurve.Place.instIsLocalHom_restrictSubringHom
  AlgebraicCurve.instHasCanonicalLocalResidueKStar
  ModularCurve.KwNo6Pin.isLocalRing_completion
  SheafOfModules.isIso_ihomModelToIhom
  AlgebraicGeometry.OModulePresheaf.isScalarTower
  AlgebraicGeometry.Scheme.OrderedAffineCover.instLinearOrder
  AlgebraicGeometry.OModulePresheaf.module
  AlgebraicGeometry.Scheme.OrderedAffineCover.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCover.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.addCommGroup
  AlgebraicGeometry.Scheme.OrderedAffineCover.instDecidableEqIdx
  AlgebraicGeometry.OModulePresheaf.moduleSections
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.instSubsingletonObjZero
attribute [-instance]
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
  AlgebraicGeometry.OModulePresheaf.Leray.biC_module
  DoubleComplex.instModuleE₂I
  DoubleComplex.Bounded.modR
  DoubleComplex.instModuleE₂II
  DoubleComplex.instAddCommGroupE₂II
  DoubleComplex.Bounded.abGrp
  DoubleComplex.instAddCommGroupE₂I
  AlgebraicGeometry.ChowDatum.hι_closed
  AlgebraicGeometry.ChowDatumProj.hιN_closed
  AlgebraicGeometry.ChowDatumProj.hp_proper
  AlgebraicGeometry.ChowDatum.hp_isoU
  AlgebraicGeometry.ChowDatum.hp_proper
  AlgebraicGeometry.ProjSpace.algebraAway
  AlgebraicGeometry.ProjSpace.instIsProperProdOverπ
  AlgebraicGeometry.ChowDatumProj.hp_isoU
  AlgebraicGeometry.ProjSpace.isProper_π
  AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
  ProjSpaceCech.GradedModule.H.module
  ProjSpaceCech.GradedModule.H.addCommGroup
  ProjSpaceCech.GradedModule.sec.instAdd
  ProjSpaceCech.GradedModule.sec.instNeg
  ProjSpaceCech.GradedModule.acg
  ProjSpaceCech.GradedModule.Frac.setoid
  ProjSpaceCech.GradedModule.modR
  ProjSpaceCech.GradedModule.sec.instModule
  ProjSpaceCech.GradedModule.sec.instAddCommGroup
  ProjSpaceCech.GradedModule.sec.instZero
  ProjSpaceCech.GradedModule.Presentation.fJ
  ProjSpaceCech.GradedModule.sec.instSMul
  ProjSpaceCech.Twist.H.module
  ProjSpaceCech.Idx.instFintype
  ProjSpaceCech.Twist.H.addCommGroup
attribute [-instance]
  ProjSpaceCech.Idx.instDecidableEq
  ProjSpaceCech.Twist.Mon.instDecidableEq
  ProjSpaceCech.Twist.cochain.instAddCommGroup
  ProjSpaceCech.Twist.cochain.instModule
  AlgebraicGeometry.FGSubalgebra.tensorStage_directedSystem
  AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
  AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
  AlgebraicCurve.CurveModel.locallyOfFiniteType_gluedToBase
  AlgebraicCurve.CurveModel.isFractionRing_overlap
  AlgebraicCurve.CurveModel.isLocallyNoetherian_glued
  AlgebraicCurve.CurveModel.jacobsonSpace_glued
  AlgebraicCurve.CurveModel.isOpenImmersion_ι₀
  AlgebraicCurve.CurveModel.isIntegral_glued
  AlgebraicCurve.CurveModel.quasiSeparated_gluedToBase
  AlgebraicCurve.CurveModel.compactSpace_glued
  AlgebraicCurve.CurveModel.isIntegral_adjoin_chartRing
  AlgebraicCurve.CurveModel.isFractionRing_overlap_functionField
  AlgebraicCurve.CurveModel.isProper_gluedToBase
  AlgebraicCurve.CurveModel.isOpenImmersion_ιU
  AlgebraicCurve.CurveModel.isOpenImmersion_f₀
  AlgebraicCurve.CurveModel.isOpenImmersion_fInf
  AlgebraicCurve.CurveModel.isOpenImmersion_ιInf
  AlgebraicCurve.CurveModel.algebra_overlap_functionField
  AlgebraicCurve.CurveModel.quasiCompact_gluedToBase
  AlgebraicCurve.CurveModel.algebraAdjoin
  AlgebraicCurve.CurveModel.isDedekindDomain_chartRing
  AlgebraicCurve.CurveModel.isIntegralClosure
  AlgebraicCurve.CurveModel.finite_chartRing
  AlgebraicCurve.CurveModel.centre_isPrime
  AlgebraicCurve.CurveModel.isFractionRing_chartRing
  AlgebraicCurve.CurveModel.finiteType_chartRing
  AlgebraicCurve.CurveModel.isNoetherianRing_chartRing
  AlgebraicCurve.CurveModel.isScalarTower_base_adjoin
  AlgebraicCurve.CurveModel.isScalarTower_adjoin
  AlgebraicCurve.CurveModel.chartRing_finitePresentation
attribute [-simp]
  GoodReductionJacobian.RelativePic0Designation.mk.sizeOf_spec
  GoodReductionJacobian.AvatarSchemeBridge.mk.injEq
  GoodReductionJacobian.AvatarSchemeBridge.mk.sizeOf_spec
  GoodReductionJacobian.RelativePic0Designation.mk.injEq
  GoodReductionJacobian.schemeHomOverComp_coe
  NeronModelInfra.schemeHomOverEquivOverHom_apply
  GoodReductionJacobian.RelativeGroupLaw.mk.sizeOf_spec
  NeronModelInfra.schemeHomOverEquivOverHom_symm_apply
  NeronModelInfra.overHomToSchemeHomOver_coe
  GoodReductionJacobian.RelativeGroupLaw.mk.injEq
  NeronModelInfra.overHomToSchemeHomOver_schemeHomOverToOverHom
  NeronModelInfra.schemeHomOverToOverHom_left
  NeronModelInfra.schemeHomOverToOverHom_overHomToSchemeHomOver
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.sizeOf_spec
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
  AlgebraicCurve.CurveModel.mk.injEq
  AlgebraicCurve.CurveModel.mk.sizeOf_spec
  AlgebraicCurve.Place.mk.injEq
  AlgebraicCurve.Divisor.degree_single
  AlgebraicCurve.Divisor.smul_single
  AlgebraicCurve.Place.smul_toValuationSubring
  AlgebraicCurve.Place.heightOneSpectrum_asIdeal
  AlgebraicCurve.Place.coe_algebraMap
  AlgebraicCurve.Place.ord_one
  AlgebraicCurve.Place.coe_smulRingEquiv_apply
  AlgebraicCurve.Pic0.coe_degZeroSMulHom
  AlgebraicCurve.Place.deg_smul
  AlgebraicCurve.Pic0.mk_zero
  AlgebraicCurve.Place.mk.sizeOf_spec
  AlgebraicCurve.Divisor.degree_smul
  AlgebraicCurve.Pic0.mk_add
  AlgebraicCurve.Place.ord_zero
  AlgebraicCurve.Place.ofHeightOneSpectrum_toValuationSubring
  AlgebraicCurve.mulAdele_apply
attribute [-simp]
  AlgebraicCurve.residuePairing_apply_coe
  AlgebraicCurve.mem_adeleBdd
  AlgebraicCurve.weilSmul_one
  AlgebraicCurve.diagonalHom_apply
  AlgebraicCurve.weilSmul_apply
  AlgebraicCurve.adeleSpaceMul_coe
  AlgebraicCurve.mulAdele_one
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U1
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.injEq
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U0
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.mk.injEq
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.pullback_U1
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.pullback_U0
  TwoChartCech.Sections.mk.injEq
  TwoChartCech.Cover.mk.injEq
  TwoChartCech.GrothendieckComplex.mk.injEq
  TwoChartCech.Sections.mk.sizeOf_spec
  TwoChartCech.Cover.mk.sizeOf_spec
  TwoChartCech.Cover.lineBundle_r0_apply
  TwoChartCech.GrothendieckComplex.mk.sizeOf_spec
  TwoChartCech.Cover.lineBundle_r1_apply
  CoherentBaseChange.TwoTermComplex.mk.sizeOf_spec
  CoherentBaseChange.TwoTermComplex.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
  AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
  CategoryTheory.Functor.OverTotal.ofFibre_fst
  CategoryTheory.Functor.overTotal_map_fst
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_J
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYoneda_toGlued_uliftYonedaGluedToSheaf
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t'
attribute [-simp]
  uliftYoneda_toGlued_uliftYonedaGluedToSheaf_assoc
attribute [-simp]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_toGlued
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_openCover_map
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_comp
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_V
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_U
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_f
attribute [-simp]
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_P
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_toBase
  AlgebraicGeometry.RelPicard.rigSection_snd
  AlgebraicGeometry.RelPicard.RigidifiedLineBundle.ofInvertible_L
  AlgebraicGeometry.RelPicard.rigSection_snd_assoc
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
  GoodReductionJacobian.relativeGroupLawOfGrpObj_inv
  GoodReductionJacobian.relativeGroupLawOfGrpObj_mul
  GoodReductionJacobian.overHomEquivSchemeHomOver_apply_coe
  GoodReductionJacobian.relativeGroupLawOfGrpObj_one
  GoodReductionJacobian.overHomEquivSchemeHomOver_symm_apply_left
  PresheafOfModules.freeεIso_hom_app
  PresheafOfModules.freeμIso_hom_app
  AlgebraicCurve.coe_cechH0Equiv_apply
  AlgebraicCurve.cechH1ToH1_mk
  AlgebraicCurve.lSpaceOn_univ
  AlgebraicCurve.lSpaceOn_empty
  AlgebraicCurve.Place.congrEquiv_symm_apply
  AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
  AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
  AlgebraicCurve.Place.congrEquiv_apply
  AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
  AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
  AlgebraicCurve.Divisor.mapRestrict_single
  AlgebraicCurve.Divisor.pushforward_single
  AlgebraicCurve.Place.coe_restrictInclusion
  AlgebraicCurve.Place.mem_fiber
  AlgebraicCurve.Place.restrict_toValuationSubring
  AlgebraicCurve.Divisor.degree_pushforward
  AlgebraicCurve.Place.restrictResidueMap_residue
  AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
  AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
  AlgebraicCurve.Place.placeOfPrime_toValuationSubring
  AlgebraicCurve.Place.mem_fiberOver
  AlgebraicCurve.Place.fiberEquiv_symm_apply
  AlgebraicCurve.Place.fiberEquiv_apply
  AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
attribute [-simp]
  AlgebraicCurve.Divisor.degree_pushforwardAlong
  AlgebraicCurve.Pic0.coe_degZeroCorrespondence
  AlgebraicCurve.Place.mem_fiberAlong
  AlgebraicCurve.SemilinearAut.toRingAut_inv
  AlgebraicCurve.SemilinearAut.smul_def
  AlgebraicCurve.SemilinearAut.smul_single
  AlgebraicCurve.SemilinearAut.smul_toValuationSubring
  AlgebraicCurve.SemilinearAut.baseAut_inv
  AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_one
  AlgebraicCurve.SemilinearAut.deg_smul
  AlgebraicCurve.SemilinearAut.degree_smul
  AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
  AlgebraicCurve.SemilinearAut.baseAut_mul
  AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
  AlgebraicCurve.SemilinearAut.baseAut_one
  AlgebraicCurve.SemilinearAut.ofAlgAut_smul
  AlgebraicCurve.SemilinearAut.coe_torsion_smul
  AlgebraicCurve.SemilinearAut.toRingAut_mul
attribute [-simp]
  AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeInfty
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_some
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeOfPoint
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_none
  AlgebraicCurve.Divisor.evalFun_zero
  AlgebraicCurve.Place.evalAt_one
  AlgebraicCurve.Place.differentialCoeff_zero
  AlgebraicCurve.Place.differentialCoeff_dCoord
  AlgebraicCurve.TranscendenceTower.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
  AlgebraicCurve.TranscendenceTower.mk.injEq
  AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec
  AlgebraicCurve.PoleDivisorPackage.mk.injEq
  AlgebraicGeometry.RelPicard.thetaBundle_def
attribute [-simp]
  AlgebraicGeometry.RelPicard.picardBundle_def
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_ofRelEffDivisor
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_I
  AlgebraicGeometry.mapOnProdOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.mk.sizeOf_spec
  AlgebraicGeometry.RelEffCartierDiv.mk.injEq
  AlgebraicGeometry.mapOnProdOver_snd
  AlgebraicGeometry.mapOnProdOver_fst
  AlgebraicGeometry.mapOnProdOver_snd_assoc
  AlgebraicGeometry.mapOnProdOver_id
  AlgebraicCurve.RelEffDivisor.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_fst
  AlgebraicCurve.mapOnProd_fst_assoc
  AlgebraicCurve.mapOnProd_snd
  AlgebraicCurve.UnivDivisorPack.mk.injEq
  AlgebraicCurve.RelEffDivisor.mk.injEq
  AlgebraicCurve.UnivDivisorPack.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_snd_assoc
  AlgebraicGeometry.Scheme.Modules.exteriorPower_obj
  PresheafOfModules.exteriorPower_map_ιMulti
  PresheafOfModules.ExteriorPower.appₗ_apply
  AlgebraicGeometry.prodKerGraph_one
  AlgebraicGeometry.fibrePowOver.proj_comp
  AlgebraicGeometry.prodKerGraph_zero
  AlgebraicGeometry.RelEffCartierDiv.empty_I
  AlgebraicGeometry.fibrePowOver.proj_comp_assoc
  AlgebraicGeometry.graphOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
  AlgebraicGeometry.graphOver_fst
  AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
  AlgebraicGeometry.graphOver_snd
  AlgebraicGeometry.graphOver_snd_assoc
  AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
  AlgebraicCurve.SymmetricPowerPackage.mk.injEq
  AlgebraicGeometry.FGSubalgebra.cocone_ι_app_apply
  AlgebraicGeometry.RelPicard.fst_toProdSpec
  AlgebraicGeometry.RelPicard.toProdSpec_fst_assoc
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_cons
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_nil
attribute [-simp]
  AlgebraicGeometry.RelPicard.fst_toProdSpec_assoc
  AlgebraicGeometry.RelPicard.toProdSpec_fst
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.sizeOf_spec
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.injEq
  AlgebraicCurve.adeleSingle_coe
  AlgebraicCurve.kaehlerResidueTermKFam_apply
  AlgebraicCurve.Place.LocalResidueData.mk.injEq
  AlgebraicCurve.Place.LocalResidueData.mk.sizeOf_spec
  AlgebraicCurve.Place.kw_ffgc_adicCompletionComapIntegers_coe
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.sizeOf_spec
  AlgebraicCurve.Place.mem_simplePoleSubmodule
  AlgebraicCurve.Place.coe_uniformizerSubring
  ModularCurve.Lg37.Lg37CompletionSection.mk.injEq
  AlgebraicCurve.Place.CoefficientFieldSection.mk.injEq
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.injEq
  ModularCurve.Lg37.Lg37CompletionSection.mk.sizeOf_spec
  AlgebraicCurve.Place.CoefficientFieldSection.mk.sizeOf_spec
  AlgebraicCurve.Place.poleSubmodule_one
  AlgebraicCurve.Place.mem_poleSubmodule
  AlgebraicGeometry.Scheme.Modules.toUnitSection_ofUnitSection
  AlgebraicGeometry.Scheme.Modules.pullbackSection_def
  AlgebraicGeometry.Scheme.Modules.ofUnitSection_toUnitSection
  PresheafOfModules.InternalHom.IsSheafAux.appAt_toPresheafHom
attribute [-simp]
  SheafOfModules.ihomSectionsEquivFamily_unit
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_apply
  SheafOfModules.ihomEval_unit_app
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_right
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_left
  AlgebraicGeometry.Scheme.Modules.homOfFamily_app_apply
  SheafOfModules.unit_ihomSectionsEquivFamily
  AlgebraicGeometry.Scheme.Modules.familyOfHom_app
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_hom_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_inv_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomOfFamily_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_symm_apply
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_right
  AlgebraicGeometry.Scheme.Modules.map_unitSection
  AlgebraicGeometry.Scheme.Modules.tensorSectionsBilin_apply
  AlgebraicGeometry.Scheme.Modules.tensorPowSection_zero
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_left
  AlgebraicGeometry.Scheme.Modules.tensorPow_zero
  AlgebraicGeometry.Scheme.Modules.tensorPow_succ
  AlgebraicGeometry.Scheme.OrderedAffineCover.mk.injEq
  AlgebraicGeometry.OModulePresheaf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCover.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.mk.injEq
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_neg
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_zero
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_sub
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_add
  AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
  AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U
  AlgebraicGeometry.OModulePresheaf.Hom.mk.injEq
  AlgebraicGeometry.OModulePresheaf.Hom.id_app
  AlgebraicGeometry.OModulePresheaf.AffHom.appSections_apply
  AlgebraicGeometry.OModulePresheaf.AffHom.comp_app
  AlgebraicGeometry.OModulePresheaf.AffSES.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.AffHom.kerMap_coe
  AlgebraicGeometry.OModulePresheaf.AffHom.id_app
  AlgebraicGeometry.OModulePresheaf.Hom.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.Hom.toAffHom_app
attribute [-simp]
  AlgebraicGeometry.OModulePresheaf.SES.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.AffHom.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.Hom.comp_app
  AlgebraicGeometry.OModulePresheaf.SES.mk.injEq
  AlgebraicGeometry.OModulePresheaf.AffHom.mk.injEq
  AlgebraicGeometry.OModulePresheaf.Hom.appSections_apply
  AlgebraicGeometry.OModulePresheaf.AffSES.mk.injEq
  AlgebraicGeometry.OModulePresheaf.prod_obj
  AlgebraicGeometry.OModulePresheaf.restrOpen_obj
  AlgebraicGeometry.OModulePresheaf.DevissageStep.mk.injEq
  AlgebraicGeometry.OModulePresheaf.pushforward_obj
  AlgebraicGeometry.OModulePresheaf.im_obj
  AlgebraicGeometry.OModulePresheaf.pow_obj
  AlgebraicGeometry.OModulePresheaf.fstHom_app
  AlgebraicGeometry.OModulePresheaf.ker_obj
  AlgebraicGeometry.OModulePresheaf.coker_obj
  AlgebraicGeometry.OModulePresheaf.DevissageStep.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCover.preimage_U
  AlgebraicGeometry.OModulePresheaf.sndHom_app
  AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
  DoubleComplex.Bounded.mk.injEq
  DoubleComplex.Bounded.mk.sizeOf_spec
  DoubleComplex.Convergence.mk.injEq
  DoubleComplex.Convergence.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.injEq
  AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatumProj.mk.injEq
  AlgebraicGeometry.ChowDatum.mk.injEq
  ProjSpaceCech.GradedModule.mk.injEq
  ProjSpaceCech.GradedModule.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Presentation.mk.injEq
  ProjSpaceCech.GradedModule.Frac.mk.injEq
  ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.shift_toLinearMap
  ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.mk.injEq
  TwoChartCech.Mumford.dK_apply
attribute [-simp]
  TwoChartCech.Mumford.ι0_apply
  TwoChartCech.Mumford.ι1_apply
  TwoChartCech.KerCoprod.dK_apply
  TwoChartCech.KerCoprod.ι1_apply
  TwoChartCech.KerCoprod.ι0_apply
  AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
  AlgebraicGeometry.RelPicard.algEquivZeroGroupCut_toSubPicCondition
  AlgebraicGeometry.RelPicard.LFP.stageHom_val
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_hom_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_inv_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.restrict_P
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp
  AlgebraicGeometry.RelEffCartierDiv.functor_map_fst
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_pullbackAlong
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_symm_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp_assoc
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top
  AlgebraicGeometry.RelEffCartierDiv.mem_supportedIn_iff
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top_eq
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
  CoherentBaseChange.FibreH0Family.mk.sizeOf_spec
  CoherentBaseChange.FibreH0Family.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.sizeOf_spec
  AlgebraicCurve.CurveModel.coe_gInf
  AlgebraicCurve.CurveModel.coe_tInvChart
  AlgebraicCurve.CurveModel.ιInf_gluedToBase_assoc
  AlgebraicCurve.CurveModel.ιInf_gluedToBase
  AlgebraicCurve.CurveModel.primeOfι₀_asIdeal
  AlgebraicCurve.CurveModel.coe_tChart
  AlgebraicCurve.CurveModel.ι₀_gluedToBase_assoc
  AlgebraicCurve.CurveModel.primeOfιInf_asIdeal
attribute [-simp]
  AlgebraicCurve.CurveModel.ι₀_gluedToBase
  AlgebraicCurve.CurveModel.coe_tma
  AlgebraicCurve.CurveModel.coe_primeEquivChartPlaces
universe u
noncomputable section
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.CategoryTheory.CartesianMonoidalCategory
open _root_.AlgebraicGeometry.RelPicard
open _root_.NeronModelInfra
namespace P2mCubeAssembly
section Slices
variable {k : Type u} [Field k]
local notation "Sk" => Spec (CommRingCat.of k)

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.ThreeSlices
attribute [-instance]
  AlgebraicGeometry.SmoothOfRelativeDimension.fiberToSpecResidueField
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_snd
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_fst
  AlgebraicGeometry.SmoothOfRelativeDimension.smooth_one
  AlgebraicGeometry.SmoothProperCurve.isIntegral_pullback_Spec_field
  AlgebraicGeometry.IsProper.fiberToSpecResidueField
  AlgebraicCurve.CurveModel.isProper
  AlgebraicCurve.CurveModel.isIntegral
  AlgebraicCurve.CurveModel.smooth
  AlgebraicCurve.Place.instIsScalarTowerSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Divisor.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instSMulAlgEquiv
  AlgebraicCurve.Place.instIsPrincipalIdealRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instIsDiscreteValuationRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Pic0.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instAlgebraSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instMulActionAlgEquiv
  AlgebraicCurve.Pic0.instSMulAlgEquiv
  TwoChartCech.Sections.M0_moduleA
  TwoChartCech.Sections.M1_module
  TwoChartCech.Cover.A01_algebra
  TwoChartCech.Cover.A0_algebra
  TwoChartCech.Cover.A1_commRing
  TwoChartCech.Cover.A1_algebra
  TwoChartCech.Sections.M01_module
  TwoChartCech.Sections.M0_addCommGroup
  TwoChartCech.Sections.M0_tower
  TwoChartCech.Sections.M01_addCommGroup
  TwoChartCech.Cover.A0_commRing
  TwoChartCech.Sections.M1_tower
  TwoChartCech.Sections.M01_moduleA
  TwoChartCech.Sections.M0_module
  TwoChartCech.Sections.M1_moduleA
  TwoChartCech.Sections.M1_addCommGroup
  TwoChartCech.Cover.A01_commRing
  TwoChartCech.Sections.M01_tower
  CoherentBaseChange.TwoTermComplex.C0_module
  CoherentBaseChange.TwoTermComplex.C0_addCommGroup
  CoherentBaseChange.TwoTermComplex.C1_module
  CoherentBaseChange.TwoTermComplex.C1_addCommGroup
attribute [-instance]
  CoherentBaseChange.TwoTermComplex.C0_free
  CoherentBaseChange.TwoTermComplex.C1_finite
  CoherentBaseChange.TwoTermComplex.C0_finite
  CoherentBaseChange.TwoTermComplex.C1_free
  AlgebraicCurve.IsCurveOver.instNontrivialKaehler
  AlgebraicCurve.IsCurveOver.instFreeKaehler
  AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
  AlgebraicCurve.IsCurveOver.instFiniteResidue
attribute [-instance]
  instIsLocallyInjectiveFunUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsLocallySurjectiveUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsOpenImmersionToGlued
attribute [-instance]
  instIsIsoSheafZariskiTopologyTypeUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.RelPicard.isOpenImmersion_toGlued
  AlgebraicGeometry.Scheme.Modules.preservesBinaryProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback_monoidal
  AlgebraicGeometry.Scheme.Modules.sheafify_isLocalization'
  AlgebraicGeometry.Scheme.Modules.preservesTerminal_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback₀_monoidal
  AlgebraicGeometry.Scheme.Modules.preservesFiniteProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.sheafifyPullback_lifting
  PresheafOfModules.PullbackMonoidal.pullback_monoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ
  PresheafOfModules.pushforward_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_η
  PresheafOfModules.free_monoidal
  PresheafOfModules.restrictScalars_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ_gS
  PresheafOfModules.pullback_oplaxMonoidal
attribute [-instance]
  instPreservesColimitsOfSizeCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierPb
attribute [-instance]
  PresheafOfModules.pullback_monoidal'
  AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
  AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
  AlgebraicCurve.Place.instIsPrimeCenter
  AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
  instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
  AlgebraicCurve.Pic0.instModuleZModTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instSMulTorsion
  AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
  AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
  AlgebraicCurve.RationalFunctionField.instNontrivialInftyValueGroup
  PresheafOfModules.ExteriorPower.instModulePresheafAb
  AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
  AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
  AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
  AlgebraicGeometry.isClosedImmersion_graphOver
  AlgebraicGeometry.FGSubalgebra.instIsDirectedLe
attribute [-instance]
  instQuasiSeparatedSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsCofilteredOpposite
  AlgebraicGeometry.FGSubalgebra.instIsAffineObjOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instNonempty
  AlgebraicGeometry.FGSubalgebra.instNonemptySubtypeLeSubalgebraValFG
attribute [-instance]
  instCompactSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsDirectedSubtypeLeSubalgebraValFG
  AlgebraicGeometry.FGSubalgebra.instIsAffineHomMapOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instIsFiltered
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instNeg
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulInt
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAddCommGroup
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAdd
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSub
attribute [-instance]
  instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
  AlgebraicCurve.instHasLocalResidue_of_hasCanonicalLocalResidueK
  AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
  AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
  ModularCurve.KwF4gRRTate.instAlgebraKAdicCompletionIntegers
  AlgebraicCurve.Place.kw_ffgc_continuousSMul_adicCompletionComap
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersCompletionCompletion
attribute [-instance]
  instLiesOverSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegersCompletionIdealAsIdeal
attribute [-instance]
  AlgebraicCurve.instHasCanonicalLocalResidueK
  AlgebraicCurve.Place.instAlgebra_restrictResidueField
  AlgebraicCurve.Place.instIsScalarTower_restrictResidueField
  AlgebraicCurve.instHasLocalResidue
  AlgebraicCurve.HasSeparableResidue.of_perfectField_of_isCurveOver
  AlgebraicCurve.HasSeparableResidue.of_perfectField
  AlgebraicCurve.Place.instIsLocalHom_restrictSubringHom
  AlgebraicCurve.instHasCanonicalLocalResidueKStar
  ModularCurve.KwNo6Pin.isLocalRing_completion
  SheafOfModules.isIso_ihomModelToIhom
  AlgebraicGeometry.OModulePresheaf.isScalarTower
  AlgebraicGeometry.Scheme.OrderedAffineCover.instLinearOrder
  AlgebraicGeometry.OModulePresheaf.module
  AlgebraicGeometry.Scheme.OrderedAffineCover.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCover.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.addCommGroup
  AlgebraicGeometry.Scheme.OrderedAffineCover.instDecidableEqIdx
  AlgebraicGeometry.OModulePresheaf.moduleSections
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.instSubsingletonObjZero
attribute [-instance]
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
  AlgebraicGeometry.OModulePresheaf.Leray.biC_module
  DoubleComplex.instModuleE₂I
  DoubleComplex.Bounded.modR
  DoubleComplex.instModuleE₂II
  DoubleComplex.instAddCommGroupE₂II
  DoubleComplex.Bounded.abGrp
  DoubleComplex.instAddCommGroupE₂I
  AlgebraicGeometry.ChowDatum.hι_closed
  AlgebraicGeometry.ChowDatumProj.hιN_closed
  AlgebraicGeometry.ChowDatumProj.hp_proper
  AlgebraicGeometry.ChowDatum.hp_isoU
  AlgebraicGeometry.ChowDatum.hp_proper
  AlgebraicGeometry.ProjSpace.algebraAway
  AlgebraicGeometry.ProjSpace.instIsProperProdOverπ
  AlgebraicGeometry.ChowDatumProj.hp_isoU
  AlgebraicGeometry.ProjSpace.isProper_π
  AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
  ProjSpaceCech.GradedModule.H.module
  ProjSpaceCech.GradedModule.H.addCommGroup
  ProjSpaceCech.GradedModule.sec.instAdd
  ProjSpaceCech.GradedModule.sec.instNeg
  ProjSpaceCech.GradedModule.acg
  ProjSpaceCech.GradedModule.Frac.setoid
  ProjSpaceCech.GradedModule.modR
  ProjSpaceCech.GradedModule.sec.instModule
  ProjSpaceCech.GradedModule.sec.instAddCommGroup
  ProjSpaceCech.GradedModule.sec.instZero
  ProjSpaceCech.GradedModule.Presentation.fJ
  ProjSpaceCech.GradedModule.sec.instSMul
  ProjSpaceCech.Twist.H.module
  ProjSpaceCech.Idx.instFintype
  ProjSpaceCech.Twist.H.addCommGroup
attribute [-instance]
  ProjSpaceCech.Idx.instDecidableEq
  ProjSpaceCech.Twist.Mon.instDecidableEq
  ProjSpaceCech.Twist.cochain.instAddCommGroup
  ProjSpaceCech.Twist.cochain.instModule
  AlgebraicGeometry.FGSubalgebra.tensorStage_directedSystem
  AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
  AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
  AlgebraicCurve.CurveModel.locallyOfFiniteType_gluedToBase
  AlgebraicCurve.CurveModel.isFractionRing_overlap
  AlgebraicCurve.CurveModel.isLocallyNoetherian_glued
  AlgebraicCurve.CurveModel.jacobsonSpace_glued
  AlgebraicCurve.CurveModel.isOpenImmersion_ι₀
  AlgebraicCurve.CurveModel.isIntegral_glued
  AlgebraicCurve.CurveModel.quasiSeparated_gluedToBase
  AlgebraicCurve.CurveModel.compactSpace_glued
  AlgebraicCurve.CurveModel.isIntegral_adjoin_chartRing
  AlgebraicCurve.CurveModel.isFractionRing_overlap_functionField
  AlgebraicCurve.CurveModel.isProper_gluedToBase
