Prove2Me

`BookProof.ChapterA.realCommutes_add` {M : System ℂ V} {S T : V →L[ℝ] V} (hS : RealCommutes M S) (hT : RealCommutes M T) : RealCommutes M (S + T)

Proved
BookProof.ChapterA.realCommutes_add

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA2c.

BookProof.ChapterA.realCommutes_add {M : System ℂ V} {S T : V →L[ℝ] V} (hS : RealCommutes M S) (hT : RealCommutes M T) : RealCommutes M (S + T)

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

Preamble
-- Generated from ChapterA2c.lean — theorem BookProof.ChapterA.realCommutes_add
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_add {M : System ℂ V} {S T : V →L[ℝ] V}
    (hS : RealCommutes M S) (hT : RealCommutes M T) : RealCommutes M (S + T) := by sorry

View graph