Mazur 13 port: goodYbar_relation

Proved

MazurProof.N13ReciprocalInfinityContraction.goodYbar_relation

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

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

Supporting lemma goodYbar_relation (namespace MazurProof.N13ReciprocalInfinityContraction).

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

open MazurProof MazurProof.N13ReciprocalInfinityContraction
open Polynomial
open Module
open scoped nonZeroDivisors TensorProduct
attribute [local instance] MazurProof.N13ReciprocalInfinityContraction.instFactPrimeOfNatNat_fLT

Formal statement

theorem MazurProof.N13ReciprocalInfinityContraction.goodYbar_relation (D : SexticMumford.Mumford Model) : goodYbar D ^ 2 + (xbar D ^ 3 + xbar D + 1) * goodYbar D = xbar D ^ 5 + xbar D ^ 4 := by sorry

Source

Xiang Huang, FLT fork, https://github.com/xiangyazi24/FLT/blob/51bbb4f/FLT/Assumptions/MazurProof/N13ReciprocalInfinityContraction.lean#L209

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