`BookProof.ChapterA3.upsilon_re` (T : Matrix (Fin 2) (Fin 2) ℂ) (μ ν : Fin 4) : ((Upsilon T μ ν : ℝ) : ℂ) = UpsilonC T μ ν

Proved

BookProof.ChapterA3.upsilon_re

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA4c.

BookProof.ChapterA3.upsilon_re (T : Matrix (Fin 2) (Fin 2) ℂ) (μ ν : Fin 4) : ((Upsilon T μ ν : ℝ) : ℂ) = UpsilonC T μ ν

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

Preamble

-- Generated from ChapterA4c.lean — theorem BookProof.ChapterA3.upsilon_re
import Mathlib
import Definitions.Def_ChapterA4c
import Definitions.Def_ChapterA3
import Definitions.Def_ChapterA3h
open BookProof.ChapterA3


open Matrix
open scoped ComplexConjugate

Formal statement

theorem BookProof.ChapterA3.upsilon_re (T : Matrix (Fin 2) (Fin 2) ℂ) (μ ν : Fin 4) :
    ((Upsilon T μ ν : ℝ) : ℂ) = UpsilonC T μ ν := by sorry

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