`BookProof.ChapterA.realCommutes_smul` {M : System ℂ V} {S : V →L[ℝ] V} (hS : RealCommutes M S) (r : ℝ) : RealCommutes M (r • S)

Proved

BookProof.ChapterA.realCommutes_smul

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA2c.

BookProof.ChapterA.realCommutes_smul {M : System ℂ V} {S : V →L[ℝ] V} (hS : RealCommutes M S) (r : ℝ) : RealCommutes M (r • S)

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

Preamble

-- Generated from ChapterA2c.lean — theorem BookProof.ChapterA.realCommutes_smul
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_smul {M : System ℂ V} {S : V →L[ℝ] V} (hS : RealCommutes M S)
    (r : ℝ) : RealCommutes M (r • S) := by sorry

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