`BookProof.NavierStokesFlow.FullEsa.IsSymmetricDom.comp_of_commute` {A B : D →ₗ[ℂ] D} (hA : IsSymmetricDom A) (hB : IsSymmetricDom B) (hcomm : A.comp B = B.comp A) : IsSymmetricDom

Proved

BookProof.NavierStokesFlow.FullEsa.IsSymmetricDom.comp_of_commute

by leonardopedro · Oct 7, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNavierStokesFullEsa.

BookProof.NavierStokesFlow.FullEsa.IsSymmetricDom.comp_of_commute {A B : D →ₗ[ℂ] D} (hA : IsSymmetricDom A) (hB : IsSymmetricDom B) (hcomm : A.comp B = B.comp A) : IsSymmetricDom (A.comp B)

Formalization note: Lean 4 identifier BookProof.NavierStokesFlow.FullEsa.IsSymmetricDom.comp_of_commute.

Preamble

-- Generated from ChapterNavierStokesFullEsa.lean — theorem BookProof.NavierStokesFlow.FullEsa.IsSymmetricDom.comp_of_commute
import Mathlib
import Definitions.Def_ChapterNavierStokesFullEsa
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
open BookProof.NavierStokesFlow


open scoped ENNReal

variable {F : Type*} [NormedAddCommGroup F] [InnerProductSpace ℂ F]
variable {D : Submodule ℂ F}

Formal statement

theorem BookProof.NavierStokesFlow.FullEsa.IsSymmetricDom.comp_of_commute {A B : D →ₗ[ℂ] D} (hA : IsSymmetricDom A)
    (hB : IsSymmetricDom B) (hcomm : A.comp B = B.comp A) : IsSymmetricDom (A.comp B) := by sorry

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