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`BookProof.ChapterA3.upsilonC_antihom` (T U : Matrix (Fin 2) (Fin 2) ℂ) : UpsilonC (T * U) = UpsilonC U * UpsilonC T

Proved
BookProof.ChapterA3.upsilonC_antihom

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA3h.

BookProof.ChapterA3.upsilonC_antihom (T U : Matrix (Fin 2) (Fin 2) ℂ) : UpsilonC (T * U) = UpsilonC U * UpsilonC T

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

Preamble
-- Generated from ChapterA3h.lean — theorem BookProof.ChapterA3.upsilonC_antihom
import Mathlib
import Definitions.Def_ChapterA3h
import Definitions.Def_ChapterA3
open BookProof.ChapterA3


open Matrix
open scoped ComplexConjugate
Formal statement
theorem BookProof.ChapterA3.upsilonC_antihom (T U : Matrix (Fin 2) (Fin 2) ℂ) :
    UpsilonC (T * U) = UpsilonC U * UpsilonC T := by sorry

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