`BookProof.ChapterPauliSU2.su2_preserves_time` {T : Matrix (Fin 2) (Fin 2) ℂ} (hT : Tᴴ * T = 1) (x : Fin 4 → ℝ) : (vecOfMat (spinorAction T (hermMat x))) 0 = x 0

Proved

BookProof.ChapterPauliSU2.su2_preserves_time

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterPauliSU2.

BookProof.ChapterPauliSU2.su2_preserves_time {T : Matrix (Fin 2) (Fin 2) ℂ} (hT : Tᴴ * T = 1) (x : Fin 4 → ℝ) : (vecOfMat (spinorAction T (hermMat x))) 0 = x 0

Formalization note: Lean 4 identifier BookProof.ChapterPauliSU2.su2_preserves_time.

Preamble

-- Generated from ChapterPauliSU2.lean — theorem BookProof.ChapterPauliSU2.su2_preserves_time
import Mathlib
import Definitions.Def_ChapterPauliSU2
import Definitions.Def_ChapterPauliLorentz
open BookProof.ChapterPauliLorentz
open BookProof.ChapterPauliSU2


open Matrix
open scoped BigOperators


open BookProof.ChapterPauliLorentz

Formal statement

theorem BookProof.ChapterPauliSU2.su2_preserves_time {T : Matrix (Fin 2) (Fin 2) ℂ} (hT : Tᴴ * T = 1)
    (x : Fin 4 → ℝ) :
    (vecOfMat (spinorAction T (hermMat x))) 0 = x 0 := by sorry

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