Prove2Me

`BookProof.ChapterA.realCommutes_thetaR` {M : System ℂ V} {θ : AntiUnitary V} (hθ : CommutesAntiUnitary M θ) : RealCommutes M (thetaR θ)

Proved
BookProof.ChapterA.realCommutes_thetaR

by leonardopedro · Oct 17, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA2c.

BookProof.ChapterA.realCommutes_thetaR {M : System ℂ V} {θ : AntiUnitary V} (hθ : CommutesAntiUnitary M θ) : RealCommutes M (thetaR θ)

Formalization note: Lean 4 identifier BookProof.ChapterA.realCommutes_thetaR.

Preamble
-- Generated from ChapterA2c.lean — theorem BookProof.ChapterA.realCommutes_thetaR
import Mathlib
import Definitions.Def_ChapterA2c
import Definitions.Def_ChapterA
import Definitions.Def_ChapterA1
open BookProof.ChapterA
open BookProof.ChapterA
open BookProof.ChapterA


open scoped ComplexConjugate InnerProductSpace Quaternion


variable {V : Type*} [NormedAddCommGroup V] [InnerProductSpace ℂ V] [CompleteSpace V]
Formal statement
theorem BookProof.ChapterA.realCommutes_thetaR {M : System ℂ V} {θ : AntiUnitary V}
    (hθ : CommutesAntiUnitary M θ) : RealCommutes M (thetaR θ) := by sorry

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