Mazur.lean`

Explanation legend Lean4 Domain Explanation Language (L4DEL)

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L4DEL: Lean4 Domain Explanation Language

Annotation provenance. This overlay contains 8 curated AI-written annotations and 1204 mechanical source-derived annotations. They have not been human-reviewed as explanations; treat them as unverified and not mathematical authority. Retained generation history: The 71 original curated annotations were produced in a Claude Sonnet 5.5 session at medium effort; Claude Opus 5.5 is recorded in that session as the advisor model, not the direct author. The bulk source-derived expansion was generated mechanically from pinned source comments by tooling developed in a GPT-5.6 Sol session at ultra reasoning; GPT-5.6 Sol did not originate the quoted source prose. On 2026-10-17 the mechanically generated source-comment annotations of the Formal Conjectures, Carleson, FLT, PFR, CompFiles, Mathematics in Lean and Theorem Proving in Lean overlays were regenerated by the same generator after three corrections made in a Claude Sonnet 5.5 session: titles no longer cut a sentence inside mathematics or end on a dangling word, workflow markers are removed from the quoted prose, and declaration names follow the scanner's namespace resolution. The boilerplate step line was dropped, and comments that were only a row of dashes no longer yield annotations. No new prose was written and no human review is claimed.

Credit: The upstream authors and contributors retain credit for the project and mathematics. lean4-explainer only renders their pinned source and adds the separately disclosed explanation layer.

Project sources: Pinned project documentation, Pinned FLT blueprint introduction

1 declarations, 0 contain sorry, 0 declared as axioms

Irreducibility of the p-torsion of the Frey curve

A deep result of Mazur implies that the Frey curve is irreducible.

Imports (7)

Imported by 2 files

theorem FreyPackage.mazur Mazur step: the p-torsion of the Frey curve is irreducible (assumed) line 30 source
Source documentation
The p-torsion in the Frey curve associated to a counterexample to FLT is irreducible.
L4DEL explanation
The statement is that the Galois representation on the p-torsion of the Frey curve is irreducible, a consequence of Mazur's work as used in Serre's 1987 Duke paper.
1. The proof is the project tactic knownin1980s, which behaves like sorry; it is not a formal proof of the claim.
2. The project's own policy (module doc of the tactic) allows it only for results the maintainers believe are provable on paper from literature known before 1990.
Prerequisites: FreyPackage, FreyPackage.freyCurve
See also: FLT.Bosses.B4_implies_B3
Sources and attribution: Pinned Lean source (f6c6a2fe9796)
depends on sorry what this means
Statement uses: FreyPackage, WeierstrassCurve, Rat, FreyPackage.freyCurve, Nat, FreyPackage.p, Fact, Nat.Prime, Fact.mk, FreyPackage.pp, GaloisRep.IsIrreducible, WeierstrassCurve.nTorsion, AlgebraicClosure, WeierstrassCurve.map, Algebra.algebraMap, Int, WeierstrassCurve.Affine.Point, WeierstrassCurve.Affine.baseChange, Submodule.torsionBy, ZMod and 2 more
Proof uses: knownin1980s
48 instances, coercions and auxiliary constants left out.

knownin1980s: a project tactic that closes any goal like sorry, reserved for results believed to follow from literature known before 1990

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem FreyPackage.mazur (P : FreyPackage) :
    let E := P.freyCurve
…
```
Mentions: FreyPackage