`BookProof.NavierStokesFlow.LagrangianEsa.LagrangianFullData.isSymmetricDom_sq` {D : Submodule ℂ F} {A : D →ₗ[ℂ] D} (hA : IsSymmetricDom A) : IsSymmetricDom (A.comp A)

Proved

BookProof.NavierStokesFlow.LagrangianEsa.LagrangianFullData.isSymmetricDom_sq

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNavierStokesLagrangianEsa.

BookProof.NavierStokesFlow.LagrangianEsa.LagrangianFullData.isSymmetricDom_sq {D : Submodule ℂ F} {A : D →ₗ[ℂ] D} (hA : IsSymmetricDom A) : IsSymmetricDom (A.comp A)

Formalization note: Lean 4 identifier BookProof.NavierStokesFlow.LagrangianEsa.LagrangianFullData.isSymmetricDom_sq.

Preamble

-- Generated from ChapterNavierStokesLagrangianEsa.lean — theorem BookProof.NavierStokesFlow.LagrangianEsa.LagrangianFullData.isSymmetricDom_sq
import Mathlib
import Definitions.Def_ChapterNavierStokesLagrangianEsa
import Definitions.Def_ChapterNavierStokesFullEsa
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow.FullEsa.NSFullData
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow.LagrangianEsa




open FullEsa

variable {F : Type*} [NormedAddCommGroup F] [InnerProductSpace ℂ F]
variable (L : LagrangianFullData F)

Formal statement

theorem BookProof.NavierStokesFlow.LagrangianEsa.LagrangianFullData.isSymmetricDom_sq {D : Submodule ℂ F} {A : D →ₗ[ℂ] D} (hA : IsSymmetricDom A) :
    IsSymmetricDom (A.comp A) := by sorry

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