  AlgebraicCurve.CurveModel.isOpenImmersion_ιU
  AlgebraicCurve.CurveModel.isOpenImmersion_f₀
  AlgebraicCurve.CurveModel.isOpenImmersion_fInf
  AlgebraicCurve.CurveModel.isOpenImmersion_ιInf
  AlgebraicCurve.CurveModel.algebra_overlap_functionField
  AlgebraicCurve.CurveModel.quasiCompact_gluedToBase
  AlgebraicCurve.CurveModel.algebraAdjoin
  AlgebraicCurve.CurveModel.isDedekindDomain_chartRing
  AlgebraicCurve.CurveModel.isIntegralClosure
  AlgebraicCurve.CurveModel.finite_chartRing
  AlgebraicCurve.CurveModel.centre_isPrime
  AlgebraicCurve.CurveModel.isFractionRing_chartRing
  AlgebraicCurve.CurveModel.finiteType_chartRing
  AlgebraicCurve.CurveModel.isNoetherianRing_chartRing
  AlgebraicCurve.CurveModel.isScalarTower_base_adjoin
  AlgebraicCurve.CurveModel.isScalarTower_adjoin
  AlgebraicCurve.CurveModel.chartRing_finitePresentation
attribute [-simp]
  GoodReductionJacobian.RelativePic0Designation.mk.sizeOf_spec
  GoodReductionJacobian.AvatarSchemeBridge.mk.injEq
  GoodReductionJacobian.AvatarSchemeBridge.mk.sizeOf_spec
  GoodReductionJacobian.RelativePic0Designation.mk.injEq
  GoodReductionJacobian.schemeHomOverComp_coe
  NeronModelInfra.schemeHomOverEquivOverHom_apply
  GoodReductionJacobian.RelativeGroupLaw.mk.sizeOf_spec
  NeronModelInfra.schemeHomOverEquivOverHom_symm_apply
  NeronModelInfra.overHomToSchemeHomOver_coe
  GoodReductionJacobian.RelativeGroupLaw.mk.injEq
  NeronModelInfra.overHomToSchemeHomOver_schemeHomOverToOverHom
  NeronModelInfra.schemeHomOverToOverHom_left
  NeronModelInfra.schemeHomOverToOverHom_overHomToSchemeHomOver
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.sizeOf_spec
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
  AlgebraicCurve.CurveModel.mk.injEq
  AlgebraicCurve.CurveModel.mk.sizeOf_spec
  AlgebraicCurve.Place.mk.injEq
  AlgebraicCurve.Divisor.degree_single
  AlgebraicCurve.Divisor.smul_single
  AlgebraicCurve.Place.smul_toValuationSubring
  AlgebraicCurve.Place.heightOneSpectrum_asIdeal
  AlgebraicCurve.Place.coe_algebraMap
  AlgebraicCurve.Place.ord_one
  AlgebraicCurve.Place.coe_smulRingEquiv_apply
  AlgebraicCurve.Pic0.coe_degZeroSMulHom
  AlgebraicCurve.Place.deg_smul
  AlgebraicCurve.Pic0.mk_zero
  AlgebraicCurve.Place.mk.sizeOf_spec
  AlgebraicCurve.Divisor.degree_smul
  AlgebraicCurve.Pic0.mk_add
  AlgebraicCurve.Place.ord_zero
  AlgebraicCurve.Place.ofHeightOneSpectrum_toValuationSubring
  AlgebraicCurve.mulAdele_apply
attribute [-simp]
  AlgebraicCurve.residuePairing_apply_coe
  AlgebraicCurve.mem_adeleBdd
  AlgebraicCurve.weilSmul_one
  AlgebraicCurve.diagonalHom_apply
  AlgebraicCurve.weilSmul_apply
  AlgebraicCurve.adeleSpaceMul_coe
  AlgebraicCurve.mulAdele_one
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U1
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.injEq
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U0
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.mk.injEq
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.pullback_U1
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.pullback_U0
  TwoChartCech.Sections.mk.injEq
  TwoChartCech.Cover.mk.injEq
  TwoChartCech.GrothendieckComplex.mk.injEq
  TwoChartCech.Sections.mk.sizeOf_spec
  TwoChartCech.Cover.mk.sizeOf_spec
  TwoChartCech.Cover.lineBundle_r0_apply
  TwoChartCech.GrothendieckComplex.mk.sizeOf_spec
  TwoChartCech.Cover.lineBundle_r1_apply
  CoherentBaseChange.TwoTermComplex.mk.sizeOf_spec
  CoherentBaseChange.TwoTermComplex.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
  AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
  CategoryTheory.Functor.OverTotal.ofFibre_fst
  CategoryTheory.Functor.overTotal_map_fst
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_J
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYoneda_toGlued_uliftYonedaGluedToSheaf
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t'
attribute [-simp]
  uliftYoneda_toGlued_uliftYonedaGluedToSheaf_assoc
attribute [-simp]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_toGlued
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_openCover_map
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_comp
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_V
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_U
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_f
attribute [-simp]
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_P
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_toBase
  AlgebraicGeometry.RelPicard.rigSection_snd
  AlgebraicGeometry.RelPicard.RigidifiedLineBundle.ofInvertible_L
  AlgebraicGeometry.RelPicard.rigSection_snd_assoc
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
  GoodReductionJacobian.relativeGroupLawOfGrpObj_inv
  GoodReductionJacobian.relativeGroupLawOfGrpObj_mul
  GoodReductionJacobian.overHomEquivSchemeHomOver_apply_coe
  GoodReductionJacobian.relativeGroupLawOfGrpObj_one
  GoodReductionJacobian.overHomEquivSchemeHomOver_symm_apply_left
  PresheafOfModules.freeεIso_hom_app
  PresheafOfModules.freeμIso_hom_app
  AlgebraicCurve.coe_cechH0Equiv_apply
  AlgebraicCurve.cechH1ToH1_mk
  AlgebraicCurve.lSpaceOn_univ
  AlgebraicCurve.lSpaceOn_empty
  AlgebraicCurve.Place.congrEquiv_symm_apply
  AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
  AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
  AlgebraicCurve.Place.congrEquiv_apply
  AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
  AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
  AlgebraicCurve.Divisor.mapRestrict_single
  AlgebraicCurve.Divisor.pushforward_single
  AlgebraicCurve.Place.coe_restrictInclusion
  AlgebraicCurve.Place.mem_fiber
  AlgebraicCurve.Place.restrict_toValuationSubring
  AlgebraicCurve.Divisor.degree_pushforward
  AlgebraicCurve.Place.restrictResidueMap_residue
  AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
  AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
  AlgebraicCurve.Place.placeOfPrime_toValuationSubring
  AlgebraicCurve.Place.mem_fiberOver
  AlgebraicCurve.Place.fiberEquiv_symm_apply
  AlgebraicCurve.Place.fiberEquiv_apply
  AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
attribute [-simp]
  AlgebraicCurve.Divisor.degree_pushforwardAlong
  AlgebraicCurve.Pic0.coe_degZeroCorrespondence
  AlgebraicCurve.Place.mem_fiberAlong
  AlgebraicCurve.SemilinearAut.toRingAut_inv
  AlgebraicCurve.SemilinearAut.smul_def
  AlgebraicCurve.SemilinearAut.smul_single
  AlgebraicCurve.SemilinearAut.smul_toValuationSubring
  AlgebraicCurve.SemilinearAut.baseAut_inv
  AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_one
  AlgebraicCurve.SemilinearAut.deg_smul
  AlgebraicCurve.SemilinearAut.degree_smul
  AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
  AlgebraicCurve.SemilinearAut.baseAut_mul
  AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
  AlgebraicCurve.SemilinearAut.baseAut_one
  AlgebraicCurve.SemilinearAut.ofAlgAut_smul
  AlgebraicCurve.SemilinearAut.coe_torsion_smul
  AlgebraicCurve.SemilinearAut.toRingAut_mul
attribute [-simp]
  AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeInfty
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_some
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeOfPoint
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_none
  AlgebraicCurve.Divisor.evalFun_zero
  AlgebraicCurve.Place.evalAt_one
  AlgebraicCurve.Place.differentialCoeff_zero
  AlgebraicCurve.Place.differentialCoeff_dCoord
  AlgebraicCurve.TranscendenceTower.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
  AlgebraicCurve.TranscendenceTower.mk.injEq
  AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec
  AlgebraicCurve.PoleDivisorPackage.mk.injEq
  AlgebraicGeometry.RelPicard.thetaBundle_def
attribute [-simp]
  AlgebraicGeometry.RelPicard.picardBundle_def
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_ofRelEffDivisor
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_I
  AlgebraicGeometry.mapOnProdOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.mk.sizeOf_spec
  AlgebraicGeometry.RelEffCartierDiv.mk.injEq
  AlgebraicGeometry.mapOnProdOver_snd
  AlgebraicGeometry.mapOnProdOver_fst
  AlgebraicGeometry.mapOnProdOver_snd_assoc
  AlgebraicGeometry.mapOnProdOver_id
  AlgebraicCurve.RelEffDivisor.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_fst
  AlgebraicCurve.mapOnProd_fst_assoc
  AlgebraicCurve.mapOnProd_snd
  AlgebraicCurve.UnivDivisorPack.mk.injEq
  AlgebraicCurve.RelEffDivisor.mk.injEq
  AlgebraicCurve.UnivDivisorPack.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_snd_assoc
  AlgebraicGeometry.Scheme.Modules.exteriorPower_obj
  PresheafOfModules.exteriorPower_map_ιMulti
  PresheafOfModules.ExteriorPower.appₗ_apply
  AlgebraicGeometry.prodKerGraph_one
  AlgebraicGeometry.fibrePowOver.proj_comp
  AlgebraicGeometry.prodKerGraph_zero
  AlgebraicGeometry.RelEffCartierDiv.empty_I
  AlgebraicGeometry.fibrePowOver.proj_comp_assoc
  AlgebraicGeometry.graphOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
  AlgebraicGeometry.graphOver_fst
  AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
  AlgebraicGeometry.graphOver_snd
  AlgebraicGeometry.graphOver_snd_assoc
  AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
  AlgebraicCurve.SymmetricPowerPackage.mk.injEq
  AlgebraicGeometry.FGSubalgebra.cocone_ι_app_apply
  AlgebraicGeometry.RelPicard.fst_toProdSpec
  AlgebraicGeometry.RelPicard.toProdSpec_fst_assoc
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_cons
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_nil
attribute [-simp]
  AlgebraicGeometry.RelPicard.fst_toProdSpec_assoc
  AlgebraicGeometry.RelPicard.toProdSpec_fst
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.sizeOf_spec
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.injEq
  AlgebraicCurve.adeleSingle_coe
  AlgebraicCurve.kaehlerResidueTermKFam_apply
  AlgebraicCurve.Place.LocalResidueData.mk.injEq
  AlgebraicCurve.Place.LocalResidueData.mk.sizeOf_spec
  AlgebraicCurve.Place.kw_ffgc_adicCompletionComapIntegers_coe
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.sizeOf_spec
  AlgebraicCurve.Place.mem_simplePoleSubmodule
  AlgebraicCurve.Place.coe_uniformizerSubring
  ModularCurve.Lg37.Lg37CompletionSection.mk.injEq
  AlgebraicCurve.Place.CoefficientFieldSection.mk.injEq
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.injEq
  ModularCurve.Lg37.Lg37CompletionSection.mk.sizeOf_spec
  AlgebraicCurve.Place.CoefficientFieldSection.mk.sizeOf_spec
  AlgebraicCurve.Place.poleSubmodule_one
  AlgebraicCurve.Place.mem_poleSubmodule
  AlgebraicGeometry.Scheme.Modules.toUnitSection_ofUnitSection
  AlgebraicGeometry.Scheme.Modules.pullbackSection_def
  AlgebraicGeometry.Scheme.Modules.ofUnitSection_toUnitSection
  PresheafOfModules.InternalHom.IsSheafAux.appAt_toPresheafHom
attribute [-simp]
  SheafOfModules.ihomSectionsEquivFamily_unit
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_apply
  SheafOfModules.ihomEval_unit_app
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_right
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_left
  AlgebraicGeometry.Scheme.Modules.homOfFamily_app_apply
  SheafOfModules.unit_ihomSectionsEquivFamily
  AlgebraicGeometry.Scheme.Modules.familyOfHom_app
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_hom_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_inv_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomOfFamily_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_symm_apply
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_right
  AlgebraicGeometry.Scheme.Modules.map_unitSection
  AlgebraicGeometry.Scheme.Modules.tensorSectionsBilin_apply
  AlgebraicGeometry.Scheme.Modules.tensorPowSection_zero
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_left
  AlgebraicGeometry.Scheme.Modules.tensorPow_zero
  AlgebraicGeometry.Scheme.Modules.tensorPow_succ
  AlgebraicGeometry.Scheme.OrderedAffineCover.mk.injEq
  AlgebraicGeometry.OModulePresheaf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCover.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.mk.injEq
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_neg
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_zero
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_sub
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_add
  AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
  AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U
  AlgebraicGeometry.OModulePresheaf.Hom.mk.injEq
  AlgebraicGeometry.OModulePresheaf.Hom.id_app
  AlgebraicGeometry.OModulePresheaf.AffHom.appSections_apply
  AlgebraicGeometry.OModulePresheaf.AffHom.comp_app
  AlgebraicGeometry.OModulePresheaf.AffSES.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.AffHom.kerMap_coe
  AlgebraicGeometry.OModulePresheaf.AffHom.id_app
  AlgebraicGeometry.OModulePresheaf.Hom.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.Hom.toAffHom_app
attribute [-simp]
  AlgebraicGeometry.OModulePresheaf.SES.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.AffHom.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.Hom.comp_app
  AlgebraicGeometry.OModulePresheaf.SES.mk.injEq
  AlgebraicGeometry.OModulePresheaf.AffHom.mk.injEq
  AlgebraicGeometry.OModulePresheaf.Hom.appSections_apply
  AlgebraicGeometry.OModulePresheaf.AffSES.mk.injEq
  AlgebraicGeometry.OModulePresheaf.prod_obj
  AlgebraicGeometry.OModulePresheaf.restrOpen_obj
  AlgebraicGeometry.OModulePresheaf.DevissageStep.mk.injEq
  AlgebraicGeometry.OModulePresheaf.pushforward_obj
  AlgebraicGeometry.OModulePresheaf.im_obj
  AlgebraicGeometry.OModulePresheaf.pow_obj
  AlgebraicGeometry.OModulePresheaf.fstHom_app
  AlgebraicGeometry.OModulePresheaf.ker_obj
  AlgebraicGeometry.OModulePresheaf.coker_obj
  AlgebraicGeometry.OModulePresheaf.DevissageStep.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCover.preimage_U
  AlgebraicGeometry.OModulePresheaf.sndHom_app
  AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
  DoubleComplex.Bounded.mk.injEq
  DoubleComplex.Bounded.mk.sizeOf_spec
  DoubleComplex.Convergence.mk.injEq
  DoubleComplex.Convergence.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.injEq
  AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatumProj.mk.injEq
  AlgebraicGeometry.ChowDatum.mk.injEq
  ProjSpaceCech.GradedModule.mk.injEq
  ProjSpaceCech.GradedModule.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Presentation.mk.injEq
  ProjSpaceCech.GradedModule.Frac.mk.injEq
  ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.shift_toLinearMap
  ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.mk.injEq
  TwoChartCech.Mumford.dK_apply
attribute [-simp]
  TwoChartCech.Mumford.ι0_apply
  TwoChartCech.Mumford.ι1_apply
  TwoChartCech.KerCoprod.dK_apply
  TwoChartCech.KerCoprod.ι1_apply
  TwoChartCech.KerCoprod.ι0_apply
  AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
  AlgebraicGeometry.RelPicard.algEquivZeroGroupCut_toSubPicCondition
  AlgebraicGeometry.RelPicard.LFP.stageHom_val
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_hom_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_inv_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.restrict_P
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp
  AlgebraicGeometry.RelEffCartierDiv.functor_map_fst
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_pullbackAlong
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_symm_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp_assoc
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top
  AlgebraicGeometry.RelEffCartierDiv.mem_supportedIn_iff
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top_eq
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
  CoherentBaseChange.FibreH0Family.mk.sizeOf_spec
  CoherentBaseChange.FibreH0Family.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.sizeOf_spec
  AlgebraicCurve.CurveModel.coe_gInf
  AlgebraicCurve.CurveModel.coe_tInvChart
  AlgebraicCurve.CurveModel.ιInf_gluedToBase_assoc
  AlgebraicCurve.CurveModel.ιInf_gluedToBase
  AlgebraicCurve.CurveModel.primeOfι₀_asIdeal
  AlgebraicCurve.CurveModel.coe_tChart
  AlgebraicCurve.CurveModel.ι₀_gluedToBase_assoc
  AlgebraicCurve.CurveModel.primeOfιInf_asIdeal
attribute [-simp]
  AlgebraicCurve.CurveModel.ι₀_gluedToBase
  AlgebraicCurve.CurveModel.coe_tma
  AlgebraicCurve.CurveModel.coe_primeEquivChartPlaces
universe u
noncomputable section
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.CategoryTheory.CartesianMonoidalCategory
open _root_.AlgebraicGeometry.RelPicard
open _root_.NeronModelInfra
namespace P2mCubeAssembly
section Slices
variable {k : Type u} [Field k]
local notation "Sk" => Spec (CommRingCat.of k)

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.ThreeSlices
attribute [-instance]
  AlgebraicGeometry.SmoothOfRelativeDimension.fiberToSpecResidueField
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_snd
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_fst
  AlgebraicGeometry.SmoothOfRelativeDimension.smooth_one
  AlgebraicGeometry.SmoothProperCurve.isIntegral_pullback_Spec_field
  AlgebraicGeometry.IsProper.fiberToSpecResidueField
  AlgebraicCurve.CurveModel.isProper
  AlgebraicCurve.CurveModel.isIntegral
  AlgebraicCurve.CurveModel.smooth
  AlgebraicCurve.Place.instIsScalarTowerSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Divisor.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instSMulAlgEquiv
  AlgebraicCurve.Place.instIsPrincipalIdealRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instIsDiscreteValuationRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Pic0.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instAlgebraSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instMulActionAlgEquiv
  AlgebraicCurve.Pic0.instSMulAlgEquiv
  TwoChartCech.Sections.M0_moduleA
  TwoChartCech.Sections.M1_module
  TwoChartCech.Cover.A01_algebra
  TwoChartCech.Cover.A0_algebra
  TwoChartCech.Cover.A1_commRing
  TwoChartCech.Cover.A1_algebra
  TwoChartCech.Sections.M01_module
  TwoChartCech.Sections.M0_addCommGroup
  TwoChartCech.Sections.M0_tower
  TwoChartCech.Sections.M01_addCommGroup
  TwoChartCech.Cover.A0_commRing
  TwoChartCech.Sections.M1_tower
  TwoChartCech.Sections.M01_moduleA
  TwoChartCech.Sections.M0_module
  TwoChartCech.Sections.M1_moduleA
  TwoChartCech.Sections.M1_addCommGroup
  TwoChartCech.Cover.A01_commRing
  TwoChartCech.Sections.M01_tower
  CoherentBaseChange.TwoTermComplex.C0_module
  CoherentBaseChange.TwoTermComplex.C0_addCommGroup
  CoherentBaseChange.TwoTermComplex.C1_module
  CoherentBaseChange.TwoTermComplex.C1_addCommGroup
attribute [-instance]
  CoherentBaseChange.TwoTermComplex.C0_free
  CoherentBaseChange.TwoTermComplex.C1_finite
  CoherentBaseChange.TwoTermComplex.C0_finite
  CoherentBaseChange.TwoTermComplex.C1_free
  AlgebraicCurve.IsCurveOver.instNontrivialKaehler
  AlgebraicCurve.IsCurveOver.instFreeKaehler
  AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
  AlgebraicCurve.IsCurveOver.instFiniteResidue
attribute [-instance]
  instIsLocallyInjectiveFunUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsLocallySurjectiveUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsOpenImmersionToGlued
attribute [-instance]
  instIsIsoSheafZariskiTopologyTypeUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.RelPicard.isOpenImmersion_toGlued
  AlgebraicGeometry.Scheme.Modules.preservesBinaryProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback_monoidal
  AlgebraicGeometry.Scheme.Modules.sheafify_isLocalization'
  AlgebraicGeometry.Scheme.Modules.preservesTerminal_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback₀_monoidal
  AlgebraicGeometry.Scheme.Modules.preservesFiniteProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.sheafifyPullback_lifting
  PresheafOfModules.PullbackMonoidal.pullback_monoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ
  PresheafOfModules.pushforward_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_η
  PresheafOfModules.free_monoidal
  PresheafOfModules.restrictScalars_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ_gS
  PresheafOfModules.pullback_oplaxMonoidal
attribute [-instance]
  instPreservesColimitsOfSizeCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierPb
attribute [-instance]
  PresheafOfModules.pullback_monoidal'
  AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
  AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
  AlgebraicCurve.Place.instIsPrimeCenter
  AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
  instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
  AlgebraicCurve.Pic0.instModuleZModTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instSMulTorsion
  AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
  AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
  AlgebraicCurve.RationalFunctionField.instNontrivialInftyValueGroup
  PresheafOfModules.ExteriorPower.instModulePresheafAb
  AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
  AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
  AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
  AlgebraicGeometry.isClosedImmersion_graphOver
  AlgebraicGeometry.FGSubalgebra.instIsDirectedLe
attribute [-instance]
  instQuasiSeparatedSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsCofilteredOpposite
  AlgebraicGeometry.FGSubalgebra.instIsAffineObjOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instNonempty
  AlgebraicGeometry.FGSubalgebra.instNonemptySubtypeLeSubalgebraValFG
attribute [-instance]
  instCompactSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsDirectedSubtypeLeSubalgebraValFG
  AlgebraicGeometry.FGSubalgebra.instIsAffineHomMapOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instIsFiltered
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instNeg
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulInt
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAddCommGroup
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAdd
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSub
attribute [-instance]
  instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
  AlgebraicCurve.instHasLocalResidue_of_hasCanonicalLocalResidueK
  AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
  AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
  ModularCurve.KwF4gRRTate.instAlgebraKAdicCompletionIntegers
  AlgebraicCurve.Place.kw_ffgc_continuousSMul_adicCompletionComap
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersCompletionCompletion
attribute [-instance]
  instLiesOverSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegersCompletionIdealAsIdeal
attribute [-instance]
  AlgebraicCurve.instHasCanonicalLocalResidueK
  AlgebraicCurve.Place.instAlgebra_restrictResidueField
  AlgebraicCurve.Place.instIsScalarTower_restrictResidueField
  AlgebraicCurve.instHasLocalResidue
  AlgebraicCurve.HasSeparableResidue.of_perfectField_of_isCurveOver
  AlgebraicCurve.HasSeparableResidue.of_perfectField
  AlgebraicCurve.Place.instIsLocalHom_restrictSubringHom
  AlgebraicCurve.instHasCanonicalLocalResidueKStar
  ModularCurve.KwNo6Pin.isLocalRing_completion
  SheafOfModules.isIso_ihomModelToIhom
  AlgebraicGeometry.OModulePresheaf.isScalarTower
  AlgebraicGeometry.Scheme.OrderedAffineCover.instLinearOrder
  AlgebraicGeometry.OModulePresheaf.module
  AlgebraicGeometry.Scheme.OrderedAffineCover.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCover.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.addCommGroup
  AlgebraicGeometry.Scheme.OrderedAffineCover.instDecidableEqIdx
  AlgebraicGeometry.OModulePresheaf.moduleSections
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.instSubsingletonObjZero
attribute [-instance]
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
  AlgebraicGeometry.OModulePresheaf.Leray.biC_module
  DoubleComplex.instModuleE₂I
  DoubleComplex.Bounded.modR
  DoubleComplex.instModuleE₂II
  DoubleComplex.instAddCommGroupE₂II
  DoubleComplex.Bounded.abGrp
  DoubleComplex.instAddCommGroupE₂I
  AlgebraicGeometry.ChowDatum.hι_closed
  AlgebraicGeometry.ChowDatumProj.hιN_closed
  AlgebraicGeometry.ChowDatumProj.hp_proper
  AlgebraicGeometry.ChowDatum.hp_isoU
  AlgebraicGeometry.ChowDatum.hp_proper
  AlgebraicGeometry.ProjSpace.algebraAway
  AlgebraicGeometry.ProjSpace.instIsProperProdOverπ
  AlgebraicGeometry.ChowDatumProj.hp_isoU
  AlgebraicGeometry.ProjSpace.isProper_π
  AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
  ProjSpaceCech.GradedModule.H.module
  ProjSpaceCech.GradedModule.H.addCommGroup
  ProjSpaceCech.GradedModule.sec.instAdd
  ProjSpaceCech.GradedModule.sec.instNeg
  ProjSpaceCech.GradedModule.acg
  ProjSpaceCech.GradedModule.Frac.setoid
  ProjSpaceCech.GradedModule.modR
  ProjSpaceCech.GradedModule.sec.instModule
  ProjSpaceCech.GradedModule.sec.instAddCommGroup
  ProjSpaceCech.GradedModule.sec.instZero
  ProjSpaceCech.GradedModule.Presentation.fJ
  ProjSpaceCech.GradedModule.sec.instSMul
  ProjSpaceCech.Twist.H.module
  ProjSpaceCech.Idx.instFintype
  ProjSpaceCech.Twist.H.addCommGroup
attribute [-instance]
  ProjSpaceCech.Idx.instDecidableEq
  ProjSpaceCech.Twist.Mon.instDecidableEq
  ProjSpaceCech.Twist.cochain.instAddCommGroup
  ProjSpaceCech.Twist.cochain.instModule
  AlgebraicGeometry.FGSubalgebra.tensorStage_directedSystem
  AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
  AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
  AlgebraicCurve.CurveModel.locallyOfFiniteType_gluedToBase
  AlgebraicCurve.CurveModel.isFractionRing_overlap
  AlgebraicCurve.CurveModel.isLocallyNoetherian_glued
  AlgebraicCurve.CurveModel.jacobsonSpace_glued
  AlgebraicCurve.CurveModel.isOpenImmersion_ι₀
  AlgebraicCurve.CurveModel.isIntegral_glued
  AlgebraicCurve.CurveModel.quasiSeparated_gluedToBase
  AlgebraicCurve.CurveModel.compactSpace_glued
  AlgebraicCurve.CurveModel.isIntegral_adjoin_chartRing
  AlgebraicCurve.CurveModel.isFractionRing_overlap_functionField
  AlgebraicCurve.CurveModel.isProper_gluedToBase
  AlgebraicCurve.CurveModel.isOpenImmersion_ιU
  AlgebraicCurve.CurveModel.isOpenImmersion_f₀
  AlgebraicCurve.CurveModel.isOpenImmersion_fInf
  AlgebraicCurve.CurveModel.isOpenImmersion_ιInf
  AlgebraicCurve.CurveModel.algebra_overlap_functionField
  AlgebraicCurve.CurveModel.quasiCompact_gluedToBase
  AlgebraicCurve.CurveModel.algebraAdjoin
  AlgebraicCurve.CurveModel.isDedekindDomain_chartRing
  AlgebraicCurve.CurveModel.isIntegralClosure
  AlgebraicCurve.CurveModel.finite_chartRing
  AlgebraicCurve.CurveModel.centre_isPrime
  AlgebraicCurve.CurveModel.isFractionRing_chartRing
  AlgebraicCurve.CurveModel.finiteType_chartRing
  AlgebraicCurve.CurveModel.isNoetherianRing_chartRing
  AlgebraicCurve.CurveModel.isScalarTower_base_adjoin
  AlgebraicCurve.CurveModel.isScalarTower_adjoin
  AlgebraicCurve.CurveModel.chartRing_finitePresentation
attribute [-simp]
  GoodReductionJacobian.RelativePic0Designation.mk.sizeOf_spec
  GoodReductionJacobian.AvatarSchemeBridge.mk.injEq
  GoodReductionJacobian.AvatarSchemeBridge.mk.sizeOf_spec
  GoodReductionJacobian.RelativePic0Designation.mk.injEq
  GoodReductionJacobian.schemeHomOverComp_coe
  NeronModelInfra.schemeHomOverEquivOverHom_apply
  GoodReductionJacobian.RelativeGroupLaw.mk.sizeOf_spec
  NeronModelInfra.schemeHomOverEquivOverHom_symm_apply
  NeronModelInfra.overHomToSchemeHomOver_coe
  GoodReductionJacobian.RelativeGroupLaw.mk.injEq
  NeronModelInfra.overHomToSchemeHomOver_schemeHomOverToOverHom
  NeronModelInfra.schemeHomOverToOverHom_left
  NeronModelInfra.schemeHomOverToOverHom_overHomToSchemeHomOver
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.sizeOf_spec
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
  AlgebraicCurve.CurveModel.mk.injEq
  AlgebraicCurve.CurveModel.mk.sizeOf_spec
  AlgebraicCurve.Place.mk.injEq
  AlgebraicCurve.Divisor.degree_single
  AlgebraicCurve.Divisor.smul_single
  AlgebraicCurve.Place.smul_toValuationSubring
  AlgebraicCurve.Place.heightOneSpectrum_asIdeal
  AlgebraicCurve.Place.coe_algebraMap
  AlgebraicCurve.Place.ord_one
  AlgebraicCurve.Place.coe_smulRingEquiv_apply
  AlgebraicCurve.Pic0.coe_degZeroSMulHom
  AlgebraicCurve.Place.deg_smul
  AlgebraicCurve.Pic0.mk_zero
  AlgebraicCurve.Place.mk.sizeOf_spec
  AlgebraicCurve.Divisor.degree_smul
  AlgebraicCurve.Pic0.mk_add
  AlgebraicCurve.Place.ord_zero
  AlgebraicCurve.Place.ofHeightOneSpectrum_toValuationSubring
  AlgebraicCurve.mulAdele_apply
attribute [-simp]
  AlgebraicCurve.residuePairing_apply_coe
  AlgebraicCurve.mem_adeleBdd
  AlgebraicCurve.weilSmul_one
  AlgebraicCurve.diagonalHom_apply
  AlgebraicCurve.weilSmul_apply
  AlgebraicCurve.adeleSpaceMul_coe
  AlgebraicCurve.mulAdele_one
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U1
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.injEq
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U0
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.mk.injEq
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.pullback_U1
