`BookProof.NavierStokesFlow.FullEsa.NSFullData.hasZeroDeficiencyOn_of_total_eigenvectors` {I : Type*} (e : I → d.D) (lam : I → ℝ) (heig : ∀ i, d.hamiltonian (e i) = ((lam i : ℂ)) •

Proved

BookProof.NavierStokesFlow.FullEsa.NSFullData.hasZeroDeficiencyOn_of_total_eigenvectors

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNavierStokesFullEsa.

BookProof.NavierStokesFlow.FullEsa.NSFullData.hasZeroDeficiencyOn_of_total_eigenvectors {I : Type*} (e : I → d.D) (lam : I → ℝ) (heig : ∀ i, d.hamiltonian (e i) = ((lam i : ℂ)) • e i) (htotal : ∀ w : F, (∀ i, (inner ℂ ((e i : F)) w : ℂ) = 0) → w = 0) : HasZeroDeficiencyOn d.D d.hamiltonian

Formalization note: Lean 4 identifier BookProof.NavierStokesFlow.FullEsa.NSFullData.hasZeroDeficiencyOn_of_total_eigenvectors.

Preamble

-- Generated from ChapterNavierStokesFullEsa.lean — theorem BookProof.NavierStokesFlow.FullEsa.NSFullData.hasZeroDeficiencyOn_of_total_eigenvectors
import Mathlib
import Definitions.Def_ChapterNavierStokesFullEsa
import Definitions.Def_ChapterNavierStokesFlow
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow.FullEsa


open scoped ENNReal

variable {F : Type*} [NormedAddCommGroup F] [InnerProductSpace ℂ F]
variable {D : Submodule ℂ F}
variable (d : NSFullData F)

Formal statement

theorem BookProof.NavierStokesFlow.FullEsa.NSFullData.hasZeroDeficiencyOn_of_total_eigenvectors {I : Type*} (e : I → d.D) (lam : I → ℝ)
    (heig : ∀ i, d.hamiltonian (e i) = ((lam i : ℂ)) • e i)
    (htotal : ∀ w : F, (∀ i, (inner ℂ ((e i : F)) w : ℂ) = 0) → w = 0) :
    HasZeroDeficiencyOn d.D d.hamiltonian := by sorry

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