`BookProof.ChapterA.realCommutes_algebraMap` (M : System ℂ V) (r : ℝ) : RealCommutes M (algebraMap ℝ (V →L[ℝ] V) r)

Proved

BookProof.ChapterA.realCommutes_algebraMap

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA2c.

BookProof.ChapterA.realCommutes_algebraMap (M : System ℂ V) (r : ℝ) : RealCommutes M (algebraMap ℝ (V →L[ℝ] V) r)

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

Preamble

-- Generated from ChapterA2c.lean — theorem BookProof.ChapterA.realCommutes_algebraMap
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.realCommutes_algebraMap (M : System ℂ V) (r : ℝ) :
    RealCommutes M (algebraMap ℝ (V →L[ℝ] V) r) := by sorry

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