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.pullback_U0
  TwoChartCech.Sections.mk.injEq
  TwoChartCech.Cover.mk.injEq
  TwoChartCech.GrothendieckComplex.mk.injEq
  TwoChartCech.Sections.mk.sizeOf_spec
  TwoChartCech.Cover.mk.sizeOf_spec
  TwoChartCech.Cover.lineBundle_r0_apply
  TwoChartCech.GrothendieckComplex.mk.sizeOf_spec
  TwoChartCech.Cover.lineBundle_r1_apply
  CoherentBaseChange.TwoTermComplex.mk.sizeOf_spec
  CoherentBaseChange.TwoTermComplex.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
  AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
  CategoryTheory.Functor.OverTotal.ofFibre_fst
  CategoryTheory.Functor.overTotal_map_fst
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_J
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYoneda_toGlued_uliftYonedaGluedToSheaf
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t'
attribute [-simp]
  uliftYoneda_toGlued_uliftYonedaGluedToSheaf_assoc
attribute [-simp]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_toGlued
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_openCover_map
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_comp
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_V
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_U
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_f
attribute [-simp]
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_P
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_toBase
  AlgebraicGeometry.RelPicard.rigSection_snd
  AlgebraicGeometry.RelPicard.RigidifiedLineBundle.ofInvertible_L
  AlgebraicGeometry.RelPicard.rigSection_snd_assoc
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
  GoodReductionJacobian.relativeGroupLawOfGrpObj_inv
  GoodReductionJacobian.relativeGroupLawOfGrpObj_mul
  GoodReductionJacobian.overHomEquivSchemeHomOver_apply_coe
  GoodReductionJacobian.relativeGroupLawOfGrpObj_one
  GoodReductionJacobian.overHomEquivSchemeHomOver_symm_apply_left
  PresheafOfModules.freeεIso_hom_app
  PresheafOfModules.freeμIso_hom_app
  AlgebraicCurve.coe_cechH0Equiv_apply
  AlgebraicCurve.cechH1ToH1_mk
  AlgebraicCurve.lSpaceOn_univ
  AlgebraicCurve.lSpaceOn_empty
  AlgebraicCurve.Place.congrEquiv_symm_apply
  AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
  AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
  AlgebraicCurve.Place.congrEquiv_apply
  AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
  AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
  AlgebraicCurve.Divisor.mapRestrict_single
  AlgebraicCurve.Divisor.pushforward_single
  AlgebraicCurve.Place.coe_restrictInclusion
  AlgebraicCurve.Place.mem_fiber
  AlgebraicCurve.Place.restrict_toValuationSubring
  AlgebraicCurve.Divisor.degree_pushforward
  AlgebraicCurve.Place.restrictResidueMap_residue
  AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
  AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
  AlgebraicCurve.Place.placeOfPrime_toValuationSubring
  AlgebraicCurve.Place.mem_fiberOver
  AlgebraicCurve.Place.fiberEquiv_symm_apply
  AlgebraicCurve.Place.fiberEquiv_apply
  AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
attribute [-simp]
  AlgebraicCurve.Divisor.degree_pushforwardAlong
  AlgebraicCurve.Pic0.coe_degZeroCorrespondence
  AlgebraicCurve.Place.mem_fiberAlong
  AlgebraicCurve.SemilinearAut.toRingAut_inv
  AlgebraicCurve.SemilinearAut.smul_def
  AlgebraicCurve.SemilinearAut.smul_single
  AlgebraicCurve.SemilinearAut.smul_toValuationSubring
  AlgebraicCurve.SemilinearAut.baseAut_inv
  AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_one
  AlgebraicCurve.SemilinearAut.deg_smul
  AlgebraicCurve.SemilinearAut.degree_smul
  AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
  AlgebraicCurve.SemilinearAut.baseAut_mul
  AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
  AlgebraicCurve.SemilinearAut.baseAut_one
  AlgebraicCurve.SemilinearAut.ofAlgAut_smul
  AlgebraicCurve.SemilinearAut.coe_torsion_smul
  AlgebraicCurve.SemilinearAut.toRingAut_mul
attribute [-simp]
  AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeInfty
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_some
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeOfPoint
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_none
  AlgebraicCurve.Divisor.evalFun_zero
  AlgebraicCurve.Place.evalAt_one
  AlgebraicCurve.Place.differentialCoeff_zero
  AlgebraicCurve.Place.differentialCoeff_dCoord
  AlgebraicCurve.TranscendenceTower.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
  AlgebraicCurve.TranscendenceTower.mk.injEq
  AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec
  AlgebraicCurve.PoleDivisorPackage.mk.injEq
  AlgebraicGeometry.RelPicard.thetaBundle_def
attribute [-simp]
  AlgebraicGeometry.RelPicard.picardBundle_def
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_ofRelEffDivisor
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_I
  AlgebraicGeometry.mapOnProdOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.mk.sizeOf_spec
  AlgebraicGeometry.RelEffCartierDiv.mk.injEq
  AlgebraicGeometry.mapOnProdOver_snd
  AlgebraicGeometry.mapOnProdOver_fst
  AlgebraicGeometry.mapOnProdOver_snd_assoc
  AlgebraicGeometry.mapOnProdOver_id
  AlgebraicCurve.RelEffDivisor.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_fst
  AlgebraicCurve.mapOnProd_fst_assoc
  AlgebraicCurve.mapOnProd_snd
  AlgebraicCurve.UnivDivisorPack.mk.injEq
  AlgebraicCurve.RelEffDivisor.mk.injEq
  AlgebraicCurve.UnivDivisorPack.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_snd_assoc
  AlgebraicGeometry.Scheme.Modules.exteriorPower_obj
  PresheafOfModules.exteriorPower_map_ιMulti
  PresheafOfModules.ExteriorPower.appₗ_apply
  AlgebraicGeometry.prodKerGraph_one
  AlgebraicGeometry.fibrePowOver.proj_comp
  AlgebraicGeometry.prodKerGraph_zero
  AlgebraicGeometry.RelEffCartierDiv.empty_I
  AlgebraicGeometry.fibrePowOver.proj_comp_assoc
  AlgebraicGeometry.graphOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
  AlgebraicGeometry.graphOver_fst
  AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
  AlgebraicGeometry.graphOver_snd
  AlgebraicGeometry.graphOver_snd_assoc
  AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
  AlgebraicCurve.SymmetricPowerPackage.mk.injEq
  AlgebraicGeometry.FGSubalgebra.cocone_ι_app_apply
  AlgebraicGeometry.RelPicard.fst_toProdSpec
  AlgebraicGeometry.RelPicard.toProdSpec_fst_assoc
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_cons
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_nil
attribute [-simp]
  AlgebraicGeometry.RelPicard.fst_toProdSpec_assoc
  AlgebraicGeometry.RelPicard.toProdSpec_fst
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.sizeOf_spec
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.injEq
  AlgebraicCurve.adeleSingle_coe
  AlgebraicCurve.kaehlerResidueTermKFam_apply
  AlgebraicCurve.Place.LocalResidueData.mk.injEq
  AlgebraicCurve.Place.LocalResidueData.mk.sizeOf_spec
  AlgebraicCurve.Place.kw_ffgc_adicCompletionComapIntegers_coe
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.sizeOf_spec
  AlgebraicCurve.Place.mem_simplePoleSubmodule
  AlgebraicCurve.Place.coe_uniformizerSubring
  ModularCurve.Lg37.Lg37CompletionSection.mk.injEq
  AlgebraicCurve.Place.CoefficientFieldSection.mk.injEq
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.injEq
  ModularCurve.Lg37.Lg37CompletionSection.mk.sizeOf_spec
  AlgebraicCurve.Place.CoefficientFieldSection.mk.sizeOf_spec
  AlgebraicCurve.Place.poleSubmodule_one
  AlgebraicCurve.Place.mem_poleSubmodule
  AlgebraicGeometry.Scheme.Modules.toUnitSection_ofUnitSection
  AlgebraicGeometry.Scheme.Modules.pullbackSection_def
  AlgebraicGeometry.Scheme.Modules.ofUnitSection_toUnitSection
  PresheafOfModules.InternalHom.IsSheafAux.appAt_toPresheafHom
attribute [-simp]
  SheafOfModules.ihomSectionsEquivFamily_unit
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_apply
  SheafOfModules.ihomEval_unit_app
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_right
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_left
  AlgebraicGeometry.Scheme.Modules.homOfFamily_app_apply
  SheafOfModules.unit_ihomSectionsEquivFamily
  AlgebraicGeometry.Scheme.Modules.familyOfHom_app
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_hom_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_inv_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomOfFamily_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_symm_apply
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_right
  AlgebraicGeometry.Scheme.Modules.map_unitSection
  AlgebraicGeometry.Scheme.Modules.tensorSectionsBilin_apply
  AlgebraicGeometry.Scheme.Modules.tensorPowSection_zero
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_left
  AlgebraicGeometry.Scheme.Modules.tensorPow_zero
  AlgebraicGeometry.Scheme.Modules.tensorPow_succ
  AlgebraicGeometry.Scheme.OrderedAffineCover.mk.injEq
  AlgebraicGeometry.OModulePresheaf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCover.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.mk.injEq
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_neg
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_zero
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_sub
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_add
  AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
  AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U
  AlgebraicGeometry.OModulePresheaf.Hom.mk.injEq
  AlgebraicGeometry.OModulePresheaf.Hom.id_app
  AlgebraicGeometry.OModulePresheaf.AffHom.appSections_apply
  AlgebraicGeometry.OModulePresheaf.AffHom.comp_app
  AlgebraicGeometry.OModulePresheaf.AffSES.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.AffHom.kerMap_coe
  AlgebraicGeometry.OModulePresheaf.AffHom.id_app
  AlgebraicGeometry.OModulePresheaf.Hom.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.Hom.toAffHom_app
attribute [-simp]
  AlgebraicGeometry.OModulePresheaf.SES.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.AffHom.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.Hom.comp_app
  AlgebraicGeometry.OModulePresheaf.SES.mk.injEq
  AlgebraicGeometry.OModulePresheaf.AffHom.mk.injEq
  AlgebraicGeometry.OModulePresheaf.Hom.appSections_apply
  AlgebraicGeometry.OModulePresheaf.AffSES.mk.injEq
  AlgebraicGeometry.OModulePresheaf.prod_obj
  AlgebraicGeometry.OModulePresheaf.restrOpen_obj
  AlgebraicGeometry.OModulePresheaf.DevissageStep.mk.injEq
  AlgebraicGeometry.OModulePresheaf.pushforward_obj
  AlgebraicGeometry.OModulePresheaf.im_obj
  AlgebraicGeometry.OModulePresheaf.pow_obj
  AlgebraicGeometry.OModulePresheaf.fstHom_app
  AlgebraicGeometry.OModulePresheaf.ker_obj
  AlgebraicGeometry.OModulePresheaf.coker_obj
  AlgebraicGeometry.OModulePresheaf.DevissageStep.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCover.preimage_U
  AlgebraicGeometry.OModulePresheaf.sndHom_app
  AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
  DoubleComplex.Bounded.mk.injEq
  DoubleComplex.Bounded.mk.sizeOf_spec
  DoubleComplex.Convergence.mk.injEq
  DoubleComplex.Convergence.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.injEq
  AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatumProj.mk.injEq
  AlgebraicGeometry.ChowDatum.mk.injEq
  ProjSpaceCech.GradedModule.mk.injEq
  ProjSpaceCech.GradedModule.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Presentation.mk.injEq
  ProjSpaceCech.GradedModule.Frac.mk.injEq
  ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.shift_toLinearMap
  ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.mk.injEq
  TwoChartCech.Mumford.dK_apply
attribute [-simp]
  TwoChartCech.Mumford.ι0_apply
  TwoChartCech.Mumford.ι1_apply
  TwoChartCech.KerCoprod.dK_apply
  TwoChartCech.KerCoprod.ι1_apply
  TwoChartCech.KerCoprod.ι0_apply
  AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
  AlgebraicGeometry.RelPicard.algEquivZeroGroupCut_toSubPicCondition
  AlgebraicGeometry.RelPicard.LFP.stageHom_val
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_hom_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_inv_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.restrict_P
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp
  AlgebraicGeometry.RelEffCartierDiv.functor_map_fst
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_pullbackAlong
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_symm_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp_assoc
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top
  AlgebraicGeometry.RelEffCartierDiv.mem_supportedIn_iff
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top_eq
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
  CoherentBaseChange.FibreH0Family.mk.sizeOf_spec
  CoherentBaseChange.FibreH0Family.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.sizeOf_spec
  AlgebraicCurve.CurveModel.coe_gInf
  AlgebraicCurve.CurveModel.coe_tInvChart
  AlgebraicCurve.CurveModel.ιInf_gluedToBase_assoc
  AlgebraicCurve.CurveModel.ιInf_gluedToBase
  AlgebraicCurve.CurveModel.primeOfι₀_asIdeal
  AlgebraicCurve.CurveModel.coe_tChart
  AlgebraicCurve.CurveModel.ι₀_gluedToBase_assoc
  AlgebraicCurve.CurveModel.primeOfιInf_asIdeal
attribute [-simp]
  AlgebraicCurve.CurveModel.ι₀_gluedToBase
  AlgebraicCurve.CurveModel.coe_tma
  AlgebraicCurve.CurveModel.coe_primeEquivChartPlaces
universe u
noncomputable section
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.CategoryTheory.CartesianMonoidalCategory
open _root_.AlgebraicGeometry.RelPicard
open _root_.NeronModelInfra
namespace P2mCubeAssembly
section Slices
variable {k : Type u} [Field k]
local notation "Sk" => Spec (CommRingCat.of k)

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.ThreeSlices
attribute [-instance]
  AlgebraicGeometry.SmoothOfRelativeDimension.fiberToSpecResidueField
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_snd
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_fst
  AlgebraicGeometry.SmoothOfRelativeDimension.smooth_one
  AlgebraicGeometry.SmoothProperCurve.isIntegral_pullback_Spec_field
  AlgebraicGeometry.IsProper.fiberToSpecResidueField
  AlgebraicCurve.CurveModel.isProper
  AlgebraicCurve.CurveModel.isIntegral
  AlgebraicCurve.CurveModel.smooth
  AlgebraicCurve.Place.instIsScalarTowerSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Divisor.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instSMulAlgEquiv
  AlgebraicCurve.Place.instIsPrincipalIdealRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instIsDiscreteValuationRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Pic0.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instAlgebraSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instMulActionAlgEquiv
  AlgebraicCurve.Pic0.instSMulAlgEquiv
  TwoChartCech.Sections.M0_moduleA
  TwoChartCech.Sections.M1_module
  TwoChartCech.Cover.A01_algebra
  TwoChartCech.Cover.A0_algebra
  TwoChartCech.Cover.A1_commRing
  TwoChartCech.Cover.A1_algebra
  TwoChartCech.Sections.M01_module
  TwoChartCech.Sections.M0_addCommGroup
  TwoChartCech.Sections.M0_tower
  TwoChartCech.Sections.M01_addCommGroup
  TwoChartCech.Cover.A0_commRing
  TwoChartCech.Sections.M1_tower
  TwoChartCech.Sections.M01_moduleA
  TwoChartCech.Sections.M0_module
  TwoChartCech.Sections.M1_moduleA
  TwoChartCech.Sections.M1_addCommGroup
  TwoChartCech.Cover.A01_commRing
  TwoChartCech.Sections.M01_tower
  CoherentBaseChange.TwoTermComplex.C0_module
  CoherentBaseChange.TwoTermComplex.C0_addCommGroup
  CoherentBaseChange.TwoTermComplex.C1_module
  CoherentBaseChange.TwoTermComplex.C1_addCommGroup
attribute [-instance]
  CoherentBaseChange.TwoTermComplex.C0_free
  CoherentBaseChange.TwoTermComplex.C1_finite
  CoherentBaseChange.TwoTermComplex.C0_finite
  CoherentBaseChange.TwoTermComplex.C1_free
  AlgebraicCurve.IsCurveOver.instNontrivialKaehler
  AlgebraicCurve.IsCurveOver.instFreeKaehler
  AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
  AlgebraicCurve.IsCurveOver.instFiniteResidue
attribute [-instance]
  instIsLocallyInjectiveFunUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsLocallySurjectiveUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsOpenImmersionToGlued
attribute [-instance]
  instIsIsoSheafZariskiTopologyTypeUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.RelPicard.isOpenImmersion_toGlued
  AlgebraicGeometry.Scheme.Modules.preservesBinaryProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback_monoidal
  AlgebraicGeometry.Scheme.Modules.sheafify_isLocalization'
  AlgebraicGeometry.Scheme.Modules.preservesTerminal_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback₀_monoidal
  AlgebraicGeometry.Scheme.Modules.preservesFiniteProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.sheafifyPullback_lifting
  PresheafOfModules.PullbackMonoidal.pullback_monoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ
  PresheafOfModules.pushforward_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_η
  PresheafOfModules.free_monoidal
  PresheafOfModules.restrictScalars_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ_gS
  PresheafOfModules.pullback_oplaxMonoidal
attribute [-instance]
  instPreservesColimitsOfSizeCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierPb
attribute [-instance]
  PresheafOfModules.pullback_monoidal'
  AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
  AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
  AlgebraicCurve.Place.instIsPrimeCenter
  AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
  instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
  AlgebraicCurve.Pic0.instModuleZModTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instSMulTorsion
  AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
  AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
  AlgebraicCurve.RationalFunctionField.instNontrivialInftyValueGroup
  PresheafOfModules.ExteriorPower.instModulePresheafAb
  AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
  AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
  AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
  AlgebraicGeometry.isClosedImmersion_graphOver
  AlgebraicGeometry.FGSubalgebra.instIsDirectedLe
attribute [-instance]
  instQuasiSeparatedSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsCofilteredOpposite
  AlgebraicGeometry.FGSubalgebra.instIsAffineObjOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instNonempty
  AlgebraicGeometry.FGSubalgebra.instNonemptySubtypeLeSubalgebraValFG
attribute [-instance]
  instCompactSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsDirectedSubtypeLeSubalgebraValFG
  AlgebraicGeometry.FGSubalgebra.instIsAffineHomMapOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instIsFiltered
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instNeg
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulInt
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAddCommGroup
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAdd
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSub
attribute [-instance]
  instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
  AlgebraicCurve.instHasLocalResidue_of_hasCanonicalLocalResidueK
  AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
  AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
  ModularCurve.KwF4gRRTate.instAlgebraKAdicCompletionIntegers
  AlgebraicCurve.Place.kw_ffgc_continuousSMul_adicCompletionComap
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersCompletionCompletion
attribute [-instance]
  instLiesOverSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegersCompletionIdealAsIdeal
attribute [-instance]
  AlgebraicCurve.instHasCanonicalLocalResidueK
  AlgebraicCurve.Place.instAlgebra_restrictResidueField
  AlgebraicCurve.Place.instIsScalarTower_restrictResidueField
  AlgebraicCurve.instHasLocalResidue
  AlgebraicCurve.HasSeparableResidue.of_perfectField_of_isCurveOver
  AlgebraicCurve.HasSeparableResidue.of_perfectField
  AlgebraicCurve.Place.instIsLocalHom_restrictSubringHom
  AlgebraicCurve.instHasCanonicalLocalResidueKStar
  ModularCurve.KwNo6Pin.isLocalRing_completion
  SheafOfModules.isIso_ihomModelToIhom
  AlgebraicGeometry.OModulePresheaf.isScalarTower
  AlgebraicGeometry.Scheme.OrderedAffineCover.instLinearOrder
  AlgebraicGeometry.OModulePresheaf.module
  AlgebraicGeometry.Scheme.OrderedAffineCover.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCover.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.addCommGroup
  AlgebraicGeometry.Scheme.OrderedAffineCover.instDecidableEqIdx
  AlgebraicGeometry.OModulePresheaf.moduleSections
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.instSubsingletonObjZero
attribute [-instance]
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
  AlgebraicGeometry.OModulePresheaf.Leray.biC_module
  DoubleComplex.instModuleE₂I
  DoubleComplex.Bounded.modR
  DoubleComplex.instModuleE₂II
  DoubleComplex.instAddCommGroupE₂II
  DoubleComplex.Bounded.abGrp
  DoubleComplex.instAddCommGroupE₂I
  AlgebraicGeometry.ChowDatum.hι_closed
  AlgebraicGeometry.ChowDatumProj.hιN_closed
  AlgebraicGeometry.ChowDatumProj.hp_proper
  AlgebraicGeometry.ChowDatum.hp_isoU
  AlgebraicGeometry.ChowDatum.hp_proper
  AlgebraicGeometry.ProjSpace.algebraAway
  AlgebraicGeometry.ProjSpace.instIsProperProdOverπ
  AlgebraicGeometry.ChowDatumProj.hp_isoU
  AlgebraicGeometry.ProjSpace.isProper_π
  AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
  ProjSpaceCech.GradedModule.H.module
  ProjSpaceCech.GradedModule.H.addCommGroup
  ProjSpaceCech.GradedModule.sec.instAdd
  ProjSpaceCech.GradedModule.sec.instNeg
  ProjSpaceCech.GradedModule.acg
  ProjSpaceCech.GradedModule.Frac.setoid
  ProjSpaceCech.GradedModule.modR
  ProjSpaceCech.GradedModule.sec.instModule
  ProjSpaceCech.GradedModule.sec.instAddCommGroup
  ProjSpaceCech.GradedModule.sec.instZero
  ProjSpaceCech.GradedModule.Presentation.fJ
  ProjSpaceCech.GradedModule.sec.instSMul
  ProjSpaceCech.Twist.H.module
  ProjSpaceCech.Idx.instFintype
  ProjSpaceCech.Twist.H.addCommGroup
attribute [-instance]
  ProjSpaceCech.Idx.instDecidableEq
  ProjSpaceCech.Twist.Mon.instDecidableEq
  ProjSpaceCech.Twist.cochain.instAddCommGroup
  ProjSpaceCech.Twist.cochain.instModule
  AlgebraicGeometry.FGSubalgebra.tensorStage_directedSystem
  AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
  AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
  AlgebraicCurve.CurveModel.locallyOfFiniteType_gluedToBase
  AlgebraicCurve.CurveModel.isFractionRing_overlap
  AlgebraicCurve.CurveModel.isLocallyNoetherian_glued
  AlgebraicCurve.CurveModel.jacobsonSpace_glued
  AlgebraicCurve.CurveModel.isOpenImmersion_ι₀
  AlgebraicCurve.CurveModel.isIntegral_glued
  AlgebraicCurve.CurveModel.quasiSeparated_gluedToBase
  AlgebraicCurve.CurveModel.compactSpace_glued
  AlgebraicCurve.CurveModel.isIntegral_adjoin_chartRing
  AlgebraicCurve.CurveModel.isFractionRing_overlap_functionField
  AlgebraicCurve.CurveModel.isProper_gluedToBase
  AlgebraicCurve.CurveModel.isOpenImmersion_ιU
  AlgebraicCurve.CurveModel.isOpenImmersion_f₀
  AlgebraicCurve.CurveModel.isOpenImmersion_fInf
  AlgebraicCurve.CurveModel.isOpenImmersion_ιInf
  AlgebraicCurve.CurveModel.algebra_overlap_functionField
  AlgebraicCurve.CurveModel.quasiCompact_gluedToBase
  AlgebraicCurve.CurveModel.algebraAdjoin
  AlgebraicCurve.CurveModel.isDedekindDomain_chartRing
  AlgebraicCurve.CurveModel.isIntegralClosure
  AlgebraicCurve.CurveModel.finite_chartRing
  AlgebraicCurve.CurveModel.centre_isPrime
  AlgebraicCurve.CurveModel.isFractionRing_chartRing
  AlgebraicCurve.CurveModel.finiteType_chartRing
  AlgebraicCurve.CurveModel.isNoetherianRing_chartRing
  AlgebraicCurve.CurveModel.isScalarTower_base_adjoin
  AlgebraicCurve.CurveModel.isScalarTower_adjoin
  AlgebraicCurve.CurveModel.chartRing_finitePresentation
attribute [-simp]
  GoodReductionJacobian.RelativePic0Designation.mk.sizeOf_spec
  GoodReductionJacobian.AvatarSchemeBridge.mk.injEq
  GoodReductionJacobian.AvatarSchemeBridge.mk.sizeOf_spec
  GoodReductionJacobian.RelativePic0Designation.mk.injEq
  GoodReductionJacobian.schemeHomOverComp_coe
  NeronModelInfra.schemeHomOverEquivOverHom_apply
  GoodReductionJacobian.RelativeGroupLaw.mk.sizeOf_spec
  NeronModelInfra.schemeHomOverEquivOverHom_symm_apply
  NeronModelInfra.overHomToSchemeHomOver_coe
  GoodReductionJacobian.RelativeGroupLaw.mk.injEq
  NeronModelInfra.overHomToSchemeHomOver_schemeHomOverToOverHom
  NeronModelInfra.schemeHomOverToOverHom_left
  NeronModelInfra.schemeHomOverToOverHom_overHomToSchemeHomOver
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.sizeOf_spec
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
  AlgebraicCurve.CurveModel.mk.injEq
  AlgebraicCurve.CurveModel.mk.sizeOf_spec
  AlgebraicCurve.Place.mk.injEq
  AlgebraicCurve.Divisor.degree_single
  AlgebraicCurve.Divisor.smul_single
  AlgebraicCurve.Place.smul_toValuationSubring
  AlgebraicCurve.Place.heightOneSpectrum_asIdeal
  AlgebraicCurve.Place.coe_algebraMap
  AlgebraicCurve.Place.ord_one
  AlgebraicCurve.Place.coe_smulRingEquiv_apply
  AlgebraicCurve.Pic0.coe_degZeroSMulHom
  AlgebraicCurve.Place.deg_smul
  AlgebraicCurve.Pic0.mk_zero
  AlgebraicCurve.Place.mk.sizeOf_spec
  AlgebraicCurve.Divisor.degree_smul
  AlgebraicCurve.Pic0.mk_add
  AlgebraicCurve.Place.ord_zero
  AlgebraicCurve.Place.ofHeightOneSpectrum_toValuationSubring
  AlgebraicCurve.mulAdele_apply
attribute [-simp]
  AlgebraicCurve.residuePairing_apply_coe
  AlgebraicCurve.mem_adeleBdd
  AlgebraicCurve.weilSmul_one
  AlgebraicCurve.diagonalHom_apply
  AlgebraicCurve.weilSmul_apply
  AlgebraicCurve.adeleSpaceMul_coe
  AlgebraicCurve.mulAdele_one
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U1
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.injEq
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U0
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.mk.injEq
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.pullback_U1
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.pullback_U0
  TwoChartCech.Sections.mk.injEq
  TwoChartCech.Cover.mk.injEq
  TwoChartCech.GrothendieckComplex.mk.injEq
  TwoChartCech.Sections.mk.sizeOf_spec
  TwoChartCech.Cover.mk.sizeOf_spec
  TwoChartCech.Cover.lineBundle_r0_apply
  TwoChartCech.GrothendieckComplex.mk.sizeOf_spec
  TwoChartCech.Cover.lineBundle_r1_apply
  CoherentBaseChange.TwoTermComplex.mk.sizeOf_spec
  CoherentBaseChange.TwoTermComplex.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
  AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
  CategoryTheory.Functor.OverTotal.ofFibre_fst
  CategoryTheory.Functor.overTotal_map_fst
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_J
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYoneda_toGlued_uliftYonedaGluedToSheaf
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t'
attribute [-simp]
  uliftYoneda_toGlued_uliftYonedaGluedToSheaf_assoc
attribute [-simp]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_toGlued
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_openCover_map
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_comp
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_V
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_U
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_f
attribute [-simp]
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_P
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_toBase
  AlgebraicGeometry.RelPicard.rigSection_snd
  AlgebraicGeometry.RelPicard.RigidifiedLineBundle.ofInvertible_L
  AlgebraicGeometry.RelPicard.rigSection_snd_assoc
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
  GoodReductionJacobian.relativeGroupLawOfGrpObj_inv
  GoodReductionJacobian.relativeGroupLawOfGrpObj_mul
  GoodReductionJacobian.overHomEquivSchemeHomOver_apply_coe
  GoodReductionJacobian.relativeGroupLawOfGrpObj_one
  GoodReductionJacobian.overHomEquivSchemeHomOver_symm_apply_left
  PresheafOfModules.freeεIso_hom_app
  PresheafOfModules.freeμIso_hom_app
  AlgebraicCurve.coe_cechH0Equiv_apply
  AlgebraicCurve.cechH1ToH1_mk
  AlgebraicCurve.lSpaceOn_univ
  AlgebraicCurve.lSpaceOn_empty
  AlgebraicCurve.Place.congrEquiv_symm_apply
  AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
  AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
  AlgebraicCurve.Place.congrEquiv_apply
  AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
  AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
  AlgebraicCurve.Divisor.mapRestrict_single
  AlgebraicCurve.Divisor.pushforward_single
  AlgebraicCurve.Place.coe_restrictInclusion
  AlgebraicCurve.Place.mem_fiber
  AlgebraicCurve.Place.restrict_toValuationSubring
  AlgebraicCurve.Divisor.degree_pushforward
  AlgebraicCurve.Place.restrictResidueMap_residue
  AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
  AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
  AlgebraicCurve.Place.placeOfPrime_toValuationSubring
  AlgebraicCurve.Place.mem_fiberOver
  AlgebraicCurve.Place.fiberEquiv_symm_apply
