`BookProof.ChapterA3.toC_conj` (M : Matrix (Fin 4) (Fin 4) ℝ) : (toC M).map (starRingEnd ℂ) = toC M

Proved

BookProof.ChapterA3.toC_conj

by leonardopedro · Oct 6, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA3b.

BookProof.ChapterA3.toC_conj (M : Matrix (Fin 4) (Fin 4) ℝ) : (toC M).map (starRingEnd ℂ) = toC M

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

Preamble

-- Generated from ChapterA3b.lean — theorem BookProof.ChapterA3.toC_conj
import Mathlib
import Definitions.Def_ChapterA3b
import Definitions.Def_ChapterA3
open BookProof.ChapterA3


open Matrix
open scoped ComplexConjugate

Formal statement

theorem BookProof.ChapterA3.toC_conj (M : Matrix (Fin 4) (Fin 4) ℝ) :
    (toC M).map (starRingEnd ℂ) = toC M := by sorry

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