`BookProof.NavierStokesFlow.LagrangianEsa.LagrangianFullData.hasZeroDeficiencyOn_of_total_eigenvectors` {I : Type*} (e : I → L.D) (lam : I → ℝ) (heig : ∀ a, L.hFull (e a) = ((lam a

Proved

BookProof.NavierStokesFlow.LagrangianEsa.LagrangianFullData.hasZeroDeficiencyOn_of_total_eigenvectors

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_total_eigenvectors {I : Type*} (e : I → L.D) (lam : I → ℝ) (heig : ∀ a, L.hFull (e a) = ((lam a : ℝ) : ℂ) • e a) (htotal : ∀ w : F, (∀ a, (inner ℂ ((e a : F)) w : ℂ) = 0) → w = 0) : HasZeroDeficiencyOn L.D L.hFull

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

Preamble

-- Generated from ChapterNavierStokesLagrangianEsa.lean — theorem BookProof.NavierStokesFlow.LagrangianEsa.LagrangianFullData.hasZeroDeficiencyOn_of_total_eigenvectors
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_total_eigenvectors {I : Type*} (e : I → L.D) (lam : I → ℝ)
    (heig : ∀ a, L.hFull (e a) = ((lam a : ℝ) : ℂ) • e a)
    (htotal : ∀ w : F, (∀ a, (inner ℂ ((e a : F)) w : ℂ) = 0) → w = 0) :
    HasZeroDeficiencyOn L.D L.hFull := by sorry

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