`BookProof.ChapterA.real_scalar_commutesConj` (θ : AntiUnitary V) (r : ℝ) : CommutesConj θ (((r : ℂ)) • (1 : V →L[ℂ] V))

Proved

BookProof.ChapterA.real_scalar_commutesConj

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA2b.

BookProof.ChapterA.real_scalar_commutesConj (θ : AntiUnitary V) (r : ℝ) : CommutesConj θ (((r : ℂ)) • (1 : V →L[ℂ] V))

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

Preamble

-- Generated from ChapterA2b.lean — theorem BookProof.ChapterA.real_scalar_commutesConj
import Mathlib
import Definitions.Def_ChapterA2b
import Definitions.Def_ChapterA1
import Definitions.Def_ChapterA
open BookProof.ChapterA
open BookProof.ChapterA


open scoped ComplexConjugate InnerProductSpace


variable {V : Type*} [NormedAddCommGroup V] [InnerProductSpace ℂ V] [CompleteSpace V]

Formal statement

theorem BookProof.ChapterA.real_scalar_commutesConj (θ : AntiUnitary V) (r : ℝ) :
    CommutesConj θ (((r : ℂ)) • (1 : V →L[ℂ] V)) := by sorry

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