`BookProof.ChapterParityHiggs.higgsDoublet_pseudoreal` (v : Fin 2 → ℂ) : realityOp pauli2 (realityOp pauli2 v) = -v

Proved

BookProof.ChapterParityHiggs.higgsDoublet_pseudoreal

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterParityHiggs.

BookProof.ChapterParityHiggs.higgsDoublet_pseudoreal (v : Fin 2 → ℂ) : realityOp pauli2 (realityOp pauli2 v) = -v

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

Preamble

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


open Matrix
open scoped Kronecker
open scoped ComplexConjugate


open BookProof.ChapterParity

Formal statement

theorem BookProof.ChapterParityHiggs.higgsDoublet_pseudoreal (v : Fin 2 → ℂ) :
    realityOp pauli2 (realityOp pauli2 v) = -v := by sorry

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