Prove2Me

`BookProof.ChapterA3.upsilonC_nullCol` (T : Matrix (Fin 2) (Fin 2) ℂ) (μ : Fin 4) : UpsilonC T μ 0 + UpsilonC T μ 3 = pauliCoeff (Tᴴ * (pauliσ 0 + pauliσ 3) * T) μ

Proved
BookProof.ChapterA3.upsilonC_nullCol

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA4d.

BookProof.ChapterA3.upsilonC_nullCol (T : Matrix (Fin 2) (Fin 2) ℂ) (μ : Fin 4) : UpsilonC T μ 0 + UpsilonC T μ 3 = pauliCoeff (Tᴴ * (pauliσ 0 + pauliσ 3) * T) μ

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

Preamble
-- Generated from ChapterA4d.lean — theorem BookProof.ChapterA3.upsilonC_nullCol
import Mathlib
import Definitions.Def_ChapterA4d
import Definitions.Def_ChapterA3
import Definitions.Def_ChapterA3h
open BookProof.ChapterA3


open Matrix
open scoped ComplexConjugate
Formal statement
theorem BookProof.ChapterA3.upsilonC_nullCol (T : Matrix (Fin 2) (Fin 2) ℂ) (μ : Fin 4) :
    UpsilonC T μ 0 + UpsilonC T μ 3 = pauliCoeff (Tᴴ * (pauliσ 0 + pauliσ 3) * T) μ := by sorry

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