`BookProof.SmGaugeConnection.diracGaugeMat_conjTranspose` {k : Fin 3 → ℝ} {m1 m2 g : ℝ} {T : Fin d → Matrix (Fin N) (Fin N) ℂ} {A : Fin d → Fin 3 → ℝ} (hT : ∀ a, (T a)ᴴ = T a) : (d

Proved

BookProof.SmGaugeConnection.diracGaugeMat_conjTranspose

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSmGaugeConnection.

BookProof.SmGaugeConnection.diracGaugeMat_conjTranspose {k : Fin 3 → ℝ} {m1 m2 g : ℝ} {T : Fin d → Matrix (Fin N) (Fin N) ℂ} {A : Fin d → Fin 3 → ℝ} (hT : ∀ a, (T a)ᴴ = T a) : (diracGaugeMat k m1 m2 g T A)ᴴ = diracGaugeMat k m1 m2 g T A

Formalization note: Lean 4 identifier BookProof.SmGaugeConnection.diracGaugeMat_conjTranspose.

Preamble

-- Generated from ChapterSmGaugeConnection.lean — theorem BookProof.SmGaugeConnection.diracGaugeMat_conjTranspose
import Definitions.Def_ChapterYangMillsSU3
import Definitions.Def_ChapterSmCarAlgebra
import Definitions.Def_ChapterSmDiracYukawa
import Definitions.Def_ChapterSmDiracSpinor
import Definitions.Def_ChapterFarisLavine
import Mathlib
import Definitions.Def_ChapterSmGaugeConnection
import Definitions.Def_ChapterCPTHamiltonian
open BookProof.ChapterCPTHamiltonian
open BookProof.SmGaugeConnection



open Matrix Kronecker
open BookProof.YangMillsSU3 BookProof.ChapterCPTHamiltonian BookProof.SmCar
open BookProof.SmDiracYukawa BookProof.SmDiracSpinor BookProof.FarisLavine

noncomputable section

variable {N d : ℕ}

Formal statement

theorem BookProof.SmGaugeConnection.diracGaugeMat_conjTranspose {k : Fin 3 → ℝ} {m1 m2 g : ℝ}
    {T : Fin d → Matrix (Fin N) (Fin N) ℂ} {A : Fin d → Fin 3 → ℝ} (hT : ∀ a, (T a)ᴴ = T a) :
    (diracGaugeMat k m1 m2 g T A)ᴴ = diracGaugeMat k m1 m2 g T A := by sorry

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