`BookProof.ChapterCPTHamiltonian.castMat_conjTranspose` (M : Matrix (Fin 4) (Fin 4) ℤ) : ((Int.castRingHom ℂ).mapMatrix M)ᴴ = (Int.castRingHom ℂ).mapMatrix Mᵀ

Proved

BookProof.ChapterCPTHamiltonian.castMat_conjTranspose

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterCPTHamiltonian.

BookProof.ChapterCPTHamiltonian.castMat_conjTranspose (M : Matrix (Fin 4) (Fin 4) ℤ) : ((Int.castRingHom ℂ).mapMatrix M)ᴴ = (Int.castRingHom ℂ).mapMatrix Mᵀ

Formalization note: Lean 4 identifier BookProof.ChapterCPTHamiltonian.castMat_conjTranspose.

Preamble

-- Generated from ChapterCPTHamiltonian.lean — theorem BookProof.ChapterCPTHamiltonian.castMat_conjTranspose
import Definitions.Def_ChapterA3
import Mathlib
import Definitions.Def_ChapterCPTHamiltonian
open BookProof.ChapterCPTHamiltonian


open Matrix


open BookProof.ChapterA3

Formal statement

theorem BookProof.ChapterCPTHamiltonian.castMat_conjTranspose (M : Matrix (Fin 4) (Fin 4) ℤ) :
    ((Int.castRingHom ℂ).mapMatrix M)ᴴ = (Int.castRingHom ℂ).mapMatrix Mᵀ := by sorry

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