  AlgebraicCurve.Place.fiberEquiv_apply
  AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
attribute [-simp]
  AlgebraicCurve.Divisor.degree_pushforwardAlong
  AlgebraicCurve.Pic0.coe_degZeroCorrespondence
  AlgebraicCurve.Place.mem_fiberAlong
  AlgebraicCurve.SemilinearAut.toRingAut_inv
  AlgebraicCurve.SemilinearAut.smul_def
  AlgebraicCurve.SemilinearAut.smul_single
  AlgebraicCurve.SemilinearAut.smul_toValuationSubring
  AlgebraicCurve.SemilinearAut.baseAut_inv
  AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_one
  AlgebraicCurve.SemilinearAut.deg_smul
  AlgebraicCurve.SemilinearAut.degree_smul
  AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
  AlgebraicCurve.SemilinearAut.baseAut_mul
  AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
  AlgebraicCurve.SemilinearAut.baseAut_one
  AlgebraicCurve.SemilinearAut.ofAlgAut_smul
  AlgebraicCurve.SemilinearAut.coe_torsion_smul
  AlgebraicCurve.SemilinearAut.toRingAut_mul
attribute [-simp]
  AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeInfty
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_some
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeOfPoint
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_none
  AlgebraicCurve.Divisor.evalFun_zero
  AlgebraicCurve.Place.evalAt_one
  AlgebraicCurve.Place.differentialCoeff_zero
  AlgebraicCurve.Place.differentialCoeff_dCoord
  AlgebraicCurve.TranscendenceTower.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
  AlgebraicCurve.TranscendenceTower.mk.injEq
  AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec
  AlgebraicCurve.PoleDivisorPackage.mk.injEq
  AlgebraicGeometry.RelPicard.thetaBundle_def
attribute [-simp]
  AlgebraicGeometry.RelPicard.picardBundle_def
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_ofRelEffDivisor
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_I
  AlgebraicGeometry.mapOnProdOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.mk.sizeOf_spec
  AlgebraicGeometry.RelEffCartierDiv.mk.injEq
  AlgebraicGeometry.mapOnProdOver_snd
  AlgebraicGeometry.mapOnProdOver_fst
  AlgebraicGeometry.mapOnProdOver_snd_assoc
  AlgebraicGeometry.mapOnProdOver_id
  AlgebraicCurve.RelEffDivisor.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_fst
  AlgebraicCurve.mapOnProd_fst_assoc
  AlgebraicCurve.mapOnProd_snd
  AlgebraicCurve.UnivDivisorPack.mk.injEq
  AlgebraicCurve.RelEffDivisor.mk.injEq
  AlgebraicCurve.UnivDivisorPack.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_snd_assoc
  AlgebraicGeometry.Scheme.Modules.exteriorPower_obj
  PresheafOfModules.exteriorPower_map_ιMulti
  PresheafOfModules.ExteriorPower.appₗ_apply
  AlgebraicGeometry.prodKerGraph_one
  AlgebraicGeometry.fibrePowOver.proj_comp
  AlgebraicGeometry.prodKerGraph_zero
  AlgebraicGeometry.RelEffCartierDiv.empty_I
  AlgebraicGeometry.fibrePowOver.proj_comp_assoc
  AlgebraicGeometry.graphOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
  AlgebraicGeometry.graphOver_fst
  AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
  AlgebraicGeometry.graphOver_snd
  AlgebraicGeometry.graphOver_snd_assoc
  AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
  AlgebraicCurve.SymmetricPowerPackage.mk.injEq
  AlgebraicGeometry.FGSubalgebra.cocone_ι_app_apply
  AlgebraicGeometry.RelPicard.fst_toProdSpec
  AlgebraicGeometry.RelPicard.toProdSpec_fst_assoc
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_cons
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_nil
attribute [-simp]
  AlgebraicGeometry.RelPicard.fst_toProdSpec_assoc
  AlgebraicGeometry.RelPicard.toProdSpec_fst
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.sizeOf_spec
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.injEq
  AlgebraicCurve.adeleSingle_coe
  AlgebraicCurve.kaehlerResidueTermKFam_apply
  AlgebraicCurve.Place.LocalResidueData.mk.injEq
  AlgebraicCurve.Place.LocalResidueData.mk.sizeOf_spec
  AlgebraicCurve.Place.kw_ffgc_adicCompletionComapIntegers_coe
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.sizeOf_spec
  AlgebraicCurve.Place.mem_simplePoleSubmodule
  AlgebraicCurve.Place.coe_uniformizerSubring
  ModularCurve.Lg37.Lg37CompletionSection.mk.injEq
  AlgebraicCurve.Place.CoefficientFieldSection.mk.injEq
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.injEq
  ModularCurve.Lg37.Lg37CompletionSection.mk.sizeOf_spec
  AlgebraicCurve.Place.CoefficientFieldSection.mk.sizeOf_spec
  AlgebraicCurve.Place.poleSubmodule_one
  AlgebraicCurve.Place.mem_poleSubmodule
  AlgebraicGeometry.Scheme.Modules.toUnitSection_ofUnitSection
  AlgebraicGeometry.Scheme.Modules.pullbackSection_def
  AlgebraicGeometry.Scheme.Modules.ofUnitSection_toUnitSection
  PresheafOfModules.InternalHom.IsSheafAux.appAt_toPresheafHom
attribute [-simp]
  SheafOfModules.ihomSectionsEquivFamily_unit
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_apply
  SheafOfModules.ihomEval_unit_app
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_right
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_left
  AlgebraicGeometry.Scheme.Modules.homOfFamily_app_apply
  SheafOfModules.unit_ihomSectionsEquivFamily
  AlgebraicGeometry.Scheme.Modules.familyOfHom_app
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_hom_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_inv_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomOfFamily_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_symm_apply
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_right
  AlgebraicGeometry.Scheme.Modules.map_unitSection
  AlgebraicGeometry.Scheme.Modules.tensorSectionsBilin_apply
  AlgebraicGeometry.Scheme.Modules.tensorPowSection_zero
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_left
  AlgebraicGeometry.Scheme.Modules.tensorPow_zero
  AlgebraicGeometry.Scheme.Modules.tensorPow_succ
  AlgebraicGeometry.Scheme.OrderedAffineCover.mk.injEq
  AlgebraicGeometry.OModulePresheaf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCover.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.mk.injEq
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_neg
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_zero
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_sub
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_add
  AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
  AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U
  AlgebraicGeometry.OModulePresheaf.Hom.mk.injEq
  AlgebraicGeometry.OModulePresheaf.Hom.id_app
  AlgebraicGeometry.OModulePresheaf.AffHom.appSections_apply
  AlgebraicGeometry.OModulePresheaf.AffHom.comp_app
  AlgebraicGeometry.OModulePresheaf.AffSES.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.AffHom.kerMap_coe
  AlgebraicGeometry.OModulePresheaf.AffHom.id_app
  AlgebraicGeometry.OModulePresheaf.Hom.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.Hom.toAffHom_app
attribute [-simp]
  AlgebraicGeometry.OModulePresheaf.SES.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.AffHom.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.Hom.comp_app
  AlgebraicGeometry.OModulePresheaf.SES.mk.injEq
  AlgebraicGeometry.OModulePresheaf.AffHom.mk.injEq
  AlgebraicGeometry.OModulePresheaf.Hom.appSections_apply
  AlgebraicGeometry.OModulePresheaf.AffSES.mk.injEq
  AlgebraicGeometry.OModulePresheaf.prod_obj
  AlgebraicGeometry.OModulePresheaf.restrOpen_obj
  AlgebraicGeometry.OModulePresheaf.DevissageStep.mk.injEq
  AlgebraicGeometry.OModulePresheaf.pushforward_obj
  AlgebraicGeometry.OModulePresheaf.im_obj
  AlgebraicGeometry.OModulePresheaf.pow_obj
  AlgebraicGeometry.OModulePresheaf.fstHom_app
  AlgebraicGeometry.OModulePresheaf.ker_obj
  AlgebraicGeometry.OModulePresheaf.coker_obj
  AlgebraicGeometry.OModulePresheaf.DevissageStep.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCover.preimage_U
  AlgebraicGeometry.OModulePresheaf.sndHom_app
  AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
  DoubleComplex.Bounded.mk.injEq
  DoubleComplex.Bounded.mk.sizeOf_spec
  DoubleComplex.Convergence.mk.injEq
  DoubleComplex.Convergence.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.injEq
  AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatumProj.mk.injEq
  AlgebraicGeometry.ChowDatum.mk.injEq
  ProjSpaceCech.GradedModule.mk.injEq
  ProjSpaceCech.GradedModule.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Presentation.mk.injEq
  ProjSpaceCech.GradedModule.Frac.mk.injEq
  ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.shift_toLinearMap
  ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.mk.injEq
  TwoChartCech.Mumford.dK_apply
attribute [-simp]
  TwoChartCech.Mumford.ι0_apply
  TwoChartCech.Mumford.ι1_apply
  TwoChartCech.KerCoprod.dK_apply
  TwoChartCech.KerCoprod.ι1_apply
  TwoChartCech.KerCoprod.ι0_apply
  AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
  AlgebraicGeometry.RelPicard.algEquivZeroGroupCut_toSubPicCondition
  AlgebraicGeometry.RelPicard.LFP.stageHom_val
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_hom_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_inv_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.restrict_P
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp
  AlgebraicGeometry.RelEffCartierDiv.functor_map_fst
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_pullbackAlong
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_symm_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp_assoc
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top
  AlgebraicGeometry.RelEffCartierDiv.mem_supportedIn_iff
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top_eq
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
  CoherentBaseChange.FibreH0Family.mk.sizeOf_spec
  CoherentBaseChange.FibreH0Family.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.sizeOf_spec
  AlgebraicCurve.CurveModel.coe_gInf
  AlgebraicCurve.CurveModel.coe_tInvChart
  AlgebraicCurve.CurveModel.ιInf_gluedToBase_assoc
  AlgebraicCurve.CurveModel.ιInf_gluedToBase
  AlgebraicCurve.CurveModel.primeOfι₀_asIdeal
  AlgebraicCurve.CurveModel.coe_tChart
  AlgebraicCurve.CurveModel.ι₀_gluedToBase_assoc
  AlgebraicCurve.CurveModel.primeOfιInf_asIdeal
attribute [-simp]
  AlgebraicCurve.CurveModel.ι₀_gluedToBase
  AlgebraicCurve.CurveModel.coe_tma
  AlgebraicCurve.CurveModel.coe_primeEquivChartPlaces
universe u
noncomputable section
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.CategoryTheory.CartesianMonoidalCategory
open _root_.AlgebraicGeometry.RelPicard
open _root_.NeronModelInfra
namespace P2mCubeAssembly
section Slices
variable {k : Type u} [Field k]
local notation "Sk" => Spec (CommRingCat.of k)

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.ThreeSlices
attribute [-instance]
  AlgebraicGeometry.SmoothOfRelativeDimension.fiberToSpecResidueField
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_snd
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_fst
  AlgebraicGeometry.SmoothOfRelativeDimension.smooth_one
  AlgebraicGeometry.SmoothProperCurve.isIntegral_pullback_Spec_field
  AlgebraicGeometry.IsProper.fiberToSpecResidueField
  AlgebraicCurve.CurveModel.isProper
  AlgebraicCurve.CurveModel.isIntegral
  AlgebraicCurve.CurveModel.smooth
  AlgebraicCurve.Place.instIsScalarTowerSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Divisor.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instSMulAlgEquiv
  AlgebraicCurve.Place.instIsPrincipalIdealRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instIsDiscreteValuationRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Pic0.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instAlgebraSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instMulActionAlgEquiv
  AlgebraicCurve.Pic0.instSMulAlgEquiv
  TwoChartCech.Sections.M0_moduleA
  TwoChartCech.Sections.M1_module
  TwoChartCech.Cover.A01_algebra
  TwoChartCech.Cover.A0_algebra
  TwoChartCech.Cover.A1_commRing
  TwoChartCech.Cover.A1_algebra
  TwoChartCech.Sections.M01_module
  TwoChartCech.Sections.M0_addCommGroup
  TwoChartCech.Sections.M0_tower
  TwoChartCech.Sections.M01_addCommGroup
  TwoChartCech.Cover.A0_commRing
  TwoChartCech.Sections.M1_tower
  TwoChartCech.Sections.M01_moduleA
  TwoChartCech.Sections.M0_module
  TwoChartCech.Sections.M1_moduleA
  TwoChartCech.Sections.M1_addCommGroup
  TwoChartCech.Cover.A01_commRing
  TwoChartCech.Sections.M01_tower
  CoherentBaseChange.TwoTermComplex.C0_module
  CoherentBaseChange.TwoTermComplex.C0_addCommGroup
  CoherentBaseChange.TwoTermComplex.C1_module
  CoherentBaseChange.TwoTermComplex.C1_addCommGroup
attribute [-instance]
  CoherentBaseChange.TwoTermComplex.C0_free
  CoherentBaseChange.TwoTermComplex.C1_finite
  CoherentBaseChange.TwoTermComplex.C0_finite
  CoherentBaseChange.TwoTermComplex.C1_free
  AlgebraicCurve.IsCurveOver.instNontrivialKaehler
  AlgebraicCurve.IsCurveOver.instFreeKaehler
  AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
  AlgebraicCurve.IsCurveOver.instFiniteResidue
attribute [-instance]
  instIsLocallyInjectiveFunUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsLocallySurjectiveUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsOpenImmersionToGlued
attribute [-instance]
  instIsIsoSheafZariskiTopologyTypeUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.RelPicard.isOpenImmersion_toGlued
  AlgebraicGeometry.Scheme.Modules.preservesBinaryProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback_monoidal
  AlgebraicGeometry.Scheme.Modules.sheafify_isLocalization'
  AlgebraicGeometry.Scheme.Modules.preservesTerminal_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback₀_monoidal
  AlgebraicGeometry.Scheme.Modules.preservesFiniteProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.sheafifyPullback_lifting
  PresheafOfModules.PullbackMonoidal.pullback_monoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ
  PresheafOfModules.pushforward_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_η
  PresheafOfModules.free_monoidal
  PresheafOfModules.restrictScalars_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ_gS
  PresheafOfModules.pullback_oplaxMonoidal
attribute [-instance]
  instPreservesColimitsOfSizeCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierPb
attribute [-instance]
  PresheafOfModules.pullback_monoidal'
  AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
  AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
  AlgebraicCurve.Place.instIsPrimeCenter
  AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
  instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
  AlgebraicCurve.Pic0.instModuleZModTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instSMulTorsion
  AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
  AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
  AlgebraicCurve.RationalFunctionField.instNontrivialInftyValueGroup
  PresheafOfModules.ExteriorPower.instModulePresheafAb
  AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
  AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
  AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
  AlgebraicGeometry.isClosedImmersion_graphOver
  AlgebraicGeometry.FGSubalgebra.instIsDirectedLe
attribute [-instance]
  instQuasiSeparatedSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsCofilteredOpposite
  AlgebraicGeometry.FGSubalgebra.instIsAffineObjOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instNonempty
  AlgebraicGeometry.FGSubalgebra.instNonemptySubtypeLeSubalgebraValFG
attribute [-instance]
  instCompactSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsDirectedSubtypeLeSubalgebraValFG
  AlgebraicGeometry.FGSubalgebra.instIsAffineHomMapOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instIsFiltered
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instNeg
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulInt
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAddCommGroup
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAdd
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSub
attribute [-instance]
  instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
  AlgebraicCurve.instHasLocalResidue_of_hasCanonicalLocalResidueK
  AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
  AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
  ModularCurve.KwF4gRRTate.instAlgebraKAdicCompletionIntegers
  AlgebraicCurve.Place.kw_ffgc_continuousSMul_adicCompletionComap
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersCompletionCompletion
attribute [-instance]
  instLiesOverSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegersCompletionIdealAsIdeal
attribute [-instance]
  AlgebraicCurve.instHasCanonicalLocalResidueK
  AlgebraicCurve.Place.instAlgebra_restrictResidueField
  AlgebraicCurve.Place.instIsScalarTower_restrictResidueField
  AlgebraicCurve.instHasLocalResidue
  AlgebraicCurve.HasSeparableResidue.of_perfectField_of_isCurveOver
  AlgebraicCurve.HasSeparableResidue.of_perfectField
  AlgebraicCurve.Place.instIsLocalHom_restrictSubringHom
  AlgebraicCurve.instHasCanonicalLocalResidueKStar
  ModularCurve.KwNo6Pin.isLocalRing_completion
  SheafOfModules.isIso_ihomModelToIhom
  AlgebraicGeometry.OModulePresheaf.isScalarTower
  AlgebraicGeometry.Scheme.OrderedAffineCover.instLinearOrder
  AlgebraicGeometry.OModulePresheaf.module
  AlgebraicGeometry.Scheme.OrderedAffineCover.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCover.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.addCommGroup
  AlgebraicGeometry.Scheme.OrderedAffineCover.instDecidableEqIdx
  AlgebraicGeometry.OModulePresheaf.moduleSections
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.instSubsingletonObjZero
attribute [-instance]
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
  AlgebraicGeometry.OModulePresheaf.Leray.biC_module
  DoubleComplex.instModuleE₂I
  DoubleComplex.Bounded.modR
  DoubleComplex.instModuleE₂II
  DoubleComplex.instAddCommGroupE₂II
  DoubleComplex.Bounded.abGrp
  DoubleComplex.instAddCommGroupE₂I
  AlgebraicGeometry.ChowDatum.hι_closed
  AlgebraicGeometry.ChowDatumProj.hιN_closed
  AlgebraicGeometry.ChowDatumProj.hp_proper
  AlgebraicGeometry.ChowDatum.hp_isoU
  AlgebraicGeometry.ChowDatum.hp_proper
  AlgebraicGeometry.ProjSpace.algebraAway
  AlgebraicGeometry.ProjSpace.instIsProperProdOverπ
  AlgebraicGeometry.ChowDatumProj.hp_isoU
  AlgebraicGeometry.ProjSpace.isProper_π
  AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
  ProjSpaceCech.GradedModule.H.module
  ProjSpaceCech.GradedModule.H.addCommGroup
  ProjSpaceCech.GradedModule.sec.instAdd
  ProjSpaceCech.GradedModule.sec.instNeg
  ProjSpaceCech.GradedModule.acg
  ProjSpaceCech.GradedModule.Frac.setoid
  ProjSpaceCech.GradedModule.modR
  ProjSpaceCech.GradedModule.sec.instModule
  ProjSpaceCech.GradedModule.sec.instAddCommGroup
  ProjSpaceCech.GradedModule.sec.instZero
  ProjSpaceCech.GradedModule.Presentation.fJ
  ProjSpaceCech.GradedModule.sec.instSMul
  ProjSpaceCech.Twist.H.module
  ProjSpaceCech.Idx.instFintype
  ProjSpaceCech.Twist.H.addCommGroup
attribute [-instance]
  ProjSpaceCech.Idx.instDecidableEq
  ProjSpaceCech.Twist.Mon.instDecidableEq
  ProjSpaceCech.Twist.cochain.instAddCommGroup
  ProjSpaceCech.Twist.cochain.instModule
  AlgebraicGeometry.FGSubalgebra.tensorStage_directedSystem
  AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
  AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
  AlgebraicCurve.CurveModel.locallyOfFiniteType_gluedToBase
  AlgebraicCurve.CurveModel.isFractionRing_overlap
  AlgebraicCurve.CurveModel.isLocallyNoetherian_glued
  AlgebraicCurve.CurveModel.jacobsonSpace_glued
  AlgebraicCurve.CurveModel.isOpenImmersion_ι₀
  AlgebraicCurve.CurveModel.isIntegral_glued
  AlgebraicCurve.CurveModel.quasiSeparated_gluedToBase
  AlgebraicCurve.CurveModel.compactSpace_glued
  AlgebraicCurve.CurveModel.isIntegral_adjoin_chartRing
  AlgebraicCurve.CurveModel.isFractionRing_overlap_functionField
  AlgebraicCurve.CurveModel.isProper_gluedToBase
  AlgebraicCurve.CurveModel.isOpenImmersion_ιU
  AlgebraicCurve.CurveModel.isOpenImmersion_f₀
  AlgebraicCurve.CurveModel.isOpenImmersion_fInf
  AlgebraicCurve.CurveModel.isOpenImmersion_ιInf
  AlgebraicCurve.CurveModel.algebra_overlap_functionField
  AlgebraicCurve.CurveModel.quasiCompact_gluedToBase
  AlgebraicCurve.CurveModel.algebraAdjoin
  AlgebraicCurve.CurveModel.isDedekindDomain_chartRing
  AlgebraicCurve.CurveModel.isIntegralClosure
  AlgebraicCurve.CurveModel.finite_chartRing
  AlgebraicCurve.CurveModel.centre_isPrime
  AlgebraicCurve.CurveModel.isFractionRing_chartRing
  AlgebraicCurve.CurveModel.finiteType_chartRing
  AlgebraicCurve.CurveModel.isNoetherianRing_chartRing
  AlgebraicCurve.CurveModel.isScalarTower_base_adjoin
  AlgebraicCurve.CurveModel.isScalarTower_adjoin
  AlgebraicCurve.CurveModel.chartRing_finitePresentation
attribute [-simp]
  GoodReductionJacobian.RelativePic0Designation.mk.sizeOf_spec
  GoodReductionJacobian.AvatarSchemeBridge.mk.injEq
  GoodReductionJacobian.AvatarSchemeBridge.mk.sizeOf_spec
  GoodReductionJacobian.RelativePic0Designation.mk.injEq
  GoodReductionJacobian.schemeHomOverComp_coe
  NeronModelInfra.schemeHomOverEquivOverHom_apply
  GoodReductionJacobian.RelativeGroupLaw.mk.sizeOf_spec
  NeronModelInfra.schemeHomOverEquivOverHom_symm_apply
  NeronModelInfra.overHomToSchemeHomOver_coe
  GoodReductionJacobian.RelativeGroupLaw.mk.injEq
  NeronModelInfra.overHomToSchemeHomOver_schemeHomOverToOverHom
  NeronModelInfra.schemeHomOverToOverHom_left
  NeronModelInfra.schemeHomOverToOverHom_overHomToSchemeHomOver
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.sizeOf_spec
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
  AlgebraicCurve.CurveModel.mk.injEq
  AlgebraicCurve.CurveModel.mk.sizeOf_spec
  AlgebraicCurve.Place.mk.injEq
  AlgebraicCurve.Divisor.degree_single
  AlgebraicCurve.Divisor.smul_single
  AlgebraicCurve.Place.smul_toValuationSubring
  AlgebraicCurve.Place.heightOneSpectrum_asIdeal
  AlgebraicCurve.Place.coe_algebraMap
  AlgebraicCurve.Place.ord_one
  AlgebraicCurve.Place.coe_smulRingEquiv_apply
  AlgebraicCurve.Pic0.coe_degZeroSMulHom
  AlgebraicCurve.Place.deg_smul
  AlgebraicCurve.Pic0.mk_zero
  AlgebraicCurve.Place.mk.sizeOf_spec
  AlgebraicCurve.Divisor.degree_smul
  AlgebraicCurve.Pic0.mk_add
  AlgebraicCurve.Place.ord_zero
  AlgebraicCurve.Place.ofHeightOneSpectrum_toValuationSubring
  AlgebraicCurve.mulAdele_apply
attribute [-simp]
  AlgebraicCurve.residuePairing_apply_coe
  AlgebraicCurve.mem_adeleBdd
  AlgebraicCurve.weilSmul_one
  AlgebraicCurve.diagonalHom_apply
  AlgebraicCurve.weilSmul_apply
  AlgebraicCurve.adeleSpaceMul_coe
  AlgebraicCurve.mulAdele_one
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U1
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.injEq
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U0
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.mk.injEq
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.pullback_U1
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.pullback_U0
  TwoChartCech.Sections.mk.injEq
  TwoChartCech.Cover.mk.injEq
  TwoChartCech.GrothendieckComplex.mk.injEq
  TwoChartCech.Sections.mk.sizeOf_spec
  TwoChartCech.Cover.mk.sizeOf_spec
  TwoChartCech.Cover.lineBundle_r0_apply
  TwoChartCech.GrothendieckComplex.mk.sizeOf_spec
  TwoChartCech.Cover.lineBundle_r1_apply
  CoherentBaseChange.TwoTermComplex.mk.sizeOf_spec
  CoherentBaseChange.TwoTermComplex.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
  AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
  CategoryTheory.Functor.OverTotal.ofFibre_fst
  CategoryTheory.Functor.overTotal_map_fst
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_J
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYoneda_toGlued_uliftYonedaGluedToSheaf
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t'
attribute [-simp]
  uliftYoneda_toGlued_uliftYonedaGluedToSheaf_assoc
attribute [-simp]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_toGlued
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_openCover_map
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_comp
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_V
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_U
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_f
attribute [-simp]
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_P
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_toBase
  AlgebraicGeometry.RelPicard.rigSection_snd
  AlgebraicGeometry.RelPicard.RigidifiedLineBundle.ofInvertible_L
  AlgebraicGeometry.RelPicard.rigSection_snd_assoc
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
  GoodReductionJacobian.relativeGroupLawOfGrpObj_inv
  GoodReductionJacobian.relativeGroupLawOfGrpObj_mul
  GoodReductionJacobian.overHomEquivSchemeHomOver_apply_coe
  GoodReductionJacobian.relativeGroupLawOfGrpObj_one
  GoodReductionJacobian.overHomEquivSchemeHomOver_symm_apply_left
  PresheafOfModules.freeεIso_hom_app
  PresheafOfModules.freeμIso_hom_app
  AlgebraicCurve.coe_cechH0Equiv_apply
  AlgebraicCurve.cechH1ToH1_mk
  AlgebraicCurve.lSpaceOn_univ
  AlgebraicCurve.lSpaceOn_empty
  AlgebraicCurve.Place.congrEquiv_symm_apply
  AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
  AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
  AlgebraicCurve.Place.congrEquiv_apply
  AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
  AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
  AlgebraicCurve.Divisor.mapRestrict_single
  AlgebraicCurve.Divisor.pushforward_single
  AlgebraicCurve.Place.coe_restrictInclusion
  AlgebraicCurve.Place.mem_fiber
  AlgebraicCurve.Place.restrict_toValuationSubring
  AlgebraicCurve.Divisor.degree_pushforward
  AlgebraicCurve.Place.restrictResidueMap_residue
  AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
  AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
  AlgebraicCurve.Place.placeOfPrime_toValuationSubring
  AlgebraicCurve.Place.mem_fiberOver
  AlgebraicCurve.Place.fiberEquiv_symm_apply
  AlgebraicCurve.Place.fiberEquiv_apply
  AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
attribute [-simp]
  AlgebraicCurve.Divisor.degree_pushforwardAlong
  AlgebraicCurve.Pic0.coe_degZeroCorrespondence
  AlgebraicCurve.Place.mem_fiberAlong
  AlgebraicCurve.SemilinearAut.toRingAut_inv
  AlgebraicCurve.SemilinearAut.smul_def
  AlgebraicCurve.SemilinearAut.smul_single
  AlgebraicCurve.SemilinearAut.smul_toValuationSubring
  AlgebraicCurve.SemilinearAut.baseAut_inv
  AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_one
  AlgebraicCurve.SemilinearAut.deg_smul
  AlgebraicCurve.SemilinearAut.degree_smul
  AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
  AlgebraicCurve.SemilinearAut.baseAut_mul
  AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
  AlgebraicCurve.SemilinearAut.baseAut_one
  AlgebraicCurve.SemilinearAut.ofAlgAut_smul
  AlgebraicCurve.SemilinearAut.coe_torsion_smul
  AlgebraicCurve.SemilinearAut.toRingAut_mul
attribute [-simp]
  AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeInfty
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_some
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeOfPoint
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_none
  AlgebraicCurve.Divisor.evalFun_zero
  AlgebraicCurve.Place.evalAt_one
  AlgebraicCurve.Place.differentialCoeff_zero
  AlgebraicCurve.Place.differentialCoeff_dCoord
  AlgebraicCurve.TranscendenceTower.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
  AlgebraicCurve.TranscendenceTower.mk.injEq
  AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec
  AlgebraicCurve.PoleDivisorPackage.mk.injEq
  AlgebraicGeometry.RelPicard.thetaBundle_def
attribute [-simp]
  AlgebraicGeometry.RelPicard.picardBundle_def
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_ofRelEffDivisor
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_I
  AlgebraicGeometry.mapOnProdOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.mk.sizeOf_spec
  AlgebraicGeometry.RelEffCartierDiv.mk.injEq
  AlgebraicGeometry.mapOnProdOver_snd
  AlgebraicGeometry.mapOnProdOver_fst
  AlgebraicGeometry.mapOnProdOver_snd_assoc
  AlgebraicGeometry.mapOnProdOver_id
  AlgebraicCurve.RelEffDivisor.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_fst
  AlgebraicCurve.mapOnProd_fst_assoc
  AlgebraicCurve.mapOnProd_snd
  AlgebraicCurve.UnivDivisorPack.mk.injEq
  AlgebraicCurve.RelEffDivisor.mk.injEq
  AlgebraicCurve.UnivDivisorPack.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_snd_assoc
  AlgebraicGeometry.Scheme.Modules.exteriorPower_obj
  PresheafOfModules.exteriorPower_map_ιMulti
  PresheafOfModules.ExteriorPower.appₗ_apply
  AlgebraicGeometry.prodKerGraph_one
  AlgebraicGeometry.fibrePowOver.proj_comp
  AlgebraicGeometry.prodKerGraph_zero
  AlgebraicGeometry.RelEffCartierDiv.empty_I
  AlgebraicGeometry.fibrePowOver.proj_comp_assoc
  AlgebraicGeometry.graphOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
  AlgebraicGeometry.graphOver_fst
  AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
  AlgebraicGeometry.graphOver_snd
  AlgebraicGeometry.graphOver_snd_assoc
  AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
  AlgebraicCurve.SymmetricPowerPackage.mk.injEq
  AlgebraicGeometry.FGSubalgebra.cocone_ι_app_apply
  AlgebraicGeometry.RelPicard.fst_toProdSpec
  AlgebraicGeometry.RelPicard.toProdSpec_fst_assoc
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_cons
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_nil
attribute [-simp]
  AlgebraicGeometry.RelPicard.fst_toProdSpec_assoc
  AlgebraicGeometry.RelPicard.toProdSpec_fst
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.sizeOf_spec
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.injEq
  AlgebraicCurve.adeleSingle_coe
  AlgebraicCurve.kaehlerResidueTermKFam_apply
  AlgebraicCurve.Place.LocalResidueData.mk.injEq
  AlgebraicCurve.Place.LocalResidueData.mk.sizeOf_spec
  AlgebraicCurve.Place.kw_ffgc_adicCompletionComapIntegers_coe
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.sizeOf_spec
  AlgebraicCurve.Place.mem_simplePoleSubmodule
  AlgebraicCurve.Place.coe_uniformizerSubring
  ModularCurve.Lg37.Lg37CompletionSection.mk.injEq
  AlgebraicCurve.Place.CoefficientFieldSection.mk.injEq
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.injEq
  ModularCurve.Lg37.Lg37CompletionSection.mk.sizeOf_spec
  AlgebraicCurve.Place.CoefficientFieldSection.mk.sizeOf_spec
  AlgebraicCurve.Place.poleSubmodule_one
  AlgebraicCurve.Place.mem_poleSubmodule
  AlgebraicGeometry.Scheme.Modules.toUnitSection_ofUnitSection
  AlgebraicGeometry.Scheme.Modules.pullbackSection_def
  AlgebraicGeometry.Scheme.Modules.ofUnitSection_toUnitSection
  PresheafOfModules.InternalHom.IsSheafAux.appAt_toPresheafHom
attribute [-simp]
  SheafOfModules.ihomSectionsEquivFamily_unit
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_apply
  SheafOfModules.ihomEval_unit_app
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_right
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_left
  AlgebraicGeometry.Scheme.Modules.homOfFamily_app_apply
  SheafOfModules.unit_ihomSectionsEquivFamily
  AlgebraicGeometry.Scheme.Modules.familyOfHom_app
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_hom_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_inv_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomOfFamily_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_symm_apply
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_right
  AlgebraicGeometry.Scheme.Modules.map_unitSection
  AlgebraicGeometry.Scheme.Modules.tensorSectionsBilin_apply
  AlgebraicGeometry.Scheme.Modules.tensorPowSection_zero
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_left
  AlgebraicGeometry.Scheme.Modules.tensorPow_zero
  AlgebraicGeometry.Scheme.Modules.tensorPow_succ
  AlgebraicGeometry.Scheme.OrderedAffineCover.mk.injEq
  AlgebraicGeometry.OModulePresheaf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCover.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.mk.injEq
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_neg
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_zero
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_sub
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_add
  AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
  AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U
  AlgebraicGeometry.OModulePresheaf.Hom.mk.injEq
  AlgebraicGeometry.OModulePresheaf.Hom.id_app
  AlgebraicGeometry.OModulePresheaf.AffHom.appSections_apply
  AlgebraicGeometry.OModulePresheaf.AffHom.comp_app
  AlgebraicGeometry.OModulePresheaf.AffSES.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.AffHom.kerMap_coe
  AlgebraicGeometry.OModulePresheaf.AffHom.id_app
  AlgebraicGeometry.OModulePresheaf.Hom.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.Hom.toAffHom_app
attribute [-simp]
  AlgebraicGeometry.OModulePresheaf.SES.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.AffHom.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.Hom.comp_app
  AlgebraicGeometry.OModulePresheaf.SES.mk.injEq
  AlgebraicGeometry.OModulePresheaf.AffHom.mk.injEq
  AlgebraicGeometry.OModulePresheaf.Hom.appSections_apply
  AlgebraicGeometry.OModulePresheaf.AffSES.mk.injEq
  AlgebraicGeometry.OModulePresheaf.prod_obj
  AlgebraicGeometry.OModulePresheaf.restrOpen_obj
  AlgebraicGeometry.OModulePresheaf.DevissageStep.mk.injEq
  AlgebraicGeometry.OModulePresheaf.pushforward_obj
  AlgebraicGeometry.OModulePresheaf.im_obj
  AlgebraicGeometry.OModulePresheaf.pow_obj
  AlgebraicGeometry.OModulePresheaf.fstHom_app
  AlgebraicGeometry.OModulePresheaf.ker_obj
  AlgebraicGeometry.OModulePresheaf.coker_obj
  AlgebraicGeometry.OModulePresheaf.DevissageStep.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCover.preimage_U
  AlgebraicGeometry.OModulePresheaf.sndHom_app
  AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
  DoubleComplex.Bounded.mk.injEq
  DoubleComplex.Bounded.mk.sizeOf_spec
  DoubleComplex.Convergence.mk.injEq
  DoubleComplex.Convergence.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.injEq
  AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatumProj.mk.injEq
  AlgebraicGeometry.ChowDatum.mk.injEq
  ProjSpaceCech.GradedModule.mk.injEq
  ProjSpaceCech.GradedModule.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Presentation.mk.injEq
  ProjSpaceCech.GradedModule.Frac.mk.injEq
  ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.shift_toLinearMap
  ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.mk.injEq
  TwoChartCech.Mumford.dK_apply
attribute [-simp]
  TwoChartCech.Mumford.ι0_apply
  TwoChartCech.Mumford.ι1_apply
  TwoChartCech.KerCoprod.dK_apply
  TwoChartCech.KerCoprod.ι1_apply
  TwoChartCech.KerCoprod.ι0_apply
  AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
  AlgebraicGeometry.RelPicard.algEquivZeroGroupCut_toSubPicCondition
  AlgebraicGeometry.RelPicard.LFP.stageHom_val
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_hom_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_inv_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.restrict_P
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp
  AlgebraicGeometry.RelEffCartierDiv.functor_map_fst
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_pullbackAlong
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_symm_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp_assoc
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top
  AlgebraicGeometry.RelEffCartierDiv.mem_supportedIn_iff
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top_eq
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
  CoherentBaseChange.FibreH0Family.mk.sizeOf_spec
  CoherentBaseChange.FibreH0Family.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.sizeOf_spec
  AlgebraicCurve.CurveModel.coe_gInf
  AlgebraicCurve.CurveModel.coe_tInvChart
  AlgebraicCurve.CurveModel.ιInf_gluedToBase_assoc
  AlgebraicCurve.CurveModel.ιInf_gluedToBase
  AlgebraicCurve.CurveModel.primeOfι₀_asIdeal
  AlgebraicCurve.CurveModel.coe_tChart
  AlgebraicCurve.CurveModel.ι₀_gluedToBase_assoc
  AlgebraicCurve.CurveModel.primeOfιInf_asIdeal
attribute [-simp]
  AlgebraicCurve.CurveModel.ι₀_gluedToBase
  AlgebraicCurve.CurveModel.coe_tma
  AlgebraicCurve.CurveModel.coe_primeEquivChartPlaces
universe u
noncomputable section
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.CategoryTheory.CartesianMonoidalCategory
open _root_.AlgebraicGeometry.RelPicard
open _root_.NeronModelInfra
namespace P2mCubeAssembly
section Slices
variable {k : Type u} [Field k]
local notation "Sk" => Spec (CommRingCat.of k)

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.ThreeSlices
attribute [-instance]
  AlgebraicGeometry.SmoothOfRelativeDimension.fiberToSpecResidueField
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_snd
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_fst
  AlgebraicGeometry.SmoothOfRelativeDimension.smooth_one
  AlgebraicGeometry.SmoothProperCurve.isIntegral_pullback_Spec_field
  AlgebraicGeometry.IsProper.fiberToSpecResidueField
  AlgebraicCurve.CurveModel.isProper
  AlgebraicCurve.CurveModel.isIntegral
  AlgebraicCurve.CurveModel.smooth
  AlgebraicCurve.Place.instIsScalarTowerSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Divisor.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instSMulAlgEquiv
  AlgebraicCurve.Place.instIsPrincipalIdealRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instIsDiscreteValuationRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Pic0.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instAlgebraSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instMulActionAlgEquiv
  AlgebraicCurve.Pic0.instSMulAlgEquiv
  TwoChartCech.Sections.M0_moduleA
  TwoChartCech.Sections.M1_module
  TwoChartCech.Cover.A01_algebra
  TwoChartCech.Cover.A0_algebra
  TwoChartCech.Cover.A1_commRing
  TwoChartCech.Cover.A1_algebra
  TwoChartCech.Sections.M01_module
  TwoChartCech.Sections.M0_addCommGroup
  TwoChartCech.Sections.M0_tower
  TwoChartCech.Sections.M01_addCommGroup
  TwoChartCech.Cover.A0_commRing
  TwoChartCech.Sections.M1_tower
  TwoChartCech.Sections.M01_moduleA
  TwoChartCech.Sections.M0_module
  TwoChartCech.Sections.M1_moduleA
  TwoChartCech.Sections.M1_addCommGroup
  TwoChartCech.Cover.A01_commRing
  TwoChartCech.Sections.M01_tower
  CoherentBaseChange.TwoTermComplex.C0_module
  CoherentBaseChange.TwoTermComplex.C0_addCommGroup
  CoherentBaseChange.TwoTermComplex.C1_module
  CoherentBaseChange.TwoTermComplex.C1_addCommGroup
attribute [-instance]
  CoherentBaseChange.TwoTermComplex.C0_free
  CoherentBaseChange.TwoTermComplex.C1_finite
  CoherentBaseChange.TwoTermComplex.C0_finite
  CoherentBaseChange.TwoTermComplex.C1_free
  AlgebraicCurve.IsCurveOver.instNontrivialKaehler
  AlgebraicCurve.IsCurveOver.instFreeKaehler
  AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
  AlgebraicCurve.IsCurveOver.instFiniteResidue
attribute [-instance]
  instIsLocallyInjectiveFunUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsLocallySurjectiveUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsOpenImmersionToGlued
attribute [-instance]
  instIsIsoSheafZariskiTopologyTypeUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.RelPicard.isOpenImmersion_toGlued
  AlgebraicGeometry.Scheme.Modules.preservesBinaryProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback_monoidal
  AlgebraicGeometry.Scheme.Modules.sheafify_isLocalization'
  AlgebraicGeometry.Scheme.Modules.preservesTerminal_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback₀_monoidal
  AlgebraicGeometry.Scheme.Modules.preservesFiniteProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.sheafifyPullback_lifting
  PresheafOfModules.PullbackMonoidal.pullback_monoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ
  PresheafOfModules.pushforward_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_η
  PresheafOfModules.free_monoidal
  PresheafOfModules.restrictScalars_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ_gS
  PresheafOfModules.pullback_oplaxMonoidal
attribute [-instance]
  instPreservesColimitsOfSizeCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierPb
attribute [-instance]
  PresheafOfModules.pullback_monoidal'
  AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
  AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
  AlgebraicCurve.Place.instIsPrimeCenter
  AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
  instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
  AlgebraicCurve.Pic0.instModuleZModTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instSMulTorsion
  AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
  AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
  AlgebraicCurve.RationalFunctionField.instNontrivialInftyValueGroup
  PresheafOfModules.ExteriorPower.instModulePresheafAb
  AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
  AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
  AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
  AlgebraicGeometry.isClosedImmersion_graphOver
  AlgebraicGeometry.FGSubalgebra.instIsDirectedLe
attribute [-instance]
  instQuasiSeparatedSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsCofilteredOpposite
  AlgebraicGeometry.FGSubalgebra.instIsAffineObjOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instNonempty
  AlgebraicGeometry.FGSubalgebra.instNonemptySubtypeLeSubalgebraValFG
attribute [-instance]
  instCompactSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsDirectedSubtypeLeSubalgebraValFG
  AlgebraicGeometry.FGSubalgebra.instIsAffineHomMapOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instIsFiltered
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instNeg
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulInt
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAddCommGroup
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAdd
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSub
attribute [-instance]
  instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
  AlgebraicCurve.instHasLocalResidue_of_hasCanonicalLocalResidueK
  AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
  AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
  ModularCurve.KwF4gRRTate.instAlgebraKAdicCompletionIntegers
  AlgebraicCurve.Place.kw_ffgc_continuousSMul_adicCompletionComap
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersCompletionCompletion
attribute [-instance]
  instLiesOverSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegersCompletionIdealAsIdeal
attribute [-instance]
  AlgebraicCurve.instHasCanonicalLocalResidueK
  AlgebraicCurve.Place.instAlgebra_restrictResidueField
  AlgebraicCurve.Place.instIsScalarTower_restrictResidueField
  AlgebraicCurve.instHasLocalResidue
  AlgebraicCurve.HasSeparableResidue.of_perfectField_of_isCurveOver
  AlgebraicCurve.HasSeparableResidue.of_perfectField
  AlgebraicCurve.Place.instIsLocalHom_restrictSubringHom
  AlgebraicCurve.instHasCanonicalLocalResidueKStar
  ModularCurve.KwNo6Pin.isLocalRing_completion
  SheafOfModules.isIso_ihomModelToIhom
  AlgebraicGeometry.OModulePresheaf.isScalarTower
  AlgebraicGeometry.Scheme.OrderedAffineCover.instLinearOrder
  AlgebraicGeometry.OModulePresheaf.module
  AlgebraicGeometry.Scheme.OrderedAffineCover.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCover.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.addCommGroup
  AlgebraicGeometry.Scheme.OrderedAffineCover.instDecidableEqIdx
  AlgebraicGeometry.OModulePresheaf.moduleSections
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.instSubsingletonObjZero
attribute [-instance]
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
  AlgebraicGeometry.OModulePresheaf.Leray.biC_module
  DoubleComplex.instModuleE₂I
  DoubleComplex.Bounded.modR
  DoubleComplex.instModuleE₂II
  DoubleComplex.instAddCommGroupE₂II
  DoubleComplex.Bounded.abGrp
  DoubleComplex.instAddCommGroupE₂I
  AlgebraicGeometry.ChowDatum.hι_closed
  AlgebraicGeometry.ChowDatumProj.hιN_closed
  AlgebraicGeometry.ChowDatumProj.hp_proper
  AlgebraicGeometry.ChowDatum.hp_isoU
  AlgebraicGeometry.ChowDatum.hp_proper
  AlgebraicGeometry.ProjSpace.algebraAway
  AlgebraicGeometry.ProjSpace.instIsProperProdOverπ
  AlgebraicGeometry.ChowDatumProj.hp_isoU
  AlgebraicGeometry.ProjSpace.isProper_π
  AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
  ProjSpaceCech.GradedModule.H.module
  ProjSpaceCech.GradedModule.H.addCommGroup
  ProjSpaceCech.GradedModule.sec.instAdd
  ProjSpaceCech.GradedModule.sec.instNeg
  ProjSpaceCech.GradedModule.acg
  ProjSpaceCech.GradedModule.Frac.setoid
  ProjSpaceCech.GradedModule.modR
  ProjSpaceCech.GradedModule.sec.instModule
  ProjSpaceCech.GradedModule.sec.instAddCommGroup
  ProjSpaceCech.GradedModule.sec.instZero
  ProjSpaceCech.GradedModule.Presentation.fJ
  ProjSpaceCech.GradedModule.sec.instSMul
  ProjSpaceCech.Twist.H.module
  ProjSpaceCech.Idx.instFintype
  ProjSpaceCech.Twist.H.addCommGroup
attribute [-instance]
  ProjSpaceCech.Idx.instDecidableEq
  ProjSpaceCech.Twist.Mon.instDecidableEq
  ProjSpaceCech.Twist.cochain.instAddCommGroup
  ProjSpaceCech.Twist.cochain.instModule
  AlgebraicGeometry.FGSubalgebra.tensorStage_directedSystem
  AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
  AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
  AlgebraicCurve.CurveModel.locallyOfFiniteType_gluedToBase
  AlgebraicCurve.CurveModel.isFractionRing_overlap
  AlgebraicCurve.CurveModel.isLocallyNoetherian_glued
  AlgebraicCurve.CurveModel.jacobsonSpace_glued
  AlgebraicCurve.CurveModel.isOpenImmersion_ι₀
  AlgebraicCurve.CurveModel.isIntegral_glued
  AlgebraicCurve.CurveModel.quasiSeparated_gluedToBase
  AlgebraicCurve.CurveModel.compactSpace_glued
  AlgebraicCurve.CurveModel.isIntegral_adjoin_chartRing
  AlgebraicCurve.CurveModel.isFractionRing_overlap_functionField
  AlgebraicCurve.CurveModel.isProper_gluedToBase
  AlgebraicCurve.CurveModel.isOpenImmersion_ιU
  AlgebraicCurve.CurveModel.isOpenImmersion_f₀
  AlgebraicCurve.CurveModel.isOpenImmersion_fInf
  AlgebraicCurve.CurveModel.isOpenImmersion_ιInf
  AlgebraicCurve.CurveModel.algebra_overlap_functionField
  AlgebraicCurve.CurveModel.quasiCompact_gluedToBase
  AlgebraicCurve.CurveModel.algebraAdjoin
  AlgebraicCurve.CurveModel.isDedekindDomain_chartRing
  AlgebraicCurve.CurveModel.isIntegralClosure
  AlgebraicCurve.CurveModel.finite_chartRing
  AlgebraicCurve.CurveModel.centre_isPrime
  AlgebraicCurve.CurveModel.isFractionRing_chartRing
  AlgebraicCurve.CurveModel.finiteType_chartRing
  AlgebraicCurve.CurveModel.isNoetherianRing_chartRing
  AlgebraicCurve.CurveModel.isScalarTower_base_adjoin
  AlgebraicCurve.CurveModel.isScalarTower_adjoin
  AlgebraicCurve.CurveModel.chartRing_finitePresentation
attribute [-simp]
  GoodReductionJacobian.RelativePic0Designation.mk.sizeOf_spec
  GoodReductionJacobian.AvatarSchemeBridge.mk.injEq
  GoodReductionJacobian.AvatarSchemeBridge.mk.sizeOf_spec
  GoodReductionJacobian.RelativePic0Designation.mk.injEq
  GoodReductionJacobian.schemeHomOverComp_coe
  NeronModelInfra.schemeHomOverEquivOverHom_apply
  GoodReductionJacobian.RelativeGroupLaw.mk.sizeOf_spec
  NeronModelInfra.schemeHomOverEquivOverHom_symm_apply
  NeronModelInfra.overHomToSchemeHomOver_coe
  GoodReductionJacobian.RelativeGroupLaw.mk.injEq
  NeronModelInfra.overHomToSchemeHomOver_schemeHomOverToOverHom
  NeronModelInfra.schemeHomOverToOverHom_left
  NeronModelInfra.schemeHomOverToOverHom_overHomToSchemeHomOver
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.sizeOf_spec
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
  AlgebraicCurve.CurveModel.mk.injEq
  AlgebraicCurve.CurveModel.mk.sizeOf_spec
  AlgebraicCurve.Place.mk.injEq
  AlgebraicCurve.Divisor.degree_single
  AlgebraicCurve.Divisor.smul_single
  AlgebraicCurve.Place.smul_toValuationSubring
  AlgebraicCurve.Place.heightOneSpectrum_asIdeal
  AlgebraicCurve.Place.coe_algebraMap
  AlgebraicCurve.Place.ord_one
  AlgebraicCurve.Place.coe_smulRingEquiv_apply
  AlgebraicCurve.Pic0.coe_degZeroSMulHom
  AlgebraicCurve.Place.deg_smul
  AlgebraicCurve.Pic0.mk_zero
  AlgebraicCurve.Place.mk.sizeOf_spec
  AlgebraicCurve.Divisor.degree_smul
  AlgebraicCurve.Pic0.mk_add
  AlgebraicCurve.Place.ord_zero
  AlgebraicCurve.Place.ofHeightOneSpectrum_toValuationSubring
  AlgebraicCurve.mulAdele_apply
attribute [-simp]
  AlgebraicCurve.residuePairing_apply_coe
  AlgebraicCurve.mem_adeleBdd
  AlgebraicCurve.weilSmul_one
  AlgebraicCurve.diagonalHom_apply
  AlgebraicCurve.weilSmul_apply
  AlgebraicCurve.adeleSpaceMul_coe
  AlgebraicCurve.mulAdele_one
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U1
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.injEq
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U0
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.mk.injEq
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.pullback_U1
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.pullback_U0
  TwoChartCech.Sections.mk.injEq
  TwoChartCech.Cover.mk.injEq
  TwoChartCech.GrothendieckComplex.mk.injEq
  TwoChartCech.Sections.mk.sizeOf_spec
  TwoChartCech.Cover.mk.sizeOf_spec
  TwoChartCech.Cover.lineBundle_r0_apply
  TwoChartCech.GrothendieckComplex.mk.sizeOf_spec
  TwoChartCech.Cover.lineBundle_r1_apply
  CoherentBaseChange.TwoTermComplex.mk.sizeOf_spec
  CoherentBaseChange.TwoTermComplex.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
  AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
  CategoryTheory.Functor.OverTotal.ofFibre_fst
  CategoryTheory.Functor.overTotal_map_fst
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_J
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYoneda_toGlued_uliftYonedaGluedToSheaf
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t'
attribute [-simp]
  uliftYoneda_toGlued_uliftYonedaGluedToSheaf_assoc
attribute [-simp]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_toGlued
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_openCover_map
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_comp
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_V
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_U
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_f
attribute [-simp]
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_P
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_toBase
  AlgebraicGeometry.RelPicard.rigSection_snd
  AlgebraicGeometry.RelPicard.RigidifiedLineBundle.ofInvertible_L
  AlgebraicGeometry.RelPicard.rigSection_snd_assoc
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
  GoodReductionJacobian.relativeGroupLawOfGrpObj_inv
  GoodReductionJacobian.relativeGroupLawOfGrpObj_mul
  GoodReductionJacobian.overHomEquivSchemeHomOver_apply_coe
  GoodReductionJacobian.relativeGroupLawOfGrpObj_one
  GoodReductionJacobian.overHomEquivSchemeHomOver_symm_apply_left
  PresheafOfModules.freeεIso_hom_app
  PresheafOfModules.freeμIso_hom_app
  AlgebraicCurve.coe_cechH0Equiv_apply
  AlgebraicCurve.cechH1ToH1_mk
  AlgebraicCurve.lSpaceOn_univ
  AlgebraicCurve.lSpaceOn_empty
  AlgebraicCurve.Place.congrEquiv_symm_apply
  AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
  AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
  AlgebraicCurve.Place.congrEquiv_apply
  AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
  AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
  AlgebraicCurve.Divisor.mapRestrict_single
  AlgebraicCurve.Divisor.pushforward_single
  AlgebraicCurve.Place.coe_restrictInclusion
  AlgebraicCurve.Place.mem_fiber
  AlgebraicCurve.Place.restrict_toValuationSubring
  AlgebraicCurve.Divisor.degree_pushforward
  AlgebraicCurve.Place.restrictResidueMap_residue
  AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
  AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
  AlgebraicCurve.Place.placeOfPrime_toValuationSubring
  AlgebraicCurve.Place.mem_fiberOver
  AlgebraicCurve.Place.fiberEquiv_symm_apply
  AlgebraicCurve.Place.fiberEquiv_apply
  AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
attribute [-simp]
  AlgebraicCurve.Divisor.degree_pushforwardAlong
  AlgebraicCurve.Pic0.coe_degZeroCorrespondence
  AlgebraicCurve.Place.mem_fiberAlong
  AlgebraicCurve.SemilinearAut.toRingAut_inv
  AlgebraicCurve.SemilinearAut.smul_def
  AlgebraicCurve.SemilinearAut.smul_single
  AlgebraicCurve.SemilinearAut.smul_toValuationSubring
  AlgebraicCurve.SemilinearAut.baseAut_inv
  AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_one
  AlgebraicCurve.SemilinearAut.deg_smul
  AlgebraicCurve.SemilinearAut.degree_smul
  AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
  AlgebraicCurve.SemilinearAut.baseAut_mul
  AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
  AlgebraicCurve.SemilinearAut.baseAut_one
  AlgebraicCurve.SemilinearAut.ofAlgAut_smul
  AlgebraicCurve.SemilinearAut.coe_torsion_smul
  AlgebraicCurve.SemilinearAut.toRingAut_mul
attribute [-simp]
  AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeInfty
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_some
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeOfPoint
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_none
  AlgebraicCurve.Divisor.evalFun_zero
  AlgebraicCurve.Place.evalAt_one
  AlgebraicCurve.Place.differentialCoeff_zero
  AlgebraicCurve.Place.differentialCoeff_dCoord
  AlgebraicCurve.TranscendenceTower.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
  AlgebraicCurve.TranscendenceTower.mk.injEq
  AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec
  AlgebraicCurve.PoleDivisorPackage.mk.injEq
  AlgebraicGeometry.RelPicard.thetaBundle_def
attribute [-simp]
  AlgebraicGeometry.RelPicard.picardBundle_def
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_ofRelEffDivisor
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_I
  AlgebraicGeometry.mapOnProdOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.mk.sizeOf_spec
  AlgebraicGeometry.RelEffCartierDiv.mk.injEq
  AlgebraicGeometry.mapOnProdOver_snd
  AlgebraicGeometry.mapOnProdOver_fst
  AlgebraicGeometry.mapOnProdOver_snd_assoc
  AlgebraicGeometry.mapOnProdOver_id
  AlgebraicCurve.RelEffDivisor.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_fst
  AlgebraicCurve.mapOnProd_fst_assoc
  AlgebraicCurve.mapOnProd_snd
  AlgebraicCurve.UnivDivisorPack.mk.injEq
  AlgebraicCurve.RelEffDivisor.mk.injEq
  AlgebraicCurve.UnivDivisorPack.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_snd_assoc
  AlgebraicGeometry.Scheme.Modules.exteriorPower_obj
  PresheafOfModules.exteriorPower_map_ιMulti
  PresheafOfModules.ExteriorPower.appₗ_apply
  AlgebraicGeometry.prodKerGraph_one
  AlgebraicGeometry.fibrePowOver.proj_comp
  AlgebraicGeometry.prodKerGraph_zero
  AlgebraicGeometry.RelEffCartierDiv.empty_I
  AlgebraicGeometry.fibrePowOver.proj_comp_assoc
  AlgebraicGeometry.graphOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
  AlgebraicGeometry.graphOver_fst
  AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
  AlgebraicGeometry.graphOver_snd
  AlgebraicGeometry.graphOver_snd_assoc
  AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
  AlgebraicCurve.SymmetricPowerPackage.mk.injEq
  AlgebraicGeometry.FGSubalgebra.cocone_ι_app_apply
  AlgebraicGeometry.RelPicard.fst_toProdSpec
  AlgebraicGeometry.RelPicard.toProdSpec_fst_assoc
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_cons
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_nil
attribute [-simp]
  AlgebraicGeometry.RelPicard.fst_toProdSpec_assoc
  AlgebraicGeometry.RelPicard.toProdSpec_fst
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.sizeOf_spec
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.injEq
  AlgebraicCurve.adeleSingle_coe
  AlgebraicCurve.kaehlerResidueTermKFam_apply
  AlgebraicCurve.Place.LocalResidueData.mk.injEq
  AlgebraicCurve.Place.LocalResidueData.mk.sizeOf_spec
  AlgebraicCurve.Place.kw_ffgc_adicCompletionComapIntegers_coe
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.sizeOf_spec
  AlgebraicCurve.Place.mem_simplePoleSubmodule
  AlgebraicCurve.Place.coe_uniformizerSubring
  ModularCurve.Lg37.Lg37CompletionSection.mk.injEq
  AlgebraicCurve.Place.CoefficientFieldSection.mk.injEq
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.injEq
  ModularCurve.Lg37.Lg37CompletionSection.mk.sizeOf_spec
  AlgebraicCurve.Place.CoefficientFieldSection.mk.sizeOf_spec
  AlgebraicCurve.Place.poleSubmodule_one
  AlgebraicCurve.Place.mem_poleSubmodule
  AlgebraicGeometry.Scheme.Modules.toUnitSection_ofUnitSection
  AlgebraicGeometry.Scheme.Modules.pullbackSection_def
  AlgebraicGeometry.Scheme.Modules.ofUnitSection_toUnitSection
  PresheafOfModules.InternalHom.IsSheafAux.appAt_toPresheafHom
attribute [-simp]
  SheafOfModules.ihomSectionsEquivFamily_unit
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_apply
  SheafOfModules.ihomEval_unit_app
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_right
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_left
  AlgebraicGeometry.Scheme.Modules.homOfFamily_app_apply
  SheafOfModules.unit_ihomSectionsEquivFamily
  AlgebraicGeometry.Scheme.Modules.familyOfHom_app
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_hom_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_inv_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomOfFamily_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_symm_apply
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_right
  AlgebraicGeometry.Scheme.Modules.map_unitSection
  AlgebraicGeometry.Scheme.Modules.tensorSectionsBilin_apply
  AlgebraicGeometry.Scheme.Modules.tensorPowSection_zero
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_left
  AlgebraicGeometry.Scheme.Modules.tensorPow_zero
  AlgebraicGeometry.Scheme.Modules.tensorPow_succ
  AlgebraicGeometry.Scheme.OrderedAffineCover.mk.injEq
  AlgebraicGeometry.OModulePresheaf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCover.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.mk.injEq
