`BookProof.NavierStokesFlow.LagrangianEsa.LagrangianFullData.hasZeroDeficiencyOn_of_boundedRealization` (A : F →L[ℂ] F) (hsym : (A : F →ₗ[ℂ] F).IsSymmetric) (hHA : ∀ x : L.D, (L.hF

Proved

BookProof.NavierStokesFlow.LagrangianEsa.LagrangianFullData.hasZeroDeficiencyOn_of_boundedRealization

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNavierStokesLagrangianEsa.

BookProof.NavierStokesFlow.LagrangianEsa.LagrangianFullData.hasZeroDeficiencyOn_of_boundedRealization (A : F →L[ℂ] F) (hsym : (A : F →ₗ[ℂ] F).IsSymmetric) (hHA : ∀ x : L.D, (L.hFull x : F) = A (x : F)) : HasZeroDeficiencyOn L.D L.hFull

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

Preamble

-- Generated from ChapterNavierStokesLagrangianEsa.lean — theorem BookProof.NavierStokesFlow.LagrangianEsa.LagrangianFullData.hasZeroDeficiencyOn_of_boundedRealization
import Mathlib
import Definitions.Def_ChapterNavierStokesLagrangianEsa
import Definitions.Def_ChapterNavierStokesFlow
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
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.hasZeroDeficiencyOn_of_boundedRealization (A : F →L[ℂ] F)
    (hsym : (A : F →ₗ[ℂ] F).IsSymmetric) (hHA : ∀ x : L.D, (L.hFull x : F) = A (x : F)) :
    HasZeroDeficiencyOn L.D L.hFull := by sorry

View graph