`BookProof.ChapterA3n.permMat_braiding` {N : ℕ} (σ : Equiv.Perm (Fin N)) (M : Fin N → Matrix (Fin 4) (Fin 4) ℂ) : permMat σ * tensorPow M = tensorPow (fun j => M (σ⁻¹ j)) * permMat

Proved

BookProof.ChapterA3n.permMat_braiding

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA3n.

BookProof.ChapterA3n.permMat_braiding {N : ℕ} (σ : Equiv.Perm (Fin N)) (M : Fin N → Matrix (Fin 4) (Fin 4) ℂ) : permMat σ * tensorPow M = tensorPow (fun j => M (σ⁻¹ j)) * permMat σ

Formalization note: Lean 4 identifier BookProof.ChapterA3n.permMat_braiding.

Preamble

-- Generated from ChapterA3n.lean — theorem BookProof.ChapterA3n.permMat_braiding
import Definitions.Def_ChapterA3
import Definitions.Def_ChapterA3j
import Mathlib
import Definitions.Def_ChapterA3n
open BookProof.ChapterA3n


open Matrix
open scoped BigOperators


open BookProof.ChapterA3 BookProof.ChapterA3j

Formal statement

theorem BookProof.ChapterA3n.permMat_braiding {N : ℕ} (σ : Equiv.Perm (Fin N))
    (M : Fin N → Matrix (Fin 4) (Fin 4) ℂ) :
    permMat σ * tensorPow M = tensorPow (fun j => M (σ⁻¹ j)) * permMat σ := by sorry

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