`BookProof.ChapterA3m.swap23_kronecker` (A B C : Matrix (Fin 4) (Fin 4) ℂ) : swap23 * ((A ⊗ₖ B) ⊗ₖ C) = ((A ⊗ₖ C) ⊗ₖ B) * swap23

Proved

BookProof.ChapterA3m.swap23_kronecker

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA3m.

BookProof.ChapterA3m.swap23_kronecker (A B C : Matrix (Fin 4) (Fin 4) ℂ) : swap23 * ((A ⊗ₖ B) ⊗ₖ C) = ((A ⊗ₖ C) ⊗ₖ B) * swap23

Formalization note: Lean 4 identifier BookProof.ChapterA3m.swap23_kronecker.

Preamble

-- Generated from ChapterA3m.lean — theorem BookProof.ChapterA3m.swap23_kronecker
import Definitions.Def_ChapterA3
import Definitions.Def_ChapterA3j
import Definitions.Def_ChapterA3k
import Definitions.Def_ChapterA3l
import Mathlib
import Definitions.Def_ChapterA3m
open BookProof.ChapterA3m


open Matrix
open scoped Kronecker


open BookProof.ChapterA3 BookProof.ChapterA3j BookProof.ChapterA3k BookProof.ChapterA3l

Formal statement

theorem BookProof.ChapterA3m.swap23_kronecker (A B C : Matrix (Fin 4) (Fin 4) ℂ) :
    swap23 * ((A ⊗ₖ B) ⊗ₖ C) = ((A ⊗ₖ C) ⊗ₖ B) * swap23 := by sorry

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