`BookProof.ChapterA3.upsilonC_real` (T : Matrix (Fin 2) (Fin 2) ℂ) (μ ν : Fin 4) : conj (UpsilonC T μ ν) = UpsilonC T μ ν

Proved

BookProof.ChapterA3.upsilonC_real

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA3h.

BookProof.ChapterA3.upsilonC_real (T : Matrix (Fin 2) (Fin 2) ℂ) (μ ν : Fin 4) : conj (UpsilonC T μ ν) = UpsilonC T μ ν

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

Preamble

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


open Matrix
open scoped ComplexConjugate

Formal statement

theorem BookProof.ChapterA3.upsilonC_real (T : Matrix (Fin 2) (Fin 2) ℂ) (μ ν : Fin 4) :
    conj (UpsilonC T μ ν) = UpsilonC T μ ν := by sorry

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