`BookProof.ChapterA3u.invariant_sameCycle` {N : ℕ} {σ : Equiv.Perm (Fin N)} {a : Idx N} (ha : a ∘ σ = a) {x y : Fin N} (h : σ.SameCycle x y) : a x = a y

Proved

BookProof.ChapterA3u.invariant_sameCycle

by leonardopedro · Oct 7, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA3u.

BookProof.ChapterA3u.invariant_sameCycle {N : ℕ} {σ : Equiv.Perm (Fin N)} {a : Idx N} (ha : a ∘ σ = a) {x y : Fin N} (h : σ.SameCycle x y) : a x = a y

Formalization note: Lean 4 identifier BookProof.ChapterA3u.invariant_sameCycle.

Preamble

-- Generated from ChapterA3u.lean — theorem BookProof.ChapterA3u.invariant_sameCycle
import Definitions.Def_ChapterA3o
import Definitions.Def_ChapterA3q
import Definitions.Def_ChapterA3r
import Mathlib
import Definitions.Def_ChapterA3u
import Definitions.Def_ChapterA3n
open BookProof.ChapterA3n
open BookProof.ChapterA3u


open Matrix
open scoped BigOperators


open BookProof.ChapterA3n BookProof.ChapterA3o BookProof.ChapterA3q
open BookProof.ChapterA3r

Formal statement

theorem BookProof.ChapterA3u.invariant_sameCycle {N : ℕ} {σ : Equiv.Perm (Fin N)} {a : Idx N}
    (ha : a ∘ σ = a) {x y : Fin N} (h : σ.SameCycle x y) : a x = a y := by sorry

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