Module

Place_evalAt_ne_zero.lean

Nyll.AlgebraicCurves.Places.Place_evalAt_ne_zero
1 declaration indexed from sourceView source ↗

Place evalAt ne zero

A nonzero function of order zero has nonzero evaluation at a rational place.

Declarations

AlgebraicCurve.Place.evalAt_ne_zero
Source context 3 commands

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

section ProofImplementation
namespace AlgebraicCurves.Places.Proofs.Place_evalAt_ne_zero
open IsLocalRing AlgebraicCurve
theorem _root_.AlgebraicCurve.Place.evalAt_ne_zero {K F : Type*} [Field K] [Field F]
  [Algebra K F] (v : Place K F) (hv : v.IsRational) {f : F} (hf : f ≠ 0) (h : v.ord f = 0) :
  v.evalAt f ≠ 0