`BookProof.ChapterA3m.swap12_kronecker` (A B C : Matrix (Fin 4) (Fin 4) ℂ) : swap12 * ((A ⊗ₖ B) ⊗ₖ C) = ((B ⊗ₖ A) ⊗ₖ C) * swap12

Proved

BookProof.ChapterA3m.swap12_kronecker

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA3m.

BookProof.ChapterA3m.swap12_kronecker (A B C : Matrix (Fin 4) (Fin 4) ℂ) : swap12 * ((A ⊗ₖ B) ⊗ₖ C) = ((B ⊗ₖ A) ⊗ₖ C) * swap12

Formalization note: Lean 4 identifier BookProof.ChapterA3m.swap12_kronecker.

Preamble

-- Generated from ChapterA3m.lean — theorem BookProof.ChapterA3m.swap12_kronecker
import Definitions.Def_ChapterA3
import Definitions.Def_ChapterA3j
import Mathlib
import Definitions.Def_ChapterA3m
import Definitions.Def_ChapterA3k
import Definitions.Def_ChapterA3l
open BookProof.ChapterA3k
open BookProof.ChapterA3l
open BookProof.ChapterA3m


open Matrix
open scoped Kronecker


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

Formal statement

theorem BookProof.ChapterA3m.swap12_kronecker (A B C : Matrix (Fin 4) (Fin 4) ℂ) :
    swap12 * ((A ⊗ₖ B) ⊗ₖ C) = ((B ⊗ₖ A) ⊗ₖ C) * swap12 := by sorry

View graph