`BookProof.ChapterPauliSU2.spinorAction_trace_of_unitary` {T : Matrix (Fin 2) (Fin 2) ℂ} (hT : Tᴴ * T = 1) (X : Matrix (Fin 2) (Fin 2) ℂ) : (spinorAction T X).trace = X.trace

Proved

BookProof.ChapterPauliSU2.spinorAction_trace_of_unitary

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterPauliSU2.

BookProof.ChapterPauliSU2.spinorAction_trace_of_unitary {T : Matrix (Fin 2) (Fin 2) ℂ} (hT : Tᴴ * T = 1) (X : Matrix (Fin 2) (Fin 2) ℂ) : (spinorAction T X).trace = X.trace

Formalization note: Lean 4 identifier BookProof.ChapterPauliSU2.spinorAction_trace_of_unitary.

Preamble

-- Generated from ChapterPauliSU2.lean — theorem BookProof.ChapterPauliSU2.spinorAction_trace_of_unitary
import Definitions.Def_ChapterPauliLorentz
import Mathlib
import Definitions.Def_ChapterPauliSU2
open BookProof.ChapterPauliSU2


open Matrix
open scoped BigOperators


open BookProof.ChapterPauliLorentz

Formal statement

theorem BookProof.ChapterPauliSU2.spinorAction_trace_of_unitary {T : Matrix (Fin 2) (Fin 2) ℂ}
    (hT : Tᴴ * T = 1) (X : Matrix (Fin 2) (Fin 2) ℂ) :
    (spinorAction T X).trace = X.trace := by sorry

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