`BookProof.ChapterA.qembed_realCommutes` {M : System ℂ V} {θ : AntiUnitary V} (hθ : ∀ x, θ (θ x) = -x) (hθc : CommutesAntiUnitary M θ) (q : Quaternion ℝ) : RealCommutes M (qembed θ

Proved

BookProof.ChapterA.qembed_realCommutes

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA2c.

BookProof.ChapterA.qembed_realCommutes {M : System ℂ V} {θ : AntiUnitary V} (hθ : ∀ x, θ (θ x) = -x) (hθc : CommutesAntiUnitary M θ) (q : Quaternion ℝ) : RealCommutes M (qembed θ hθ q)

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

Preamble

-- Generated from ChapterA2c.lean — theorem BookProof.ChapterA.qembed_realCommutes
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.qembed_realCommutes {M : System ℂ V} {θ : AntiUnitary V} (hθ : ∀ x, θ (θ x) = -x)
    (hθc : CommutesAntiUnitary M θ) (q : Quaternion ℝ) :
    RealCommutes M (qembed θ hθ q) := by sorry

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