`BookProof.ChapterA3j.projChirL_parity_commutator` : projChirL * mgamma 0 - mgamma 0 * projChirL = Complex.I • (mgamma 0 * chir)

Proved

BookProof.ChapterA3j.projChirL_parity_commutator

by leonardopedro · Oct 6, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA3j.

BookProof.ChapterA3j.projChirL_parity_commutator : projChirL * mgamma 0 - mgamma 0 * projChirL = Complex.I • (mgamma 0 * chir)

Formalization note: Lean 4 identifier BookProof.ChapterA3j.projChirL_parity_commutator.

Preamble

-- Generated from ChapterA3j.lean — theorem BookProof.ChapterA3j.projChirL_parity_commutator
import Mathlib
import Definitions.Def_ChapterA3j
import Definitions.Def_ChapterA3
open BookProof.ChapterA3
open BookProof.ChapterA3j


open Matrix


open BookProof.ChapterA3

Formal statement

theorem BookProof.ChapterA3j.projChirL_parity_commutator :
    projChirL * mgamma 0 - mgamma 0 * projChirL
      = Complex.I • (mgamma 0 * chir) := by sorry

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