`BookProof.ChapterPauliLorentz.hermMat_eq_pauli` (x : Fin 4 → ℝ) : hermMat x = (x 0 : ℂ) • σ0 + (x 1 : ℂ) • σ1 + (x 2 : ℂ) • σ2 + (x 3 : ℂ) • σ3

Proved

BookProof.ChapterPauliLorentz.hermMat_eq_pauli

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterPauliLorentz.

BookProof.ChapterPauliLorentz.hermMat_eq_pauli (x : Fin 4 → ℝ) : hermMat x = (x 0 : ℂ) • σ0 + (x 1 : ℂ) • σ1 + (x 2 : ℂ) • σ2 + (x 3 : ℂ) • σ3

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

Preamble

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


open Matrix
open scoped BigOperators

Formal statement

theorem BookProof.ChapterPauliLorentz.hermMat_eq_pauli (x : Fin 4 → ℝ) :
    hermMat x = (x 0 : ℂ) • σ0 + (x 1 : ℂ) • σ1 + (x 2 : ℂ) • σ2 + (x 3 : ℂ) • σ3 := by sorry

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