Mazur 13 port: nonZeroDivisors_le_comap

Proved

MazurProof.SexticMumford.OrientedBaseChange.nonZeroDivisors_le_comap

by xuanji · Oct 9, 2026 · Mathlib 0df444a (Lean v4.33.1)

huang-flt-portmazur-full-torsionmazur-n13-portorder13

A nonzero element of the source coordinate ring stays nonzero after coefficient extension.

This lemma is one step of a machine-checked proof that the genus-two curve

Y^2 = X^6+4X^5+6X^4+2X^3+X^2+2X+1

(a model of $X_1(13)$ ) has no rational affine points other than the cusps $X\in\{0,-1\}$ , which gives the case $N=13$ of Mazur's torsion theorem. The proof is Xiang Huang's Lean development, ported to this Mathlib and split into one node per large lemma; definitions live in the layered entries MazurN13_L0, MazurN13_L1, ….

Preamble

import Mathlib
import Definitions.Def_MazurN13_L1

set_option backward.isDefEq.respectTransparency false
set_option backward.isDefEq.respectTransparency.types false
open MazurProof MazurProof.SexticMumford MazurProof.SexticMumford.OrientedBaseChange
open Polynomial
open scoped nonZeroDivisors
universe u v
variable {K : Type u} {K' : Type v}
variable [Field K] [Field K']
variable {M : Model K} {M' : Model K'}

Formal statement

theorem MazurProof.SexticMumford.OrientedBaseChange.nonZeroDivisors_le_comap (ι : K →+* K') (hι : Function.Injective ι) (hM : M.f.map ι = M'.f) : (CoordinateRing M)⁰ ≤ Submonoid.comap (coordinateMap ι hM) (CoordinateRing M')⁰ := by sorry

Source

Xiang Huang, FLT fork, https://github.com/xiangyazi24/FLT/blob/51bbb4f/FLT/Assumptions/MazurProof/SexticMumfordOrientedBaseChange.lean#L121

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