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_neg
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_zero
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_sub
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_add
  AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
  AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U
  AlgebraicGeometry.OModulePresheaf.Hom.mk.injEq
  AlgebraicGeometry.OModulePresheaf.Hom.id_app
  AlgebraicGeometry.OModulePresheaf.AffHom.appSections_apply
  AlgebraicGeometry.OModulePresheaf.AffHom.comp_app
  AlgebraicGeometry.OModulePresheaf.AffSES.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.AffHom.kerMap_coe
  AlgebraicGeometry.OModulePresheaf.AffHom.id_app
  AlgebraicGeometry.OModulePresheaf.Hom.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.Hom.toAffHom_app
attribute [-simp]
  AlgebraicGeometry.OModulePresheaf.SES.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.AffHom.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.Hom.comp_app
  AlgebraicGeometry.OModulePresheaf.SES.mk.injEq
  AlgebraicGeometry.OModulePresheaf.AffHom.mk.injEq
  AlgebraicGeometry.OModulePresheaf.Hom.appSections_apply
  AlgebraicGeometry.OModulePresheaf.AffSES.mk.injEq
  AlgebraicGeometry.OModulePresheaf.prod_obj
  AlgebraicGeometry.OModulePresheaf.restrOpen_obj
  AlgebraicGeometry.OModulePresheaf.DevissageStep.mk.injEq
  AlgebraicGeometry.OModulePresheaf.pushforward_obj
  AlgebraicGeometry.OModulePresheaf.im_obj
  AlgebraicGeometry.OModulePresheaf.pow_obj
  AlgebraicGeometry.OModulePresheaf.fstHom_app
  AlgebraicGeometry.OModulePresheaf.ker_obj
  AlgebraicGeometry.OModulePresheaf.coker_obj
  AlgebraicGeometry.OModulePresheaf.DevissageStep.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCover.preimage_U
  AlgebraicGeometry.OModulePresheaf.sndHom_app
  AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
  DoubleComplex.Bounded.mk.injEq
  DoubleComplex.Bounded.mk.sizeOf_spec
  DoubleComplex.Convergence.mk.injEq
  DoubleComplex.Convergence.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.injEq
  AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatumProj.mk.injEq
  AlgebraicGeometry.ChowDatum.mk.injEq
  ProjSpaceCech.GradedModule.mk.injEq
  ProjSpaceCech.GradedModule.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Presentation.mk.injEq
  ProjSpaceCech.GradedModule.Frac.mk.injEq
  ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.shift_toLinearMap
  ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.mk.injEq
  TwoChartCech.Mumford.dK_apply
attribute [-simp]
  TwoChartCech.Mumford.ι0_apply
  TwoChartCech.Mumford.ι1_apply
  TwoChartCech.KerCoprod.dK_apply
  TwoChartCech.KerCoprod.ι1_apply
  TwoChartCech.KerCoprod.ι0_apply
  AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
  AlgebraicGeometry.RelPicard.algEquivZeroGroupCut_toSubPicCondition
  AlgebraicGeometry.RelPicard.LFP.stageHom_val
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_hom_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_inv_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.restrict_P
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp
  AlgebraicGeometry.RelEffCartierDiv.functor_map_fst
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_pullbackAlong
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_symm_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp_assoc
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top
  AlgebraicGeometry.RelEffCartierDiv.mem_supportedIn_iff
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top_eq
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
  CoherentBaseChange.FibreH0Family.mk.sizeOf_spec
  CoherentBaseChange.FibreH0Family.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.sizeOf_spec
  AlgebraicCurve.CurveModel.coe_gInf
  AlgebraicCurve.CurveModel.coe_tInvChart
  AlgebraicCurve.CurveModel.ιInf_gluedToBase_assoc
  AlgebraicCurve.CurveModel.ιInf_gluedToBase
  AlgebraicCurve.CurveModel.primeOfι₀_asIdeal
  AlgebraicCurve.CurveModel.coe_tChart
  AlgebraicCurve.CurveModel.ι₀_gluedToBase_assoc
  AlgebraicCurve.CurveModel.primeOfιInf_asIdeal
attribute [-simp]
  AlgebraicCurve.CurveModel.ι₀_gluedToBase
  AlgebraicCurve.CurveModel.coe_tma
  AlgebraicCurve.CurveModel.coe_primeEquivChartPlaces
universe u
noncomputable section
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.CategoryTheory.CartesianMonoidalCategory
open _root_.AlgebraicGeometry.RelPicard
open _root_.NeronModelInfra
namespace P2mCubeAssembly
section Slices
variable {k : Type u} [Field k]
local notation "Sk" => Spec (CommRingCat.of k)

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.ThreeSlices
attribute [-instance]
  AlgebraicGeometry.SmoothOfRelativeDimension.fiberToSpecResidueField
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_snd
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_fst
  AlgebraicGeometry.SmoothOfRelativeDimension.smooth_one
  AlgebraicGeometry.SmoothProperCurve.isIntegral_pullback_Spec_field
  AlgebraicGeometry.IsProper.fiberToSpecResidueField
  AlgebraicCurve.CurveModel.isProper
  AlgebraicCurve.CurveModel.isIntegral
  AlgebraicCurve.CurveModel.smooth
  AlgebraicCurve.Place.instIsScalarTowerSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Divisor.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instSMulAlgEquiv
  AlgebraicCurve.Place.instIsPrincipalIdealRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instIsDiscreteValuationRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Pic0.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instAlgebraSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instMulActionAlgEquiv
  AlgebraicCurve.Pic0.instSMulAlgEquiv
  TwoChartCech.Sections.M0_moduleA
  TwoChartCech.Sections.M1_module
  TwoChartCech.Cover.A01_algebra
  TwoChartCech.Cover.A0_algebra
  TwoChartCech.Cover.A1_commRing
  TwoChartCech.Cover.A1_algebra
  TwoChartCech.Sections.M01_module
  TwoChartCech.Sections.M0_addCommGroup
  TwoChartCech.Sections.M0_tower
  TwoChartCech.Sections.M01_addCommGroup
  TwoChartCech.Cover.A0_commRing
  TwoChartCech.Sections.M1_tower
  TwoChartCech.Sections.M01_moduleA
  TwoChartCech.Sections.M0_module
  TwoChartCech.Sections.M1_moduleA
  TwoChartCech.Sections.M1_addCommGroup
  TwoChartCech.Cover.A01_commRing
  TwoChartCech.Sections.M01_tower
  CoherentBaseChange.TwoTermComplex.C0_module
  CoherentBaseChange.TwoTermComplex.C0_addCommGroup
  CoherentBaseChange.TwoTermComplex.C1_module
  CoherentBaseChange.TwoTermComplex.C1_addCommGroup
attribute [-instance]
  CoherentBaseChange.TwoTermComplex.C0_free
  CoherentBaseChange.TwoTermComplex.C1_finite
  CoherentBaseChange.TwoTermComplex.C0_finite
  CoherentBaseChange.TwoTermComplex.C1_free
  AlgebraicCurve.IsCurveOver.instNontrivialKaehler
  AlgebraicCurve.IsCurveOver.instFreeKaehler
  AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
  AlgebraicCurve.IsCurveOver.instFiniteResidue
attribute [-instance]
  instIsLocallyInjectiveFunUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsLocallySurjectiveUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsOpenImmersionToGlued
attribute [-instance]
  instIsIsoSheafZariskiTopologyTypeUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.RelPicard.isOpenImmersion_toGlued
  AlgebraicGeometry.Scheme.Modules.preservesBinaryProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback_monoidal
  AlgebraicGeometry.Scheme.Modules.sheafify_isLocalization'
  AlgebraicGeometry.Scheme.Modules.preservesTerminal_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback₀_monoidal
  AlgebraicGeometry.Scheme.Modules.preservesFiniteProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.sheafifyPullback_lifting
  PresheafOfModules.PullbackMonoidal.pullback_monoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ
  PresheafOfModules.pushforward_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_η
  PresheafOfModules.free_monoidal
  PresheafOfModules.restrictScalars_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ_gS
  PresheafOfModules.pullback_oplaxMonoidal
attribute [-instance]
  instPreservesColimitsOfSizeCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierPb
attribute [-instance]
  PresheafOfModules.pullback_monoidal'
  AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
  AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
  AlgebraicCurve.Place.instIsPrimeCenter
  AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
  instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
  AlgebraicCurve.Pic0.instModuleZModTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instSMulTorsion
  AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
  AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
  AlgebraicCurve.RationalFunctionField.instNontrivialInftyValueGroup
  PresheafOfModules.ExteriorPower.instModulePresheafAb
  AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
  AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
  AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
  AlgebraicGeometry.isClosedImmersion_graphOver
  AlgebraicGeometry.FGSubalgebra.instIsDirectedLe
attribute [-instance]
  instQuasiSeparatedSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsCofilteredOpposite
  AlgebraicGeometry.FGSubalgebra.instIsAffineObjOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instNonempty
  AlgebraicGeometry.FGSubalgebra.instNonemptySubtypeLeSubalgebraValFG
attribute [-instance]
  instCompactSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsDirectedSubtypeLeSubalgebraValFG
  AlgebraicGeometry.FGSubalgebra.instIsAffineHomMapOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instIsFiltered
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instNeg
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulInt
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAddCommGroup
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAdd
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSub
attribute [-instance]
  instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
  AlgebraicCurve.instHasLocalResidue_of_hasCanonicalLocalResidueK
  AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
  AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
  ModularCurve.KwF4gRRTate.instAlgebraKAdicCompletionIntegers
  AlgebraicCurve.Place.kw_ffgc_continuousSMul_adicCompletionComap
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersCompletionCompletion
attribute [-instance]
  instLiesOverSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegersCompletionIdealAsIdeal
attribute [-instance]
  AlgebraicCurve.instHasCanonicalLocalResidueK
  AlgebraicCurve.Place.instAlgebra_restrictResidueField
  AlgebraicCurve.Place.instIsScalarTower_restrictResidueField
  AlgebraicCurve.instHasLocalResidue
  AlgebraicCurve.HasSeparableResidue.of_perfectField_of_isCurveOver
  AlgebraicCurve.HasSeparableResidue.of_perfectField
  AlgebraicCurve.Place.instIsLocalHom_restrictSubringHom
  AlgebraicCurve.instHasCanonicalLocalResidueKStar
  ModularCurve.KwNo6Pin.isLocalRing_completion
  SheafOfModules.isIso_ihomModelToIhom
  AlgebraicGeometry.OModulePresheaf.isScalarTower
  AlgebraicGeometry.Scheme.OrderedAffineCover.instLinearOrder
  AlgebraicGeometry.OModulePresheaf.module
  AlgebraicGeometry.Scheme.OrderedAffineCover.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCover.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.addCommGroup
  AlgebraicGeometry.Scheme.OrderedAffineCover.instDecidableEqIdx
  AlgebraicGeometry.OModulePresheaf.moduleSections
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.instSubsingletonObjZero
attribute [-instance]
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
  AlgebraicGeometry.OModulePresheaf.Leray.biC_module
  DoubleComplex.instModuleE₂I
  DoubleComplex.Bounded.modR
  DoubleComplex.instModuleE₂II
  DoubleComplex.instAddCommGroupE₂II
  DoubleComplex.Bounded.abGrp
  DoubleComplex.instAddCommGroupE₂I
  AlgebraicGeometry.ChowDatum.hι_closed
  AlgebraicGeometry.ChowDatumProj.hιN_closed
  AlgebraicGeometry.ChowDatumProj.hp_proper
  AlgebraicGeometry.ChowDatum.hp_isoU
  AlgebraicGeometry.ChowDatum.hp_proper
  AlgebraicGeometry.ProjSpace.algebraAway
  AlgebraicGeometry.ProjSpace.instIsProperProdOverπ
  AlgebraicGeometry.ChowDatumProj.hp_isoU
  AlgebraicGeometry.ProjSpace.isProper_π
  AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
  ProjSpaceCech.GradedModule.H.module
  ProjSpaceCech.GradedModule.H.addCommGroup
  ProjSpaceCech.GradedModule.sec.instAdd
  ProjSpaceCech.GradedModule.sec.instNeg
  ProjSpaceCech.GradedModule.acg
  ProjSpaceCech.GradedModule.Frac.setoid
  ProjSpaceCech.GradedModule.modR
  ProjSpaceCech.GradedModule.sec.instModule
  ProjSpaceCech.GradedModule.sec.instAddCommGroup
  ProjSpaceCech.GradedModule.sec.instZero
  ProjSpaceCech.GradedModule.Presentation.fJ
  ProjSpaceCech.GradedModule.sec.instSMul
  ProjSpaceCech.Twist.H.module
  ProjSpaceCech.Idx.instFintype
  ProjSpaceCech.Twist.H.addCommGroup
attribute [-instance]
  ProjSpaceCech.Idx.instDecidableEq
  ProjSpaceCech.Twist.Mon.instDecidableEq
  ProjSpaceCech.Twist.cochain.instAddCommGroup
  ProjSpaceCech.Twist.cochain.instModule
  AlgebraicGeometry.FGSubalgebra.tensorStage_directedSystem
  AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
  AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
  AlgebraicCurve.CurveModel.locallyOfFiniteType_gluedToBase
  AlgebraicCurve.CurveModel.isFractionRing_overlap
  AlgebraicCurve.CurveModel.isLocallyNoetherian_glued
  AlgebraicCurve.CurveModel.jacobsonSpace_glued
  AlgebraicCurve.CurveModel.isOpenImmersion_ι₀
  AlgebraicCurve.CurveModel.isIntegral_glued
  AlgebraicCurve.CurveModel.quasiSeparated_gluedToBase
  AlgebraicCurve.CurveModel.compactSpace_glued
  AlgebraicCurve.CurveModel.isIntegral_adjoin_chartRing
  AlgebraicCurve.CurveModel.isFractionRing_overlap_functionField
  AlgebraicCurve.CurveModel.isProper_gluedToBase
  AlgebraicCurve.CurveModel.isOpenImmersion_ιU
  AlgebraicCurve.CurveModel.isOpenImmersion_f₀
  AlgebraicCurve.CurveModel.isOpenImmersion_fInf
  AlgebraicCurve.CurveModel.isOpenImmersion_ιInf
  AlgebraicCurve.CurveModel.algebra_overlap_functionField
  AlgebraicCurve.CurveModel.quasiCompact_gluedToBase
  AlgebraicCurve.CurveModel.algebraAdjoin
  AlgebraicCurve.CurveModel.isDedekindDomain_chartRing
  AlgebraicCurve.CurveModel.isIntegralClosure
  AlgebraicCurve.CurveModel.finite_chartRing
  AlgebraicCurve.CurveModel.centre_isPrime
  AlgebraicCurve.CurveModel.isFractionRing_chartRing
  AlgebraicCurve.CurveModel.finiteType_chartRing
  AlgebraicCurve.CurveModel.isNoetherianRing_chartRing
  AlgebraicCurve.CurveModel.isScalarTower_base_adjoin
  AlgebraicCurve.CurveModel.isScalarTower_adjoin
  AlgebraicCurve.CurveModel.chartRing_finitePresentation
attribute [-simp]
  GoodReductionJacobian.RelativePic0Designation.mk.sizeOf_spec
  GoodReductionJacobian.AvatarSchemeBridge.mk.injEq
  GoodReductionJacobian.AvatarSchemeBridge.mk.sizeOf_spec
  GoodReductionJacobian.RelativePic0Designation.mk.injEq
  GoodReductionJacobian.schemeHomOverComp_coe
  NeronModelInfra.schemeHomOverEquivOverHom_apply
  GoodReductionJacobian.RelativeGroupLaw.mk.sizeOf_spec
  NeronModelInfra.schemeHomOverEquivOverHom_symm_apply
  NeronModelInfra.overHomToSchemeHomOver_coe
  GoodReductionJacobian.RelativeGroupLaw.mk.injEq
  NeronModelInfra.overHomToSchemeHomOver_schemeHomOverToOverHom
  NeronModelInfra.schemeHomOverToOverHom_left
  NeronModelInfra.schemeHomOverToOverHom_overHomToSchemeHomOver
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.sizeOf_spec
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
  AlgebraicCurve.CurveModel.mk.injEq
  AlgebraicCurve.CurveModel.mk.sizeOf_spec
  AlgebraicCurve.Place.mk.injEq
  AlgebraicCurve.Divisor.degree_single
  AlgebraicCurve.Divisor.smul_single
  AlgebraicCurve.Place.smul_toValuationSubring
  AlgebraicCurve.Place.heightOneSpectrum_asIdeal
  AlgebraicCurve.Place.coe_algebraMap
  AlgebraicCurve.Place.ord_one
  AlgebraicCurve.Place.coe_smulRingEquiv_apply
  AlgebraicCurve.Pic0.coe_degZeroSMulHom
  AlgebraicCurve.Place.deg_smul
  AlgebraicCurve.Pic0.mk_zero
  AlgebraicCurve.Place.mk.sizeOf_spec
  AlgebraicCurve.Divisor.degree_smul
  AlgebraicCurve.Pic0.mk_add
  AlgebraicCurve.Place.ord_zero
  AlgebraicCurve.Place.ofHeightOneSpectrum_toValuationSubring
  AlgebraicCurve.mulAdele_apply
attribute [-simp]
  AlgebraicCurve.residuePairing_apply_coe
  AlgebraicCurve.mem_adeleBdd
  AlgebraicCurve.weilSmul_one
  AlgebraicCurve.diagonalHom_apply
  AlgebraicCurve.weilSmul_apply
  AlgebraicCurve.adeleSpaceMul_coe
  AlgebraicCurve.mulAdele_one
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U1
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.injEq
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U0
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.mk.injEq
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.pullback_U1
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.pullback_U0
  TwoChartCech.Sections.mk.injEq
  TwoChartCech.Cover.mk.injEq
  TwoChartCech.GrothendieckComplex.mk.injEq
  TwoChartCech.Sections.mk.sizeOf_spec
  TwoChartCech.Cover.mk.sizeOf_spec
  TwoChartCech.Cover.lineBundle_r0_apply
  TwoChartCech.GrothendieckComplex.mk.sizeOf_spec
  TwoChartCech.Cover.lineBundle_r1_apply
  CoherentBaseChange.TwoTermComplex.mk.sizeOf_spec
  CoherentBaseChange.TwoTermComplex.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
  AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
  CategoryTheory.Functor.OverTotal.ofFibre_fst
  CategoryTheory.Functor.overTotal_map_fst
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_J
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYoneda_toGlued_uliftYonedaGluedToSheaf
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t'
attribute [-simp]
  uliftYoneda_toGlued_uliftYonedaGluedToSheaf_assoc
attribute [-simp]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_toGlued
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_openCover_map
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_comp
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_V
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_U
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_f
attribute [-simp]
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_P
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_toBase
  AlgebraicGeometry.RelPicard.rigSection_snd
  AlgebraicGeometry.RelPicard.RigidifiedLineBundle.ofInvertible_L
  AlgebraicGeometry.RelPicard.rigSection_snd_assoc
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
  GoodReductionJacobian.relativeGroupLawOfGrpObj_inv
  GoodReductionJacobian.relativeGroupLawOfGrpObj_mul
  GoodReductionJacobian.overHomEquivSchemeHomOver_apply_coe
  GoodReductionJacobian.relativeGroupLawOfGrpObj_one
  GoodReductionJacobian.overHomEquivSchemeHomOver_symm_apply_left
  PresheafOfModules.freeεIso_hom_app
  PresheafOfModules.freeμIso_hom_app
  AlgebraicCurve.coe_cechH0Equiv_apply
  AlgebraicCurve.cechH1ToH1_mk
  AlgebraicCurve.lSpaceOn_univ
  AlgebraicCurve.lSpaceOn_empty
  AlgebraicCurve.Place.congrEquiv_symm_apply
  AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
  AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
  AlgebraicCurve.Place.congrEquiv_apply
  AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
  AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
  AlgebraicCurve.Divisor.mapRestrict_single
  AlgebraicCurve.Divisor.pushforward_single
  AlgebraicCurve.Place.coe_restrictInclusion
  AlgebraicCurve.Place.mem_fiber
  AlgebraicCurve.Place.restrict_toValuationSubring
  AlgebraicCurve.Divisor.degree_pushforward
  AlgebraicCurve.Place.restrictResidueMap_residue
  AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
  AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
  AlgebraicCurve.Place.placeOfPrime_toValuationSubring
  AlgebraicCurve.Place.mem_fiberOver
  AlgebraicCurve.Place.fiberEquiv_symm_apply
  AlgebraicCurve.Place.fiberEquiv_apply
  AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
attribute [-simp]
  AlgebraicCurve.Divisor.degree_pushforwardAlong
  AlgebraicCurve.Pic0.coe_degZeroCorrespondence
  AlgebraicCurve.Place.mem_fiberAlong
  AlgebraicCurve.SemilinearAut.toRingAut_inv
  AlgebraicCurve.SemilinearAut.smul_def
  AlgebraicCurve.SemilinearAut.smul_single
  AlgebraicCurve.SemilinearAut.smul_toValuationSubring
  AlgebraicCurve.SemilinearAut.baseAut_inv
  AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_one
  AlgebraicCurve.SemilinearAut.deg_smul
  AlgebraicCurve.SemilinearAut.degree_smul
  AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
  AlgebraicCurve.SemilinearAut.baseAut_mul
  AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
  AlgebraicCurve.SemilinearAut.baseAut_one
  AlgebraicCurve.SemilinearAut.ofAlgAut_smul
  AlgebraicCurve.SemilinearAut.coe_torsion_smul
  AlgebraicCurve.SemilinearAut.toRingAut_mul
attribute [-simp]
  AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeInfty
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_some
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeOfPoint
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_none
  AlgebraicCurve.Divisor.evalFun_zero
  AlgebraicCurve.Place.evalAt_one
  AlgebraicCurve.Place.differentialCoeff_zero
  AlgebraicCurve.Place.differentialCoeff_dCoord
  AlgebraicCurve.TranscendenceTower.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
  AlgebraicCurve.TranscendenceTower.mk.injEq
  AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec
  AlgebraicCurve.PoleDivisorPackage.mk.injEq
  AlgebraicGeometry.RelPicard.thetaBundle_def
attribute [-simp]
  AlgebraicGeometry.RelPicard.picardBundle_def
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_ofRelEffDivisor
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_I
  AlgebraicGeometry.mapOnProdOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.mk.sizeOf_spec
  AlgebraicGeometry.RelEffCartierDiv.mk.injEq
  AlgebraicGeometry.mapOnProdOver_snd
  AlgebraicGeometry.mapOnProdOver_fst
  AlgebraicGeometry.mapOnProdOver_snd_assoc
  AlgebraicGeometry.mapOnProdOver_id
  AlgebraicCurve.RelEffDivisor.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_fst
  AlgebraicCurve.mapOnProd_fst_assoc
  AlgebraicCurve.mapOnProd_snd
  AlgebraicCurve.UnivDivisorPack.mk.injEq
  AlgebraicCurve.RelEffDivisor.mk.injEq
  AlgebraicCurve.UnivDivisorPack.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_snd_assoc
  AlgebraicGeometry.Scheme.Modules.exteriorPower_obj
  PresheafOfModules.exteriorPower_map_ιMulti
  PresheafOfModules.ExteriorPower.appₗ_apply
  AlgebraicGeometry.prodKerGraph_one
  AlgebraicGeometry.fibrePowOver.proj_comp
  AlgebraicGeometry.prodKerGraph_zero
  AlgebraicGeometry.RelEffCartierDiv.empty_I
  AlgebraicGeometry.fibrePowOver.proj_comp_assoc
  AlgebraicGeometry.graphOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
  AlgebraicGeometry.graphOver_fst
  AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
  AlgebraicGeometry.graphOver_snd
  AlgebraicGeometry.graphOver_snd_assoc
  AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
  AlgebraicCurve.SymmetricPowerPackage.mk.injEq
  AlgebraicGeometry.FGSubalgebra.cocone_ι_app_apply
  AlgebraicGeometry.RelPicard.fst_toProdSpec
  AlgebraicGeometry.RelPicard.toProdSpec_fst_assoc
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_cons
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_nil
attribute [-simp]
  AlgebraicGeometry.RelPicard.fst_toProdSpec_assoc
  AlgebraicGeometry.RelPicard.toProdSpec_fst
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.sizeOf_spec
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.injEq
  AlgebraicCurve.adeleSingle_coe
  AlgebraicCurve.kaehlerResidueTermKFam_apply
  AlgebraicCurve.Place.LocalResidueData.mk.injEq
  AlgebraicCurve.Place.LocalResidueData.mk.sizeOf_spec
  AlgebraicCurve.Place.kw_ffgc_adicCompletionComapIntegers_coe
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.sizeOf_spec
  AlgebraicCurve.Place.mem_simplePoleSubmodule
  AlgebraicCurve.Place.coe_uniformizerSubring
  ModularCurve.Lg37.Lg37CompletionSection.mk.injEq
  AlgebraicCurve.Place.CoefficientFieldSection.mk.injEq
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.injEq
  ModularCurve.Lg37.Lg37CompletionSection.mk.sizeOf_spec
  AlgebraicCurve.Place.CoefficientFieldSection.mk.sizeOf_spec
  AlgebraicCurve.Place.poleSubmodule_one
  AlgebraicCurve.Place.mem_poleSubmodule
  AlgebraicGeometry.Scheme.Modules.toUnitSection_ofUnitSection
  AlgebraicGeometry.Scheme.Modules.pullbackSection_def
  AlgebraicGeometry.Scheme.Modules.ofUnitSection_toUnitSection
  PresheafOfModules.InternalHom.IsSheafAux.appAt_toPresheafHom
attribute [-simp]
  SheafOfModules.ihomSectionsEquivFamily_unit
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_apply
  SheafOfModules.ihomEval_unit_app
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_right
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_left
  AlgebraicGeometry.Scheme.Modules.homOfFamily_app_apply
  SheafOfModules.unit_ihomSectionsEquivFamily
  AlgebraicGeometry.Scheme.Modules.familyOfHom_app
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_hom_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_inv_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomOfFamily_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_symm_apply
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_right
  AlgebraicGeometry.Scheme.Modules.map_unitSection
  AlgebraicGeometry.Scheme.Modules.tensorSectionsBilin_apply
  AlgebraicGeometry.Scheme.Modules.tensorPowSection_zero
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_left
  AlgebraicGeometry.Scheme.Modules.tensorPow_zero
  AlgebraicGeometry.Scheme.Modules.tensorPow_succ
  AlgebraicGeometry.Scheme.OrderedAffineCover.mk.injEq
  AlgebraicGeometry.OModulePresheaf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCover.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.mk.injEq
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_neg
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_zero
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_sub
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_add
  AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
  AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U
  AlgebraicGeometry.OModulePresheaf.Hom.mk.injEq
  AlgebraicGeometry.OModulePresheaf.Hom.id_app
  AlgebraicGeometry.OModulePresheaf.AffHom.appSections_apply
  AlgebraicGeometry.OModulePresheaf.AffHom.comp_app
  AlgebraicGeometry.OModulePresheaf.AffSES.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.AffHom.kerMap_coe
  AlgebraicGeometry.OModulePresheaf.AffHom.id_app
  AlgebraicGeometry.OModulePresheaf.Hom.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.Hom.toAffHom_app
attribute [-simp]
  AlgebraicGeometry.OModulePresheaf.SES.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.AffHom.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.Hom.comp_app
  AlgebraicGeometry.OModulePresheaf.SES.mk.injEq
  AlgebraicGeometry.OModulePresheaf.AffHom.mk.injEq
  AlgebraicGeometry.OModulePresheaf.Hom.appSections_apply
  AlgebraicGeometry.OModulePresheaf.AffSES.mk.injEq
  AlgebraicGeometry.OModulePresheaf.prod_obj
  AlgebraicGeometry.OModulePresheaf.restrOpen_obj
  AlgebraicGeometry.OModulePresheaf.DevissageStep.mk.injEq
  AlgebraicGeometry.OModulePresheaf.pushforward_obj
  AlgebraicGeometry.OModulePresheaf.im_obj
  AlgebraicGeometry.OModulePresheaf.pow_obj
  AlgebraicGeometry.OModulePresheaf.fstHom_app
  AlgebraicGeometry.OModulePresheaf.ker_obj
  AlgebraicGeometry.OModulePresheaf.coker_obj
  AlgebraicGeometry.OModulePresheaf.DevissageStep.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCover.preimage_U
  AlgebraicGeometry.OModulePresheaf.sndHom_app
  AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
  DoubleComplex.Bounded.mk.injEq
  DoubleComplex.Bounded.mk.sizeOf_spec
  DoubleComplex.Convergence.mk.injEq
  DoubleComplex.Convergence.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.injEq
  AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatumProj.mk.injEq
  AlgebraicGeometry.ChowDatum.mk.injEq
  ProjSpaceCech.GradedModule.mk.injEq
  ProjSpaceCech.GradedModule.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Presentation.mk.injEq
  ProjSpaceCech.GradedModule.Frac.mk.injEq
  ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.shift_toLinearMap
  ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.mk.injEq
  TwoChartCech.Mumford.dK_apply
attribute [-simp]
  TwoChartCech.Mumford.ι0_apply
  TwoChartCech.Mumford.ι1_apply
  TwoChartCech.KerCoprod.dK_apply
  TwoChartCech.KerCoprod.ι1_apply
  TwoChartCech.KerCoprod.ι0_apply
  AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
  AlgebraicGeometry.RelPicard.algEquivZeroGroupCut_toSubPicCondition
  AlgebraicGeometry.RelPicard.LFP.stageHom_val
