`BookProof.ChapterParityHiggs.higgs_real_structure` (v : Fin 2 × Fin 2 → ℂ) : realityOp higgsReal (realityOp higgsReal v) = v

Proved

BookProof.ChapterParityHiggs.higgs_real_structure

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterParityHiggs.

BookProof.ChapterParityHiggs.higgs_real_structure (v : Fin 2 × Fin 2 → ℂ) : realityOp higgsReal (realityOp higgsReal v) = v

Formalization note: Lean 4 identifier BookProof.ChapterParityHiggs.higgs_real_structure.

Preamble

-- Generated from ChapterParityHiggs.lean — theorem BookProof.ChapterParityHiggs.higgs_real_structure
import Definitions.Def_ChapterParity
import Mathlib
import Definitions.Def_ChapterParityHiggs
open BookProof.ChapterParityHiggs


open Matrix
open scoped Kronecker
open scoped ComplexConjugate


open BookProof.ChapterParity

Formal statement

theorem BookProof.ChapterParityHiggs.higgs_real_structure (v : Fin 2 × Fin 2 → ℂ) :
    realityOp higgsReal (realityOp higgsReal v) = v := by sorry

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