Module

Place_ord_eq_zero_of_isAlgebraic.lean

Nyll.AlgebraicCurves.Places.Place_ord_eq_zero_of_isAlgebraic
3 declarations indexed from sourceView source ↗

Place ord eq zero of is Algebraic

Declarations

AlgebraicCurves.Places.Proofs.Place_ord_eq_zero_of_isAlgebraic.AlgebraicCurve.Place.FF2R0.mem_of_isAlgebraic
Source context 12 commands

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

section ProofImplementation
namespace AlgebraicCurves.Places.Proofs.Place_ord_eq_zero_of_isAlgebraic
noncomputable section
open Polynomial
namespace AlgebraicCurve
open _root_.AlgebraicCurve
namespace Place
open _root_.AlgebraicCurve.Place
namespace FF2R0
open _root_.AlgebraicCurve.Place
open _root_.AlgebraicCurve
variable {K F : Type*} [Field K] [Field F] [Algebra K F] (v : AlgebraicCurve.Place K F)
theorem mem_of_isAlgebraic {x : F} (hx : IsAlgebraic K x) : x ∈ v.toValuationSubring
AlgebraicCurves.Places.Proofs.Place_ord_eq_zero_of_isAlgebraic.AlgebraicCurve.Place.FF2R0.ord_eq_zero_of_isAlgebraic'
Source context 12 commands

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

section ProofImplementation
namespace AlgebraicCurves.Places.Proofs.Place_ord_eq_zero_of_isAlgebraic
noncomputable section
open Polynomial
namespace AlgebraicCurve
open _root_.AlgebraicCurve
namespace Place
open _root_.AlgebraicCurve.Place
namespace FF2R0
open _root_.AlgebraicCurve.Place
open _root_.AlgebraicCurve
variable {K F : Type*} [Field K] [Field F] [Algebra K F] (v : AlgebraicCurve.Place K F)
theorem ord_eq_zero_of_isAlgebraic' {x : F} (hx : IsAlgebraic K x) : v.ord x = 0
AlgebraicCurve.Place.ord_eq_zero_of_isAlgebraic
Source context 4 commands

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

section ProofImplementation
namespace AlgebraicCurves.Places.Proofs.Place_ord_eq_zero_of_isAlgebraic
noncomputable section
open Polynomial
theorem _root_.AlgebraicCurve.Place.ord_eq_zero_of_isAlgebraic {K F : Type*} [Field K] [Field F]
  [Algebra K F] (v : AlgebraicCurve.Place K F) {x : F} (hx : IsAlgebraic K x) :
    v.ord x = 0