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_hom_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_inv_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.restrict_P
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp
  AlgebraicGeometry.RelEffCartierDiv.functor_map_fst
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_pullbackAlong
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_symm_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp_assoc
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top
  AlgebraicGeometry.RelEffCartierDiv.mem_supportedIn_iff
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top_eq
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
  CoherentBaseChange.FibreH0Family.mk.sizeOf_spec
  CoherentBaseChange.FibreH0Family.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.sizeOf_spec
  AlgebraicCurve.CurveModel.coe_gInf
  AlgebraicCurve.CurveModel.coe_tInvChart
  AlgebraicCurve.CurveModel.ιInf_gluedToBase_assoc
  AlgebraicCurve.CurveModel.ιInf_gluedToBase
  AlgebraicCurve.CurveModel.primeOfι₀_asIdeal
  AlgebraicCurve.CurveModel.coe_tChart
  AlgebraicCurve.CurveModel.ι₀_gluedToBase_assoc
  AlgebraicCurve.CurveModel.primeOfιInf_asIdeal
attribute [-simp]
  AlgebraicCurve.CurveModel.ι₀_gluedToBase
  AlgebraicCurve.CurveModel.coe_tma
  AlgebraicCurve.CurveModel.coe_primeEquivChartPlaces
universe u
noncomputable section
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.CategoryTheory.CartesianMonoidalCategory
open _root_.AlgebraicGeometry.RelPicard
open _root_.NeronModelInfra
namespace P2mCubeAssembly
section Main
variable (k : Type u) [Field k] [IsAlgClosed k]
local notation "Sk" => Spec (CommRingCat.of k)
variable (X Y Z : Over (Spec (CommRingCat.of k)))
  [IsProper X.hom] [IsIntegral X.left] [IsProper Y.hom] [IsIntegral Y.left]
  [IsSeparated Z.hom] [LocallyOfFiniteType Z.hom] [QuasiCompact Z.hom] [IsIntegral Z.left]
  (x₀ : 𝟙_ (Over (Spec (CommRingCat.of k))) ⟶ X) (y₀ : 𝟙_ (Over (Spec (CommRingCat.of k))) ⟶ Y)
  (z₀ : 𝟙_ (Over (Spec (CommRingCat.of k))) ⟶ Z)
  (L : (X ⊗ Y ⊗ Z).left.Modules) (hL : Scheme.Modules.IsInvertible L)
  (h₁ : Triv (slice₁ X (Y ⊗ Z) x₀).left L) (h₂ : Triv (slice₂ X Y Z y₀).left L)
  (h₃ : Triv (slice₃ X Y Z z₀).left L)
include hL h₁ h₂ h₃ in
omit [IsSeparated Z.hom] [QuasiCompact Z.hom] in
open _root_.AlgebraicGeometry.Scheme.Modules in

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.ThreeSlices
attribute [-instance]
  AlgebraicGeometry.SmoothOfRelativeDimension.fiberToSpecResidueField
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_snd
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_fst
  AlgebraicGeometry.SmoothOfRelativeDimension.smooth_one
  AlgebraicGeometry.SmoothProperCurve.isIntegral_pullback_Spec_field
  AlgebraicGeometry.IsProper.fiberToSpecResidueField
  AlgebraicCurve.CurveModel.isProper
  AlgebraicCurve.CurveModel.isIntegral
  AlgebraicCurve.CurveModel.smooth
  AlgebraicCurve.Place.instIsScalarTowerSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Divisor.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instSMulAlgEquiv
  AlgebraicCurve.Place.instIsPrincipalIdealRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instIsDiscreteValuationRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Pic0.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instAlgebraSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instMulActionAlgEquiv
  AlgebraicCurve.Pic0.instSMulAlgEquiv
  TwoChartCech.Sections.M0_moduleA
  TwoChartCech.Sections.M1_module
  TwoChartCech.Cover.A01_algebra
  TwoChartCech.Cover.A0_algebra
  TwoChartCech.Cover.A1_commRing
  TwoChartCech.Cover.A1_algebra
  TwoChartCech.Sections.M01_module
  TwoChartCech.Sections.M0_addCommGroup
  TwoChartCech.Sections.M0_tower
  TwoChartCech.Sections.M01_addCommGroup
  TwoChartCech.Cover.A0_commRing
  TwoChartCech.Sections.M1_tower
  TwoChartCech.Sections.M01_moduleA
  TwoChartCech.Sections.M0_module
  TwoChartCech.Sections.M1_moduleA
  TwoChartCech.Sections.M1_addCommGroup
  TwoChartCech.Cover.A01_commRing
  TwoChartCech.Sections.M01_tower
  CoherentBaseChange.TwoTermComplex.C0_module
  CoherentBaseChange.TwoTermComplex.C0_addCommGroup
  CoherentBaseChange.TwoTermComplex.C1_module
  CoherentBaseChange.TwoTermComplex.C1_addCommGroup
attribute [-instance]
  CoherentBaseChange.TwoTermComplex.C0_free
  CoherentBaseChange.TwoTermComplex.C1_finite
  CoherentBaseChange.TwoTermComplex.C0_finite
  CoherentBaseChange.TwoTermComplex.C1_free
  AlgebraicCurve.IsCurveOver.instNontrivialKaehler
  AlgebraicCurve.IsCurveOver.instFreeKaehler
  AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
  AlgebraicCurve.IsCurveOver.instFiniteResidue
attribute [-instance]
  instIsLocallyInjectiveFunUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsLocallySurjectiveUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsOpenImmersionToGlued
attribute [-instance]
  instIsIsoSheafZariskiTopologyTypeUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.RelPicard.isOpenImmersion_toGlued
  AlgebraicGeometry.Scheme.Modules.preservesBinaryProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback_monoidal
  AlgebraicGeometry.Scheme.Modules.sheafify_isLocalization'
  AlgebraicGeometry.Scheme.Modules.preservesTerminal_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback₀_monoidal
  AlgebraicGeometry.Scheme.Modules.preservesFiniteProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.sheafifyPullback_lifting
  PresheafOfModules.PullbackMonoidal.pullback_monoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ
  PresheafOfModules.pushforward_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_η
  PresheafOfModules.free_monoidal
  PresheafOfModules.restrictScalars_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ_gS
  PresheafOfModules.pullback_oplaxMonoidal
attribute [-instance]
  instPreservesColimitsOfSizeCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierPb
attribute [-instance]
  PresheafOfModules.pullback_monoidal'
  AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
  AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
  AlgebraicCurve.Place.instIsPrimeCenter
  AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
  instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
  AlgebraicCurve.Pic0.instModuleZModTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instSMulTorsion
  AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
  AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
  AlgebraicCurve.RationalFunctionField.instNontrivialInftyValueGroup
  PresheafOfModules.ExteriorPower.instModulePresheafAb
  AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
  AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
  AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
  AlgebraicGeometry.isClosedImmersion_graphOver
  AlgebraicGeometry.FGSubalgebra.instIsDirectedLe
attribute [-instance]
  instQuasiSeparatedSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsCofilteredOpposite
  AlgebraicGeometry.FGSubalgebra.instIsAffineObjOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instNonempty
  AlgebraicGeometry.FGSubalgebra.instNonemptySubtypeLeSubalgebraValFG
attribute [-instance]
  instCompactSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsDirectedSubtypeLeSubalgebraValFG
  AlgebraicGeometry.FGSubalgebra.instIsAffineHomMapOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instIsFiltered
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instNeg
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulInt
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAddCommGroup
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAdd
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSub
attribute [-instance]
  instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
  AlgebraicCurve.instHasLocalResidue_of_hasCanonicalLocalResidueK
  AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
  AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
  ModularCurve.KwF4gRRTate.instAlgebraKAdicCompletionIntegers
  AlgebraicCurve.Place.kw_ffgc_continuousSMul_adicCompletionComap
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersCompletionCompletion
attribute [-instance]
  instLiesOverSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegersCompletionIdealAsIdeal
attribute [-instance]
  AlgebraicCurve.instHasCanonicalLocalResidueK
  AlgebraicCurve.Place.instAlgebra_restrictResidueField
  AlgebraicCurve.Place.instIsScalarTower_restrictResidueField
  AlgebraicCurve.instHasLocalResidue
  AlgebraicCurve.HasSeparableResidue.of_perfectField_of_isCurveOver
  AlgebraicCurve.HasSeparableResidue.of_perfectField
  AlgebraicCurve.Place.instIsLocalHom_restrictSubringHom
  AlgebraicCurve.instHasCanonicalLocalResidueKStar
  ModularCurve.KwNo6Pin.isLocalRing_completion
  SheafOfModules.isIso_ihomModelToIhom
  AlgebraicGeometry.OModulePresheaf.isScalarTower
  AlgebraicGeometry.Scheme.OrderedAffineCover.instLinearOrder
  AlgebraicGeometry.OModulePresheaf.module
  AlgebraicGeometry.Scheme.OrderedAffineCover.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCover.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.addCommGroup
  AlgebraicGeometry.Scheme.OrderedAffineCover.instDecidableEqIdx
  AlgebraicGeometry.OModulePresheaf.moduleSections
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.instSubsingletonObjZero
attribute [-instance]
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
  AlgebraicGeometry.OModulePresheaf.Leray.biC_module
  DoubleComplex.instModuleE₂I
  DoubleComplex.Bounded.modR
  DoubleComplex.instModuleE₂II
  DoubleComplex.instAddCommGroupE₂II
  DoubleComplex.Bounded.abGrp
  DoubleComplex.instAddCommGroupE₂I
  AlgebraicGeometry.ChowDatum.hι_closed
  AlgebraicGeometry.ChowDatumProj.hιN_closed
  AlgebraicGeometry.ChowDatumProj.hp_proper
  AlgebraicGeometry.ChowDatum.hp_isoU
  AlgebraicGeometry.ChowDatum.hp_proper
  AlgebraicGeometry.ProjSpace.algebraAway
  AlgebraicGeometry.ProjSpace.instIsProperProdOverπ
  AlgebraicGeometry.ChowDatumProj.hp_isoU
  AlgebraicGeometry.ProjSpace.isProper_π
  AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
  ProjSpaceCech.GradedModule.H.module
  ProjSpaceCech.GradedModule.H.addCommGroup
  ProjSpaceCech.GradedModule.sec.instAdd
  ProjSpaceCech.GradedModule.sec.instNeg
  ProjSpaceCech.GradedModule.acg
  ProjSpaceCech.GradedModule.Frac.setoid
  ProjSpaceCech.GradedModule.modR
  ProjSpaceCech.GradedModule.sec.instModule
  ProjSpaceCech.GradedModule.sec.instAddCommGroup
  ProjSpaceCech.GradedModule.sec.instZero
  ProjSpaceCech.GradedModule.Presentation.fJ
  ProjSpaceCech.GradedModule.sec.instSMul
  ProjSpaceCech.Twist.H.module
  ProjSpaceCech.Idx.instFintype
  ProjSpaceCech.Twist.H.addCommGroup
attribute [-instance]
  ProjSpaceCech.Idx.instDecidableEq
  ProjSpaceCech.Twist.Mon.instDecidableEq
  ProjSpaceCech.Twist.cochain.instAddCommGroup
  ProjSpaceCech.Twist.cochain.instModule
  AlgebraicGeometry.FGSubalgebra.tensorStage_directedSystem
  AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
  AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
  AlgebraicCurve.CurveModel.locallyOfFiniteType_gluedToBase
  AlgebraicCurve.CurveModel.isFractionRing_overlap
  AlgebraicCurve.CurveModel.isLocallyNoetherian_glued
  AlgebraicCurve.CurveModel.jacobsonSpace_glued
  AlgebraicCurve.CurveModel.isOpenImmersion_ι₀
  AlgebraicCurve.CurveModel.isIntegral_glued
  AlgebraicCurve.CurveModel.quasiSeparated_gluedToBase
  AlgebraicCurve.CurveModel.compactSpace_glued
  AlgebraicCurve.CurveModel.isIntegral_adjoin_chartRing
  AlgebraicCurve.CurveModel.isFractionRing_overlap_functionField
  AlgebraicCurve.CurveModel.isProper_gluedToBase
  AlgebraicCurve.CurveModel.isOpenImmersion_ιU
  AlgebraicCurve.CurveModel.isOpenImmersion_f₀
  AlgebraicCurve.CurveModel.isOpenImmersion_fInf
  AlgebraicCurve.CurveModel.isOpenImmersion_ιInf
  AlgebraicCurve.CurveModel.algebra_overlap_functionField
  AlgebraicCurve.CurveModel.quasiCompact_gluedToBase
  AlgebraicCurve.CurveModel.algebraAdjoin
  AlgebraicCurve.CurveModel.isDedekindDomain_chartRing
  AlgebraicCurve.CurveModel.isIntegralClosure
  AlgebraicCurve.CurveModel.finite_chartRing
  AlgebraicCurve.CurveModel.centre_isPrime
  AlgebraicCurve.CurveModel.isFractionRing_chartRing
  AlgebraicCurve.CurveModel.finiteType_chartRing
  AlgebraicCurve.CurveModel.isNoetherianRing_chartRing
  AlgebraicCurve.CurveModel.isScalarTower_base_adjoin
  AlgebraicCurve.CurveModel.isScalarTower_adjoin
  AlgebraicCurve.CurveModel.chartRing_finitePresentation
attribute [-simp]
  GoodReductionJacobian.RelativePic0Designation.mk.sizeOf_spec
  GoodReductionJacobian.AvatarSchemeBridge.mk.injEq
  GoodReductionJacobian.AvatarSchemeBridge.mk.sizeOf_spec
  GoodReductionJacobian.RelativePic0Designation.mk.injEq
  GoodReductionJacobian.schemeHomOverComp_coe
  NeronModelInfra.schemeHomOverEquivOverHom_apply
  GoodReductionJacobian.RelativeGroupLaw.mk.sizeOf_spec
  NeronModelInfra.schemeHomOverEquivOverHom_symm_apply
  NeronModelInfra.overHomToSchemeHomOver_coe
  GoodReductionJacobian.RelativeGroupLaw.mk.injEq
  NeronModelInfra.overHomToSchemeHomOver_schemeHomOverToOverHom
  NeronModelInfra.schemeHomOverToOverHom_left
  NeronModelInfra.schemeHomOverToOverHom_overHomToSchemeHomOver
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.sizeOf_spec
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
  AlgebraicCurve.CurveModel.mk.injEq
  AlgebraicCurve.CurveModel.mk.sizeOf_spec
  AlgebraicCurve.Place.mk.injEq
  AlgebraicCurve.Divisor.degree_single
  AlgebraicCurve.Divisor.smul_single
  AlgebraicCurve.Place.smul_toValuationSubring
  AlgebraicCurve.Place.heightOneSpectrum_asIdeal
  AlgebraicCurve.Place.coe_algebraMap
  AlgebraicCurve.Place.ord_one
  AlgebraicCurve.Place.coe_smulRingEquiv_apply
  AlgebraicCurve.Pic0.coe_degZeroSMulHom
  AlgebraicCurve.Place.deg_smul
  AlgebraicCurve.Pic0.mk_zero
  AlgebraicCurve.Place.mk.sizeOf_spec
  AlgebraicCurve.Divisor.degree_smul
  AlgebraicCurve.Pic0.mk_add
  AlgebraicCurve.Place.ord_zero
  AlgebraicCurve.Place.ofHeightOneSpectrum_toValuationSubring
  AlgebraicCurve.mulAdele_apply
attribute [-simp]
  AlgebraicCurve.residuePairing_apply_coe
  AlgebraicCurve.mem_adeleBdd
  AlgebraicCurve.weilSmul_one
  AlgebraicCurve.diagonalHom_apply
  AlgebraicCurve.weilSmul_apply
  AlgebraicCurve.adeleSpaceMul_coe
  AlgebraicCurve.mulAdele_one
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U1
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.injEq
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U0
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.mk.injEq
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.pullback_U1
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.pullback_U0
  TwoChartCech.Sections.mk.injEq
  TwoChartCech.Cover.mk.injEq
  TwoChartCech.GrothendieckComplex.mk.injEq
  TwoChartCech.Sections.mk.sizeOf_spec
  TwoChartCech.Cover.mk.sizeOf_spec
  TwoChartCech.Cover.lineBundle_r0_apply
  TwoChartCech.GrothendieckComplex.mk.sizeOf_spec
  TwoChartCech.Cover.lineBundle_r1_apply
  CoherentBaseChange.TwoTermComplex.mk.sizeOf_spec
  CoherentBaseChange.TwoTermComplex.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
  AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
  CategoryTheory.Functor.OverTotal.ofFibre_fst
  CategoryTheory.Functor.overTotal_map_fst
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_J
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYoneda_toGlued_uliftYonedaGluedToSheaf
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t'
attribute [-simp]
  uliftYoneda_toGlued_uliftYonedaGluedToSheaf_assoc
attribute [-simp]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_toGlued
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_openCover_map
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_comp
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_V
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_U
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_f
attribute [-simp]
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_P
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_toBase
  AlgebraicGeometry.RelPicard.rigSection_snd
  AlgebraicGeometry.RelPicard.RigidifiedLineBundle.ofInvertible_L
  AlgebraicGeometry.RelPicard.rigSection_snd_assoc
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
  GoodReductionJacobian.relativeGroupLawOfGrpObj_inv
  GoodReductionJacobian.relativeGroupLawOfGrpObj_mul
  GoodReductionJacobian.overHomEquivSchemeHomOver_apply_coe
  GoodReductionJacobian.relativeGroupLawOfGrpObj_one
  GoodReductionJacobian.overHomEquivSchemeHomOver_symm_apply_left
  PresheafOfModules.freeεIso_hom_app
  PresheafOfModules.freeμIso_hom_app
  AlgebraicCurve.coe_cechH0Equiv_apply
  AlgebraicCurve.cechH1ToH1_mk
  AlgebraicCurve.lSpaceOn_univ
  AlgebraicCurve.lSpaceOn_empty
  AlgebraicCurve.Place.congrEquiv_symm_apply
  AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
  AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
  AlgebraicCurve.Place.congrEquiv_apply
  AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
  AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
  AlgebraicCurve.Divisor.mapRestrict_single
  AlgebraicCurve.Divisor.pushforward_single
  AlgebraicCurve.Place.coe_restrictInclusion
  AlgebraicCurve.Place.mem_fiber
  AlgebraicCurve.Place.restrict_toValuationSubring
  AlgebraicCurve.Divisor.degree_pushforward
  AlgebraicCurve.Place.restrictResidueMap_residue
  AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
  AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
  AlgebraicCurve.Place.placeOfPrime_toValuationSubring
  AlgebraicCurve.Place.mem_fiberOver
  AlgebraicCurve.Place.fiberEquiv_symm_apply
  AlgebraicCurve.Place.fiberEquiv_apply
  AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
attribute [-simp]
  AlgebraicCurve.Divisor.degree_pushforwardAlong
  AlgebraicCurve.Pic0.coe_degZeroCorrespondence
  AlgebraicCurve.Place.mem_fiberAlong
  AlgebraicCurve.SemilinearAut.toRingAut_inv
  AlgebraicCurve.SemilinearAut.smul_def
  AlgebraicCurve.SemilinearAut.smul_single
  AlgebraicCurve.SemilinearAut.smul_toValuationSubring
  AlgebraicCurve.SemilinearAut.baseAut_inv
  AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_one
  AlgebraicCurve.SemilinearAut.deg_smul
  AlgebraicCurve.SemilinearAut.degree_smul
  AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
  AlgebraicCurve.SemilinearAut.baseAut_mul
  AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
  AlgebraicCurve.SemilinearAut.baseAut_one
  AlgebraicCurve.SemilinearAut.ofAlgAut_smul
  AlgebraicCurve.SemilinearAut.coe_torsion_smul
  AlgebraicCurve.SemilinearAut.toRingAut_mul
attribute [-simp]
  AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeInfty
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_some
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeOfPoint
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_none
  AlgebraicCurve.Divisor.evalFun_zero
  AlgebraicCurve.Place.evalAt_one
  AlgebraicCurve.Place.differentialCoeff_zero
  AlgebraicCurve.Place.differentialCoeff_dCoord
  AlgebraicCurve.TranscendenceTower.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
  AlgebraicCurve.TranscendenceTower.mk.injEq
  AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec
  AlgebraicCurve.PoleDivisorPackage.mk.injEq
  AlgebraicGeometry.RelPicard.thetaBundle_def
attribute [-simp]
  AlgebraicGeometry.RelPicard.picardBundle_def
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_ofRelEffDivisor
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_I
  AlgebraicGeometry.mapOnProdOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.mk.sizeOf_spec
  AlgebraicGeometry.RelEffCartierDiv.mk.injEq
  AlgebraicGeometry.mapOnProdOver_snd
  AlgebraicGeometry.mapOnProdOver_fst
  AlgebraicGeometry.mapOnProdOver_snd_assoc
  AlgebraicGeometry.mapOnProdOver_id
  AlgebraicCurve.RelEffDivisor.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_fst
  AlgebraicCurve.mapOnProd_fst_assoc
  AlgebraicCurve.mapOnProd_snd
  AlgebraicCurve.UnivDivisorPack.mk.injEq
  AlgebraicCurve.RelEffDivisor.mk.injEq
  AlgebraicCurve.UnivDivisorPack.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_snd_assoc
  AlgebraicGeometry.Scheme.Modules.exteriorPower_obj
  PresheafOfModules.exteriorPower_map_ιMulti
  PresheafOfModules.ExteriorPower.appₗ_apply
  AlgebraicGeometry.prodKerGraph_one
  AlgebraicGeometry.fibrePowOver.proj_comp
  AlgebraicGeometry.prodKerGraph_zero
  AlgebraicGeometry.RelEffCartierDiv.empty_I
  AlgebraicGeometry.fibrePowOver.proj_comp_assoc
  AlgebraicGeometry.graphOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
  AlgebraicGeometry.graphOver_fst
  AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
  AlgebraicGeometry.graphOver_snd
  AlgebraicGeometry.graphOver_snd_assoc
  AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
  AlgebraicCurve.SymmetricPowerPackage.mk.injEq
  AlgebraicGeometry.FGSubalgebra.cocone_ι_app_apply
  AlgebraicGeometry.RelPicard.fst_toProdSpec
  AlgebraicGeometry.RelPicard.toProdSpec_fst_assoc
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_cons
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_nil
attribute [-simp]
  AlgebraicGeometry.RelPicard.fst_toProdSpec_assoc
  AlgebraicGeometry.RelPicard.toProdSpec_fst
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.sizeOf_spec
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.injEq
  AlgebraicCurve.adeleSingle_coe
  AlgebraicCurve.kaehlerResidueTermKFam_apply
  AlgebraicCurve.Place.LocalResidueData.mk.injEq
  AlgebraicCurve.Place.LocalResidueData.mk.sizeOf_spec
  AlgebraicCurve.Place.kw_ffgc_adicCompletionComapIntegers_coe
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.sizeOf_spec
  AlgebraicCurve.Place.mem_simplePoleSubmodule
  AlgebraicCurve.Place.coe_uniformizerSubring
  ModularCurve.Lg37.Lg37CompletionSection.mk.injEq
  AlgebraicCurve.Place.CoefficientFieldSection.mk.injEq
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.injEq
  ModularCurve.Lg37.Lg37CompletionSection.mk.sizeOf_spec
  AlgebraicCurve.Place.CoefficientFieldSection.mk.sizeOf_spec
  AlgebraicCurve.Place.poleSubmodule_one
  AlgebraicCurve.Place.mem_poleSubmodule
  AlgebraicGeometry.Scheme.Modules.toUnitSection_ofUnitSection
  AlgebraicGeometry.Scheme.Modules.pullbackSection_def
  AlgebraicGeometry.Scheme.Modules.ofUnitSection_toUnitSection
  PresheafOfModules.InternalHom.IsSheafAux.appAt_toPresheafHom
attribute [-simp]
  SheafOfModules.ihomSectionsEquivFamily_unit
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_apply
  SheafOfModules.ihomEval_unit_app
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_right
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_left
  AlgebraicGeometry.Scheme.Modules.homOfFamily_app_apply
  SheafOfModules.unit_ihomSectionsEquivFamily
  AlgebraicGeometry.Scheme.Modules.familyOfHom_app
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_hom_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_inv_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomOfFamily_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_symm_apply
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_right
  AlgebraicGeometry.Scheme.Modules.map_unitSection
  AlgebraicGeometry.Scheme.Modules.tensorSectionsBilin_apply
  AlgebraicGeometry.Scheme.Modules.tensorPowSection_zero
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_left
  AlgebraicGeometry.Scheme.Modules.tensorPow_zero
  AlgebraicGeometry.Scheme.Modules.tensorPow_succ
  AlgebraicGeometry.Scheme.OrderedAffineCover.mk.injEq
  AlgebraicGeometry.OModulePresheaf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCover.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.mk.injEq
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_neg
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_zero
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_sub
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_add
  AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
  AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U
  AlgebraicGeometry.OModulePresheaf.Hom.mk.injEq
  AlgebraicGeometry.OModulePresheaf.Hom.id_app
  AlgebraicGeometry.OModulePresheaf.AffHom.appSections_apply
  AlgebraicGeometry.OModulePresheaf.AffHom.comp_app
  AlgebraicGeometry.OModulePresheaf.AffSES.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.AffHom.kerMap_coe
  AlgebraicGeometry.OModulePresheaf.AffHom.id_app
  AlgebraicGeometry.OModulePresheaf.Hom.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.Hom.toAffHom_app
attribute [-simp]
  AlgebraicGeometry.OModulePresheaf.SES.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.AffHom.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.Hom.comp_app
  AlgebraicGeometry.OModulePresheaf.SES.mk.injEq
  AlgebraicGeometry.OModulePresheaf.AffHom.mk.injEq
  AlgebraicGeometry.OModulePresheaf.Hom.appSections_apply
  AlgebraicGeometry.OModulePresheaf.AffSES.mk.injEq
  AlgebraicGeometry.OModulePresheaf.prod_obj
  AlgebraicGeometry.OModulePresheaf.restrOpen_obj
  AlgebraicGeometry.OModulePresheaf.DevissageStep.mk.injEq
  AlgebraicGeometry.OModulePresheaf.pushforward_obj
  AlgebraicGeometry.OModulePresheaf.im_obj
  AlgebraicGeometry.OModulePresheaf.pow_obj
  AlgebraicGeometry.OModulePresheaf.fstHom_app
  AlgebraicGeometry.OModulePresheaf.ker_obj
  AlgebraicGeometry.OModulePresheaf.coker_obj
  AlgebraicGeometry.OModulePresheaf.DevissageStep.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCover.preimage_U
  AlgebraicGeometry.OModulePresheaf.sndHom_app
  AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
  DoubleComplex.Bounded.mk.injEq
  DoubleComplex.Bounded.mk.sizeOf_spec
  DoubleComplex.Convergence.mk.injEq
  DoubleComplex.Convergence.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.injEq
  AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatumProj.mk.injEq
  AlgebraicGeometry.ChowDatum.mk.injEq
  ProjSpaceCech.GradedModule.mk.injEq
  ProjSpaceCech.GradedModule.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Presentation.mk.injEq
  ProjSpaceCech.GradedModule.Frac.mk.injEq
  ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.shift_toLinearMap
  ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.mk.injEq
  TwoChartCech.Mumford.dK_apply
attribute [-simp]
  TwoChartCech.Mumford.ι0_apply
  TwoChartCech.Mumford.ι1_apply
  TwoChartCech.KerCoprod.dK_apply
  TwoChartCech.KerCoprod.ι1_apply
  TwoChartCech.KerCoprod.ι0_apply
  AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
  AlgebraicGeometry.RelPicard.algEquivZeroGroupCut_toSubPicCondition
  AlgebraicGeometry.RelPicard.LFP.stageHom_val
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_hom_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_inv_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.restrict_P
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp
  AlgebraicGeometry.RelEffCartierDiv.functor_map_fst
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_pullbackAlong
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_symm_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp_assoc
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top
  AlgebraicGeometry.RelEffCartierDiv.mem_supportedIn_iff
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top_eq
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
  CoherentBaseChange.FibreH0Family.mk.sizeOf_spec
  CoherentBaseChange.FibreH0Family.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.sizeOf_spec
  AlgebraicCurve.CurveModel.coe_gInf
  AlgebraicCurve.CurveModel.coe_tInvChart
  AlgebraicCurve.CurveModel.ιInf_gluedToBase_assoc
  AlgebraicCurve.CurveModel.ιInf_gluedToBase
  AlgebraicCurve.CurveModel.primeOfι₀_asIdeal
  AlgebraicCurve.CurveModel.coe_tChart
  AlgebraicCurve.CurveModel.ι₀_gluedToBase_assoc
  AlgebraicCurve.CurveModel.primeOfιInf_asIdeal
attribute [-simp]
  AlgebraicCurve.CurveModel.ι₀_gluedToBase
  AlgebraicCurve.CurveModel.coe_tma
  AlgebraicCurve.CurveModel.coe_primeEquivChartPlaces
universe u
noncomputable section
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.CategoryTheory.CartesianMonoidalCategory
open _root_.AlgebraicGeometry.RelPicard
open _root_.NeronModelInfra
namespace P2mCubeAssembly
section Main
variable (k : Type u) [Field k] [IsAlgClosed k]
local notation "Sk" => Spec (CommRingCat.of k)
variable (X Y Z : Over (Spec (CommRingCat.of k)))
  [IsProper X.hom] [IsIntegral X.left] [IsProper Y.hom] [IsIntegral Y.left]
  [IsSeparated Z.hom] [LocallyOfFiniteType Z.hom] [QuasiCompact Z.hom] [IsIntegral Z.left]
  (x₀ : 𝟙_ (Over (Spec (CommRingCat.of k))) ⟶ X) (y₀ : 𝟙_ (Over (Spec (CommRingCat.of k))) ⟶ Y)
  (z₀ : 𝟙_ (Over (Spec (CommRingCat.of k))) ⟶ Z)
  (L : (X ⊗ Y ⊗ Z).left.Modules) (hL : Scheme.Modules.IsInvertible L)
  (h₁ : Triv (slice₁ X (Y ⊗ Z) x₀).left L) (h₂ : Triv (slice₂ X Y Z y₀).left L)
  (h₃ : Triv (slice₃ X Y Z z₀).left L)
include hL h₁ h₂ h₃ in
omit [IsSeparated Z.hom] [QuasiCompact Z.hom] in

Surrounding namespaces, section variables, and local commands at this declaration.

