Prove2Me

`BookProof.ChapterParityChirality.chirality_iff` (v : Fin 2 × Fin 4 → ℂ) : isigma3 *ᵥ v = igamma5 *ᵥ v ↔ chi *ᵥ v = -v

Proved
BookProof.ChapterParityChirality.chirality_iff

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterParityChirality.

BookProof.ChapterParityChirality.chirality_iff (v : Fin 2 × Fin 4 → ℂ) : isigma3 *ᵥ v = igamma5 *ᵥ v ↔ chi *ᵥ v = -v

Formalization note: Lean 4 identifier BookProof.ChapterParityChirality.chirality_iff.

Preamble
-- Generated from ChapterParityChirality.lean — theorem BookProof.ChapterParityChirality.chirality_iff
import Definitions.Def_ChapterA3
import Definitions.Def_ChapterParity
import Definitions.Def_ChapterParitySU2
import Mathlib
import Definitions.Def_ChapterParityChirality
open BookProof.ChapterParityChirality


open Matrix
open scoped Kronecker


open BookProof.ChapterA3
open BookProof.ChapterParity
open BookProof.ChapterParitySU2
Formal statement
theorem BookProof.ChapterParityChirality.chirality_iff (v : Fin 2 × Fin 4 → ℂ) :
    isigma3 *ᵥ v = igamma5 *ᵥ v ↔ chi *ᵥ v = -v := by sorry

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