`BookProof.ChapterA3.Treal_mul` (A B : Matrix (Fin 2) (Fin 2) ℂ) : Treal (A * B) = Treal A * Treal B

Proved

BookProof.ChapterA3.Treal_mul

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA3i.

BookProof.ChapterA3.Treal_mul (A B : Matrix (Fin 2) (Fin 2) ℂ) : Treal (A * B) = Treal A * Treal B

Formalization note: Lean 4 identifier BookProof.ChapterA3.Treal_mul.

Preamble

-- Generated from ChapterA3i.lean — theorem BookProof.ChapterA3.Treal_mul
import Mathlib
import Definitions.Def_ChapterA3i
import Definitions.Def_ChapterA3
open BookProof.ChapterA3


open Matrix
open scoped ComplexConjugate

Formal statement

theorem BookProof.ChapterA3.Treal_mul (A B : Matrix (Fin 2) (Fin 2) ℂ) :
    Treal (A * B) = Treal A * Treal B := by sorry

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