section ProofImplementation
namespace JacobianVarieties.Picard.Proofs.ThreeSlices
attribute [-instance]
  AlgebraicGeometry.SmoothOfRelativeDimension.fiberToSpecResidueField
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_snd
  AlgebraicGeometry.SmoothOfRelativeDimension.pullback_fst
  AlgebraicGeometry.SmoothOfRelativeDimension.smooth_one
  AlgebraicGeometry.SmoothProperCurve.isIntegral_pullback_Spec_field
  AlgebraicGeometry.IsProper.fiberToSpecResidueField
  AlgebraicCurve.CurveModel.isProper
  AlgebraicCurve.CurveModel.isIntegral
  AlgebraicCurve.CurveModel.smooth
  AlgebraicCurve.Place.instIsScalarTowerSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Divisor.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instSMulAlgEquiv
  AlgebraicCurve.Place.instIsPrincipalIdealRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instIsDiscreteValuationRingSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Pic0.instDistribMulActionAlgEquiv
  AlgebraicCurve.Place.instAlgebraSubtypeMemValuationSubringToValuationSubring
  AlgebraicCurve.Place.instMulActionAlgEquiv
  AlgebraicCurve.Pic0.instSMulAlgEquiv
  TwoChartCech.Sections.M0_moduleA
  TwoChartCech.Sections.M1_module
  TwoChartCech.Cover.A01_algebra
  TwoChartCech.Cover.A0_algebra
  TwoChartCech.Cover.A1_commRing
  TwoChartCech.Cover.A1_algebra
  TwoChartCech.Sections.M01_module
  TwoChartCech.Sections.M0_addCommGroup
  TwoChartCech.Sections.M0_tower
  TwoChartCech.Sections.M01_addCommGroup
  TwoChartCech.Cover.A0_commRing
  TwoChartCech.Sections.M1_tower
  TwoChartCech.Sections.M01_moduleA
  TwoChartCech.Sections.M0_module
  TwoChartCech.Sections.M1_moduleA
  TwoChartCech.Sections.M1_addCommGroup
  TwoChartCech.Cover.A01_commRing
  TwoChartCech.Sections.M01_tower
  CoherentBaseChange.TwoTermComplex.C0_module
  CoherentBaseChange.TwoTermComplex.C0_addCommGroup
  CoherentBaseChange.TwoTermComplex.C1_module
  CoherentBaseChange.TwoTermComplex.C1_addCommGroup
attribute [-instance]
  CoherentBaseChange.TwoTermComplex.C0_free
  CoherentBaseChange.TwoTermComplex.C1_finite
  CoherentBaseChange.TwoTermComplex.C0_finite
  CoherentBaseChange.TwoTermComplex.C1_free
  AlgebraicCurve.IsCurveOver.instNontrivialKaehler
  AlgebraicCurve.IsCurveOver.instFreeKaehler
  AlgebraicCurve.IsCurveOver.toHasPrincipalDivisors
  AlgebraicCurve.IsCurveOver.instFiniteResidue
attribute [-instance]
  instIsLocallyInjectiveFunUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsLocallySurjectiveUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.instIsOpenImmersionToGlued
attribute [-instance]
  instIsIsoSheafZariskiTopologyTypeUliftYonedaGluedToSheaf
attribute [-instance]
  AlgebraicGeometry.RelPicard.isOpenImmersion_toGlued
  AlgebraicGeometry.Scheme.Modules.preservesBinaryProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback_monoidal
  AlgebraicGeometry.Scheme.Modules.sheafify_isLocalization'
  AlgebraicGeometry.Scheme.Modules.preservesTerminal_opensMap
  AlgebraicGeometry.Scheme.Modules.pullback₀_monoidal
  AlgebraicGeometry.Scheme.Modules.preservesFiniteProducts_opensMap
  AlgebraicGeometry.Scheme.Modules.sheafifyPullback_lifting
  PresheafOfModules.PullbackMonoidal.pullback_monoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ
  PresheafOfModules.pushforward_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_η
  PresheafOfModules.free_monoidal
  PresheafOfModules.restrictScalars_laxMonoidal
  PresheafOfModules.PullbackMonoidal.isIso_δ_gS
  PresheafOfModules.pullback_oplaxMonoidal
attribute [-instance]
  instPreservesColimitsOfSizeCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierPb
attribute [-instance]
  PresheafOfModules.pullback_monoidal'
  AlgebraicCurve.Place.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.Place.instIsTrivialOnWithZeroMultiplicativeIntAdicValuation
  AlgebraicCurve.instFundamentalIdentityOfSumRamificationInertia
  AlgebraicCurve.Place.instIsScalarTowerResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instAlgebraResidueFieldRestrictPushforward
  AlgebraicCurve.Place.instIsLocalHomRestrictInclusion
  AlgebraicCurve.Place.instIsPrimeCenter
  AlgebraicCurve.Place.instIsFractionRingIntegralClosureAt
attribute [-instance]
  instIsTorsionFreeSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instIsDedekindDomainIntegralClosureAt
attribute [-instance]
  AlgebraicCurve.Place.instFiniteSubtypeMemValuationSubringToValuationSubringIntegralClosureAt
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instDistribMulActionSubtypeProdRingAutMemSubgroupDivisor
  AlgebraicCurve.Pic0.instModuleZModTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instDistribMulActionTorsion
  AlgebraicCurve.SemilinearAut.instSMulSubtypeProdRingAutMemSubgroupPic0
  AlgebraicCurve.SemilinearAut.instSMulTorsion
  AlgebraicCurve.SemilinearAut.instMulActionSubtypeProdRingAutMemSubgroupPlace
  AlgebraicCurve.SemilinearAut.instSMulCommClassZModTorsion
  AlgebraicCurve.SemilinearAut.instMulSemiringActionSubtypeProdRingAutMemSubgroup
  AlgebraicCurve.RationalFunctionField.instNontrivialInftyValueGroup
  PresheafOfModules.ExteriorPower.instModulePresheafAb
  AlgebraicGeometry.RelEffCartierDiv.subsingleton_of_degree_zero
  AlgebraicGeometry.RelEffCartierDiv.isIso_subschemeIota_snd_of_degree_one
  AlgebraicGeometry.isIso_ker_graphOver_subschemeIota_snd
  AlgebraicGeometry.isClosedImmersion_graphOver
  AlgebraicGeometry.FGSubalgebra.instIsDirectedLe
attribute [-instance]
  instQuasiSeparatedSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsCofilteredOpposite
  AlgebraicGeometry.FGSubalgebra.instIsAffineObjOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instNonempty
  AlgebraicGeometry.FGSubalgebra.instNonemptySubtypeLeSubalgebraValFG
attribute [-instance]
  instCompactSpaceCarrierCarrierCommRingCatObjOppositeSchemeSpecDiagram
attribute [-instance]
  AlgebraicGeometry.FGSubalgebra.instIsDirectedSubtypeLeSubalgebraValFG
  AlgebraicGeometry.FGSubalgebra.instIsAffineHomMapOppositeSchemeSpecDiagram
  AlgebraicGeometry.FGSubalgebra.instIsFiltered
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instNeg
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulInt
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAddCommGroup
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instAdd
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSub
attribute [-instance]
  instModuleCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  instSMulCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTop
attribute [-instance]
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instSMulNat
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.instZero
  AlgebraicCurve.instHasLocalResidue_of_hasCanonicalLocalResidueK
  AlgebraicCurve.instHasCanonicalLocalResidueK_of_hasCanonicalLocalResidueKStar
  AlgebraicCurve.Place.kw_ffgc_finiteDimensional_adicCompletion
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersIntegersCompletion
  ModularCurve.KwF4gRRTate.instAlgebraKAdicCompletionIntegers
  AlgebraicCurve.Place.kw_ffgc_continuousSMul_adicCompletionComap
  AlgebraicCurve.Place.kw_ffgc_isScalarTower_integersCompletionCompletion
attribute [-instance]
  instLiesOverSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegersCompletionIdealAsIdeal
attribute [-instance]
  AlgebraicCurve.instHasCanonicalLocalResidueK
  AlgebraicCurve.Place.instAlgebra_restrictResidueField
  AlgebraicCurve.Place.instIsScalarTower_restrictResidueField
  AlgebraicCurve.instHasLocalResidue
  AlgebraicCurve.HasSeparableResidue.of_perfectField_of_isCurveOver
  AlgebraicCurve.HasSeparableResidue.of_perfectField
  AlgebraicCurve.Place.instIsLocalHom_restrictSubringHom
  AlgebraicCurve.instHasCanonicalLocalResidueKStar
  ModularCurve.KwNo6Pin.isLocalRing_completion
  SheafOfModules.isIso_ihomModelToIhom
  AlgebraicGeometry.OModulePresheaf.isScalarTower
  AlgebraicGeometry.Scheme.OrderedAffineCover.instLinearOrder
  AlgebraicGeometry.OModulePresheaf.module
  AlgebraicGeometry.Scheme.OrderedAffineCover.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCover.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.addCommGroup
  AlgebraicGeometry.Scheme.OrderedAffineCover.instDecidableEqIdx
  AlgebraicGeometry.OModulePresheaf.moduleSections
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx
  AlgebraicGeometry.OModulePresheaf.instSubsingletonObjZero
attribute [-instance]
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
  AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
  AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
  AlgebraicGeometry.OModulePresheaf.Leray.biC_module
  DoubleComplex.instModuleE₂I
  DoubleComplex.Bounded.modR
  DoubleComplex.instModuleE₂II
  DoubleComplex.instAddCommGroupE₂II
  DoubleComplex.Bounded.abGrp
  DoubleComplex.instAddCommGroupE₂I
  AlgebraicGeometry.ChowDatum.hι_closed
  AlgebraicGeometry.ChowDatumProj.hιN_closed
  AlgebraicGeometry.ChowDatumProj.hp_proper
  AlgebraicGeometry.ChowDatum.hp_isoU
  AlgebraicGeometry.ChowDatum.hp_proper
  AlgebraicGeometry.ProjSpace.algebraAway
  AlgebraicGeometry.ProjSpace.instIsProperProdOverπ
  AlgebraicGeometry.ChowDatumProj.hp_isoU
  AlgebraicGeometry.ProjSpace.isProper_π
  AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
  ProjSpaceCech.GradedModule.H.module
  ProjSpaceCech.GradedModule.H.addCommGroup
  ProjSpaceCech.GradedModule.sec.instAdd
  ProjSpaceCech.GradedModule.sec.instNeg
  ProjSpaceCech.GradedModule.acg
  ProjSpaceCech.GradedModule.Frac.setoid
  ProjSpaceCech.GradedModule.modR
  ProjSpaceCech.GradedModule.sec.instModule
  ProjSpaceCech.GradedModule.sec.instAddCommGroup
  ProjSpaceCech.GradedModule.sec.instZero
  ProjSpaceCech.GradedModule.Presentation.fJ
  ProjSpaceCech.GradedModule.sec.instSMul
  ProjSpaceCech.Twist.H.module
  ProjSpaceCech.Idx.instFintype
  ProjSpaceCech.Twist.H.addCommGroup
attribute [-instance]
  ProjSpaceCech.Idx.instDecidableEq
  ProjSpaceCech.Twist.Mon.instDecidableEq
  ProjSpaceCech.Twist.cochain.instAddCommGroup
  ProjSpaceCech.Twist.cochain.instModule
  AlgebraicGeometry.FGSubalgebra.tensorStage_directedSystem
  AlgebraicGeometry.RelEffCartierDiv.isClosedImmersion_subschemeι_resProdMap
  AlgebraicGeometry.RelEffCartierDiv.isOpenImmersion_resProdMap
  AlgebraicCurve.CurveModel.locallyOfFiniteType_gluedToBase
  AlgebraicCurve.CurveModel.isFractionRing_overlap
  AlgebraicCurve.CurveModel.isLocallyNoetherian_glued
  AlgebraicCurve.CurveModel.jacobsonSpace_glued
  AlgebraicCurve.CurveModel.isOpenImmersion_ι₀
  AlgebraicCurve.CurveModel.isIntegral_glued
  AlgebraicCurve.CurveModel.quasiSeparated_gluedToBase
  AlgebraicCurve.CurveModel.compactSpace_glued
  AlgebraicCurve.CurveModel.isIntegral_adjoin_chartRing
  AlgebraicCurve.CurveModel.isFractionRing_overlap_functionField
  AlgebraicCurve.CurveModel.isProper_gluedToBase
  AlgebraicCurve.CurveModel.isOpenImmersion_ιU
  AlgebraicCurve.CurveModel.isOpenImmersion_f₀
  AlgebraicCurve.CurveModel.isOpenImmersion_fInf
  AlgebraicCurve.CurveModel.isOpenImmersion_ιInf
  AlgebraicCurve.CurveModel.algebra_overlap_functionField
  AlgebraicCurve.CurveModel.quasiCompact_gluedToBase
  AlgebraicCurve.CurveModel.algebraAdjoin
  AlgebraicCurve.CurveModel.isDedekindDomain_chartRing
  AlgebraicCurve.CurveModel.isIntegralClosure
  AlgebraicCurve.CurveModel.finite_chartRing
  AlgebraicCurve.CurveModel.centre_isPrime
  AlgebraicCurve.CurveModel.isFractionRing_chartRing
  AlgebraicCurve.CurveModel.finiteType_chartRing
  AlgebraicCurve.CurveModel.isNoetherianRing_chartRing
  AlgebraicCurve.CurveModel.isScalarTower_base_adjoin
  AlgebraicCurve.CurveModel.isScalarTower_adjoin
  AlgebraicCurve.CurveModel.chartRing_finitePresentation
attribute [-simp]
  GoodReductionJacobian.RelativePic0Designation.mk.sizeOf_spec
  GoodReductionJacobian.AvatarSchemeBridge.mk.injEq
  GoodReductionJacobian.AvatarSchemeBridge.mk.sizeOf_spec
  GoodReductionJacobian.RelativePic0Designation.mk.injEq
  GoodReductionJacobian.schemeHomOverComp_coe
  NeronModelInfra.schemeHomOverEquivOverHom_apply
  GoodReductionJacobian.RelativeGroupLaw.mk.sizeOf_spec
  NeronModelInfra.schemeHomOverEquivOverHom_symm_apply
  NeronModelInfra.overHomToSchemeHomOver_coe
  GoodReductionJacobian.RelativeGroupLaw.mk.injEq
  NeronModelInfra.overHomToSchemeHomOver_schemeHomOverToOverHom
  NeronModelInfra.schemeHomOverToOverHom_left
  NeronModelInfra.schemeHomOverToOverHom_overHomToSchemeHomOver
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.mk.sizeOf_spec
  AlgebraicGeometry.RelPicard.RepresentsRelSubPic.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_snd
  AlgebraicGeometry.SmoothProperCurve.sectionBaseChange_coe_fst
  AlgebraicCurve.CurveModel.mk.injEq
  AlgebraicCurve.CurveModel.mk.sizeOf_spec
  AlgebraicCurve.Place.mk.injEq
  AlgebraicCurve.Divisor.degree_single
  AlgebraicCurve.Divisor.smul_single
  AlgebraicCurve.Place.smul_toValuationSubring
  AlgebraicCurve.Place.heightOneSpectrum_asIdeal
  AlgebraicCurve.Place.coe_algebraMap
  AlgebraicCurve.Place.ord_one
  AlgebraicCurve.Place.coe_smulRingEquiv_apply
  AlgebraicCurve.Pic0.coe_degZeroSMulHom
  AlgebraicCurve.Place.deg_smul
  AlgebraicCurve.Pic0.mk_zero
  AlgebraicCurve.Place.mk.sizeOf_spec
  AlgebraicCurve.Divisor.degree_smul
  AlgebraicCurve.Pic0.mk_add
  AlgebraicCurve.Place.ord_zero
  AlgebraicCurve.Place.ofHeightOneSpectrum_toValuationSubring
  AlgebraicCurve.mulAdele_apply
attribute [-simp]
  AlgebraicCurve.residuePairing_apply_coe
  AlgebraicCurve.mem_adeleBdd
  AlgebraicCurve.weilSmul_one
  AlgebraicCurve.diagonalHom_apply
  AlgebraicCurve.weilSmul_apply
  AlgebraicCurve.adeleSpaceMul_coe
  AlgebraicCurve.mulAdele_one
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U1
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.injEq
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.mk.sizeOf_spec
  AlgebraicGeometry.SmoothProperCurve.FiniteMapData.twoAffineOpenCover_U0
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.mk.injEq
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.pullback_U1
  AlgebraicGeometry.Scheme.TwoAffineOpenCover.pullback_U0
  TwoChartCech.Sections.mk.injEq
  TwoChartCech.Cover.mk.injEq
  TwoChartCech.GrothendieckComplex.mk.injEq
  TwoChartCech.Sections.mk.sizeOf_spec
  TwoChartCech.Cover.mk.sizeOf_spec
  TwoChartCech.Cover.lineBundle_r0_apply
  TwoChartCech.GrothendieckComplex.mk.sizeOf_spec
  TwoChartCech.Cover.lineBundle_r1_apply
  CoherentBaseChange.TwoTermComplex.mk.sizeOf_spec
  CoherentBaseChange.TwoTermComplex.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicCondition.onClasses_mk
  AlgebraicGeometry.RelPicard.relSubPicPresheaf_map_coe
  CategoryTheory.Functor.OverTotal.ofFibre_fst
  CategoryTheory.Functor.overTotal_map_fst
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_J
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYoneda_toGlued_uliftYonedaGluedToSheaf
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t'
attribute [-simp]
  uliftYoneda_toGlued_uliftYonedaGluedToSheaf_assoc
attribute [-simp]
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_toGlued
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_openCover_map
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.uliftYonedaGluedToSheaf_app_comp
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_V
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_t
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_U
  AlgebraicGeometry.Scheme.LocalRepresentabilityULift.glueData_f
attribute [-simp]
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_P
  AlgebraicGeometry.RelPicard.designationOfRepresentableBy_toBase
  AlgebraicGeometry.RelPicard.rigSection_snd
  AlgebraicGeometry.RelPicard.RigidifiedLineBundle.ofInvertible_L
  AlgebraicGeometry.RelPicard.rigSection_snd_assoc
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.injEq
  AlgebraicGeometry.RelPicard.SubPicGroupCondition.mk.sizeOf_spec
  GoodReductionJacobian.relativeGroupLawOfGrpObj_inv
  GoodReductionJacobian.relativeGroupLawOfGrpObj_mul
  GoodReductionJacobian.overHomEquivSchemeHomOver_apply_coe
  GoodReductionJacobian.relativeGroupLawOfGrpObj_one
  GoodReductionJacobian.overHomEquivSchemeHomOver_symm_apply_left
  PresheafOfModules.freeεIso_hom_app
  PresheafOfModules.freeμIso_hom_app
  AlgebraicCurve.coe_cechH0Equiv_apply
  AlgebraicCurve.cechH1ToH1_mk
  AlgebraicCurve.lSpaceOn_univ
  AlgebraicCurve.lSpaceOn_empty
  AlgebraicCurve.Place.congrEquiv_symm_apply
  AlgebraicCurve.RationalFunctionField.heightOneSpectrumOfIrreducible_asIdeal
  AlgebraicCurve.Place.congrRingEquiv_toValuationSubring
  AlgebraicCurve.Place.congrEquiv_apply
  AlgebraicCurve.Place.coe_comapSymmRingEquiv_apply
  AlgebraicCurve.RationalFunctionField.deg_placeOfPoint
  AlgebraicCurve.Divisor.mapRestrict_single
  AlgebraicCurve.Divisor.pushforward_single
  AlgebraicCurve.Place.coe_restrictInclusion
  AlgebraicCurve.Place.mem_fiber
  AlgebraicCurve.Place.restrict_toValuationSubring
  AlgebraicCurve.Divisor.degree_pushforward
  AlgebraicCurve.Place.restrictResidueMap_residue
  AlgebraicCurve.Pic0.coe_pushforwardDegZeroHom
  AlgebraicCurve.Pic0.coe_pullbackDegZeroHom
  AlgebraicCurve.Place.placeOfPrime_toValuationSubring
  AlgebraicCurve.Place.mem_fiberOver
  AlgebraicCurve.Place.fiberEquiv_symm_apply
  AlgebraicCurve.Place.fiberEquiv_apply
  AlgebraicCurve.Place.centerHeightOneSpectrum_asIdeal
attribute [-simp]
  AlgebraicCurve.Divisor.degree_pushforwardAlong
  AlgebraicCurve.Pic0.coe_degZeroCorrespondence
  AlgebraicCurve.Place.mem_fiberAlong
  AlgebraicCurve.SemilinearAut.toRingAut_inv
  AlgebraicCurve.SemilinearAut.smul_def
  AlgebraicCurve.SemilinearAut.smul_single
  AlgebraicCurve.SemilinearAut.smul_toValuationSubring
  AlgebraicCurve.SemilinearAut.baseAut_inv
  AlgebraicCurve.SemilinearAut.baseAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_ofAlgAut
  AlgebraicCurve.SemilinearAut.toRingAut_one
  AlgebraicCurve.SemilinearAut.deg_smul
  AlgebraicCurve.SemilinearAut.degree_smul
  AlgebraicCurve.SemilinearAut.coe_degZeroSMulHom
  AlgebraicCurve.SemilinearAut.baseAut_mul
  AlgebraicCurve.SemilinearAut.coe_smulValuationSubringEquiv_apply
  AlgebraicCurve.SemilinearAut.baseAut_one
  AlgebraicCurve.SemilinearAut.ofAlgAut_smul
  AlgebraicCurve.SemilinearAut.coe_torsion_smul
  AlgebraicCurve.SemilinearAut.toRingAut_mul
attribute [-simp]
  AlgebraicCurve.RationalFunctionField.placeInfty_toValuationSubring
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeInfty
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_some
  AlgebraicCurve.RationalFunctionField.placeEquivOption_placeOfPoint
  AlgebraicCurve.RationalFunctionField.placeEquivOption_symm_none
  AlgebraicCurve.Divisor.evalFun_zero
  AlgebraicCurve.Place.evalAt_one
  AlgebraicCurve.Place.differentialCoeff_zero
  AlgebraicCurve.Place.differentialCoeff_dCoord
  AlgebraicCurve.TranscendenceTower.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.injEq
  AlgebraicCurve.TranscendenceTower.mk.injEq
  AlgebraicCurve.PoleDivisorPackage.mk.sizeOf_spec
  AlgebraicCurve.IntegralBasisInLSpace.mk.sizeOf_spec
  AlgebraicCurve.PoleDivisorPackage.mk.injEq
  AlgebraicGeometry.RelPicard.thetaBundle_def
attribute [-simp]
  AlgebraicGeometry.RelPicard.picardBundle_def
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_ofRelEffDivisor
  AlgebraicGeometry.RelEffCartierDiv.toRelEffDivisor_I
  AlgebraicGeometry.mapOnProdOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.mk.sizeOf_spec
  AlgebraicGeometry.RelEffCartierDiv.mk.injEq
  AlgebraicGeometry.mapOnProdOver_snd
  AlgebraicGeometry.mapOnProdOver_fst
  AlgebraicGeometry.mapOnProdOver_snd_assoc
  AlgebraicGeometry.mapOnProdOver_id
  AlgebraicCurve.RelEffDivisor.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_fst
  AlgebraicCurve.mapOnProd_fst_assoc
  AlgebraicCurve.mapOnProd_snd
  AlgebraicCurve.UnivDivisorPack.mk.injEq
  AlgebraicCurve.RelEffDivisor.mk.injEq
  AlgebraicCurve.UnivDivisorPack.mk.sizeOf_spec
  AlgebraicCurve.mapOnProd_snd_assoc
  AlgebraicGeometry.Scheme.Modules.exteriorPower_obj
  PresheafOfModules.exteriorPower_map_ιMulti
  PresheafOfModules.ExteriorPower.appₗ_apply
  AlgebraicGeometry.prodKerGraph_one
  AlgebraicGeometry.fibrePowOver.proj_comp
  AlgebraicGeometry.prodKerGraph_zero
  AlgebraicGeometry.RelEffCartierDiv.empty_I
  AlgebraicGeometry.fibrePowOver.proj_comp_assoc
  AlgebraicGeometry.graphOver_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp
  AlgebraicGeometry.RelEffCartierDiv.toPoint_comp_assoc
  AlgebraicGeometry.graphOver_fst
  AlgebraicGeometry.RelEffCartierDiv.ofPoint_I
  AlgebraicGeometry.graphOver_snd
  AlgebraicGeometry.graphOver_snd_assoc
  AlgebraicCurve.SymmetricPowerPackage.mk.sizeOf_spec
  AlgebraicCurve.SymmetricPowerPackage.mk.injEq
  AlgebraicGeometry.FGSubalgebra.cocone_ι_app_apply
  AlgebraicGeometry.RelPicard.fst_toProdSpec
  AlgebraicGeometry.RelPicard.toProdSpec_fst_assoc
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_cons
  AlgebraicGeometry.RelPicard.pointsSubBasepointModule_nil
attribute [-simp]
  AlgebraicGeometry.RelPicard.fst_toProdSpec_assoc
  AlgebraicGeometry.RelPicard.toProdSpec_fst
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.sub_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sresTop
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.add_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.IdealSheafData.coe_resLE
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.smul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_ofLE_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.ideal_range
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zero_app
  AlgebraicGeometry.Scheme.IdealSheafData.sres_sres
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.comp_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.neg_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.id_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.coe_mulRight_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.nsmul_app
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.mk.injEq
  AlgebraicGeometry.Scheme.IdealSheafData.IdealHom.zsmul_app
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.sizeOf_spec
  AlgebraicCurve.Place.CanonicalLocalResidueDataK.mk.injEq
  AlgebraicCurve.adeleSingle_coe
  AlgebraicCurve.kaehlerResidueTermKFam_apply
  AlgebraicCurve.Place.LocalResidueData.mk.injEq
  AlgebraicCurve.Place.LocalResidueData.mk.sizeOf_spec
  AlgebraicCurve.Place.kw_ffgc_adicCompletionComapIntegers_coe
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.sizeOf_spec
  AlgebraicCurve.Place.mem_simplePoleSubmodule
  AlgebraicCurve.Place.coe_uniformizerSubring
  ModularCurve.Lg37.Lg37CompletionSection.mk.injEq
  AlgebraicCurve.Place.CoefficientFieldSection.mk.injEq
  AlgebraicCurve.Place.CanonicalLocalResidueDataS.mk.injEq
  ModularCurve.Lg37.Lg37CompletionSection.mk.sizeOf_spec
  AlgebraicCurve.Place.CoefficientFieldSection.mk.sizeOf_spec
  AlgebraicCurve.Place.poleSubmodule_one
  AlgebraicCurve.Place.mem_poleSubmodule
  AlgebraicGeometry.Scheme.Modules.toUnitSection_ofUnitSection
  AlgebraicGeometry.Scheme.Modules.pullbackSection_def
  AlgebraicGeometry.Scheme.Modules.ofUnitSection_toUnitSection
  PresheafOfModules.InternalHom.IsSheafAux.appAt_toPresheafHom
attribute [-simp]
  SheafOfModules.ihomSectionsEquivFamily_unit
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_apply
  SheafOfModules.ihomEval_unit_app
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_right
  AlgebraicGeometry.Scheme.Modules.ihomEval_zero_left
  AlgebraicGeometry.Scheme.Modules.homOfFamily_app_apply
  SheafOfModules.unit_ihomSectionsEquivFamily
  AlgebraicGeometry.Scheme.Modules.familyOfHom_app
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_hom_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictUnitIso_inv_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomOfFamily_app_apply
  AlgebraicGeometry.Scheme.Modules.restrictHomEquivFamily_symm_apply
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_right
  AlgebraicGeometry.Scheme.Modules.map_unitSection
  AlgebraicGeometry.Scheme.Modules.tensorSectionsBilin_apply
  AlgebraicGeometry.Scheme.Modules.tensorPowSection_zero
  AlgebraicGeometry.Scheme.Modules.tensorSections_zero_left
  AlgebraicGeometry.Scheme.Modules.tensorPow_zero
  AlgebraicGeometry.Scheme.Modules.tensorPow_succ
  AlgebraicGeometry.Scheme.OrderedAffineCover.mk.injEq
  AlgebraicGeometry.OModulePresheaf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCover.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.mk.injEq
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_neg
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_zero
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_sub
  AlgebraicGeometry.Scheme.Modules.pullbackLocalSection_add
  AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
  AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U
  AlgebraicGeometry.OModulePresheaf.Hom.mk.injEq
  AlgebraicGeometry.OModulePresheaf.Hom.id_app
  AlgebraicGeometry.OModulePresheaf.AffHom.appSections_apply
  AlgebraicGeometry.OModulePresheaf.AffHom.comp_app
  AlgebraicGeometry.OModulePresheaf.AffSES.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.AffHom.kerMap_coe
  AlgebraicGeometry.OModulePresheaf.AffHom.id_app
  AlgebraicGeometry.OModulePresheaf.Hom.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.Hom.toAffHom_app
attribute [-simp]
  AlgebraicGeometry.OModulePresheaf.SES.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.AffHom.mk.sizeOf_spec
  AlgebraicGeometry.OModulePresheaf.Hom.comp_app
  AlgebraicGeometry.OModulePresheaf.SES.mk.injEq
  AlgebraicGeometry.OModulePresheaf.AffHom.mk.injEq
  AlgebraicGeometry.OModulePresheaf.Hom.appSections_apply
  AlgebraicGeometry.OModulePresheaf.AffSES.mk.injEq
  AlgebraicGeometry.OModulePresheaf.prod_obj
  AlgebraicGeometry.OModulePresheaf.restrOpen_obj
  AlgebraicGeometry.OModulePresheaf.DevissageStep.mk.injEq
  AlgebraicGeometry.OModulePresheaf.pushforward_obj
  AlgebraicGeometry.OModulePresheaf.im_obj
  AlgebraicGeometry.OModulePresheaf.pow_obj
  AlgebraicGeometry.OModulePresheaf.fstHom_app
  AlgebraicGeometry.OModulePresheaf.ker_obj
  AlgebraicGeometry.OModulePresheaf.coker_obj
  AlgebraicGeometry.OModulePresheaf.DevissageStep.mk.sizeOf_spec
  AlgebraicGeometry.Scheme.OrderedAffineCover.preimage_U
  AlgebraicGeometry.OModulePresheaf.sndHom_app
  AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
  DoubleComplex.Bounded.mk.injEq
  DoubleComplex.Bounded.mk.sizeOf_spec
  DoubleComplex.Convergence.mk.injEq
  DoubleComplex.Convergence.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.sizeOf_spec
  DoubleComplex.SubQuot.mk.injEq
  AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
  AlgebraicGeometry.ChowDatumProj.mk.injEq
  AlgebraicGeometry.ChowDatum.mk.injEq
  ProjSpaceCech.GradedModule.mk.injEq
  ProjSpaceCech.GradedModule.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Presentation.mk.injEq
  ProjSpaceCech.GradedModule.Frac.mk.injEq
  ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.shift_toLinearMap
  ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
  ProjSpaceCech.GradedModule.Hom.mk.injEq
  TwoChartCech.Mumford.dK_apply
attribute [-simp]
  TwoChartCech.Mumford.ι0_apply
  TwoChartCech.Mumford.ι1_apply
  TwoChartCech.KerCoprod.dK_apply
  TwoChartCech.KerCoprod.ι1_apply
  TwoChartCech.KerCoprod.ι0_apply
  AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
  AlgebraicGeometry.RelPicard.algEquivZeroGroupCut_toSubPicCondition
  AlgebraicGeometry.RelPicard.LFP.stageHom_val
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_hom_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.relSubPicPresheafRestrictIso_inv_app_coe
  AlgebraicGeometry.RelPicard.BaseChange.restrict_P
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp
  AlgebraicGeometry.RelEffCartierDiv.functor_map_fst
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_pullbackAlong
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.homEquiv_symm_apply
  AlgebraicGeometry.RelEffCartierDiv.IsUniversal.lift_comp_assoc
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top
  AlgebraicGeometry.RelEffCartierDiv.mem_supportedIn_iff
  AlgebraicGeometry.RelEffCartierDiv.supportedIn_top_eq
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_extendAlong
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_I
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd
  AlgebraicGeometry.RelEffCartierDiv.restrictAlong_I
  AlgebraicGeometry.RelEffCartierDiv.extendAlong_restrictAlong
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_snd_assoc
  AlgebraicGeometry.RelEffCartierDiv.resProdMap_fst
  CoherentBaseChange.FibreH0Family.mk.sizeOf_spec
  CoherentBaseChange.FibreH0Family.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.injEq
  AlgebraicGeometry.Scheme.Modules.ProjPresentation.mk.sizeOf_spec
  AlgebraicCurve.CurveModel.coe_gInf
  AlgebraicCurve.CurveModel.coe_tInvChart
  AlgebraicCurve.CurveModel.ιInf_gluedToBase_assoc
  AlgebraicCurve.CurveModel.ιInf_gluedToBase
  AlgebraicCurve.CurveModel.primeOfι₀_asIdeal
  AlgebraicCurve.CurveModel.coe_tChart
  AlgebraicCurve.CurveModel.ι₀_gluedToBase_assoc
  AlgebraicCurve.CurveModel.primeOfιInf_asIdeal
attribute [-simp]
  AlgebraicCurve.CurveModel.ι₀_gluedToBase
  AlgebraicCurve.CurveModel.coe_tma
  AlgebraicCurve.CurveModel.coe_primeEquivChartPlaces
universe u
open _root_.CategoryTheory
open _root_.CategoryTheory.Limits
open _root_.CategoryTheory.MonoidalCategory
open _root_.AlgebraicGeometry
open _root_.CategoryTheory.CartesianMonoidalCategory
with_weak_namespace _root_.AlgebraicGeometry.Scheme.Modules