Prove2Me

`BookProof.ChapterA.cplxify_commutes` {M : System ℂ V} {T : V →L[ℝ] V} (hT : ∀ x, T (Complex.I • x) = Complex.I • T x) (hTc : RealCommutes M T) : M.Commutes (cplxify T hT)

Proved
BookProof.ChapterA.cplxify_commutes

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA2c.

BookProof.ChapterA.cplxify_commutes {M : System ℂ V} {T : V →L[ℝ] V} (hT : ∀ x, T (Complex.I • x) = Complex.I • T x) (hTc : RealCommutes M T) : M.Commutes (cplxify T hT)

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

Preamble
-- Generated from ChapterA2c.lean — theorem BookProof.ChapterA.cplxify_commutes
import Mathlib
import Definitions.Def_ChapterA2c
import Definitions.Def_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.cplxify_commutes {M : System ℂ V} {T : V →L[ℝ] V}
    (hT : ∀ x, T (Complex.I • x) = Complex.I • T x) (hTc : RealCommutes M T) :
    M.Commutes (cplxify T hT) := by sorry

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