`BookProof.ChapterPauliLorentz.spinorMap_preserves_mink` (T : Matrix (Fin 2) (Fin 2) ℂ) (hT : T.det = 1) (x : Fin 4 → ℝ) : mink (vecOfMat (Tᴴ * hermMat x * T)) = mink x

Proved

BookProof.ChapterPauliLorentz.spinorMap_preserves_mink

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterPauliLorentz.

BookProof.ChapterPauliLorentz.spinorMap_preserves_mink (T : Matrix (Fin 2) (Fin 2) ℂ) (hT : T.det = 1) (x : Fin 4 → ℝ) : mink (vecOfMat (Tᴴ * hermMat x * T)) = mink x

Formalization note: Lean 4 identifier BookProof.ChapterPauliLorentz.spinorMap_preserves_mink.

Preamble

-- Generated from ChapterPauliLorentz.lean — theorem BookProof.ChapterPauliLorentz.spinorMap_preserves_mink
import Mathlib
import Definitions.Def_ChapterPauliLorentz
open BookProof.ChapterPauliLorentz


open Matrix
open scoped BigOperators

Formal statement

theorem BookProof.ChapterPauliLorentz.spinorMap_preserves_mink (T : Matrix (Fin 2) (Fin 2) ℂ) (hT : T.det = 1)
    (x : Fin 4 → ℝ) :
    mink (vecOfMat (Tᴴ * hermMat x * T)) = mink x := by sorry

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