Prove2Me

`BookProof.NavierStokesFlow.LagrangianEsa.diagLagData_hFull` (p q dr : Fin 3 → ℕ → ℝ) (c : ℕ → ℝ) (fr : Fin 3 → ℝ) {nu : ℝ} (hnu : 0 ≤ nu) : HasZeroDeficiencyOn (diagLagData...

Proved
BookProof.NavierStokesFlow.LagrangianEsa.diagLagData_hFull

by leonardopedro · Oct 11, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNavierStokesLagrangianEsa.

BookProof.NavierStokesFlow.LagrangianEsa.diagLagData_hFull (p q dr : Fin 3 → ℕ → ℝ) (c : ℕ → ℝ) (fr : Fin 3 → ℝ) {nu : ℝ} (hnu : 0 ≤ nu) : HasZeroDeficiencyOn (diagLagData p q dr c fr hnu).D (diagLagData p q dr c fr hnu).hFull

Formalization note: Lean 4 identifier BookProof.NavierStokesFlow.LagrangianEsa.diagLagData_hFull.

Preamble
-- Generated from ChapterNavierStokesLagrangianEsa.lean — theorem BookProof.NavierStokesFlow.LagrangianEsa.diagLagData_hFull
import Mathlib
import Definitions.Def_ChapterNavierStokesLagrangianEsa
import Definitions.Def_ChapterAbelianDiagonalCountable
import Definitions.Def_ChapterBRSTNilpotent
import Definitions.Def_ChapterF7
import Definitions.Def_ChapterNavierStokesDeficiency
import Definitions.Def_ChapterNavierStokesEsa
import Definitions.Def_ChapterNavierStokesFlow
import Definitions.Def_ChapterNavierStokesFullEsa
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
open BookProof.ChapterAbelianDiagonalCountable
open BookProof.BRSTNilpotent
open BookProof.ChapterF7
open BookProof.NavierStokesFlow.DiagonalEsa
open BookProof.NavierStokesFlow.JacobiDeficiency
open BookProof.NavierStokesFlow.LpNat
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)
variable {F G : Type*} [NormedAddCommGroup F] [InnerProductSpace ℂ F]
  [NormedAddCommGroup G] [InnerProductSpace ℂ G]
Formal statement
theorem BookProof.NavierStokesFlow.LagrangianEsa.diagLagData_hFull (p q dr : Fin 3 → ℕ → ℝ) (c : ℕ → ℝ) (fr : Fin 3 → ℝ)
    {nu : ℝ} (hnu : 0 ≤ nu) :
    HasZeroDeficiencyOn (diagLagData p q dr c fr hnu).D (diagLagData p q dr c fr hnu).hFull := by sorry

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