Mazur 13 port: principal_is_constant

Proved

MazurProof.N13SmallMumfordRigidity.principal_is_constant

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

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

Supporting lemma principal_is_constant (namespace MazurProof.N13SmallMumfordRigidity).

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_L2

set_option backward.isDefEq.respectTransparency false
set_option backward.isDefEq.respectTransparency.types false
open MazurProof
open Polynomial
open scoped LaurentSeries nonZeroDivisors
universe u
variable (K : Type u) [Field K] [CharZero K]
open SexticMumford

Formal statement

theorem MazurProof.N13SmallMumfordRigidity.principal_is_constant (D₁ D₂ : Mumford (N13Mumford.model K)) (α : (N13Mumford.FunctionField K)ˣ) (hIdeal : mumfordIdealUnit (N13Mumford.model K) D₁.toSemi * toPrincipalIdeal (N13Mumford.CoordinateRing K) (N13Mumford.FunctionField K) α = mumfordIdealUnit (N13Mumford.model K) D₂.toSemi) (hInf : Multiplicative.ofAdd ((D₁.nInf : ℤ) - 1) * (N13Infinity.positiveInfinityOrder K).ordPlus α = Multiplicative.ofAdd ((D₂.nInf : ℤ) - 1)) : ∃ c : Kˣ, α = N13Infinity.functionConstUnit K c := by sorry

Source

Xiang Huang, FLT fork, https://github.com/xiangyazi24/FLT/blob/51bbb4f/FLT/Assumptions/MazurProof/N13SmallMumfordRigidity.lean#L129

View graph