Prove2Me

`BookProof.NavierStokesFlow.LagrangianEsa.latticeLagData_hFull_apply` (v : Fin 3 → LinfZ) (w : LinfZ) (fr : Fin 3 → ℝ) {nu : ℝ} (hnu : 0 ≤ nu) (x : (latticeLagData v w fr hnu).D) :

Proved
BookProof.NavierStokesFlow.LagrangianEsa.latticeLagData_hFull_apply

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNavierStokesLagrangianEsa.

BookProof.NavierStokesFlow.LagrangianEsa.latticeLagData_hFull_apply (v : Fin 3 → LinfZ) (w : LinfZ) (fr : Fin 3 → ℝ) {nu : ℝ} (hnu : 0 ≤ nu) (x : (latticeLagData v w fr hnu).D) : ((latticeLagData v w fr hnu).hFull x : L2Z) = latticeLagCLM v w fr nu (x : L2Z)

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

Preamble
-- Generated from ChapterNavierStokesLagrangianEsa.lean — theorem BookProof.NavierStokesFlow.LagrangianEsa.latticeLagData_hFull_apply
import Mathlib
import Definitions.Def_ChapterNavierStokesLagrangianEsa
import Definitions.Def_ChapterContinuityUnitary
import Definitions.Def_ChapterContinuityUnitaryInfinite
import Definitions.Def_ChapterNavierStokesEsa
import Definitions.Def_ChapterNavierStokesFlow
import Definitions.Def_ChapterNavierStokesFullEsa
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
open BookProof.ChapterContinuityUnitary
open BookProof.ChapterContinuityUnitaryInfinite
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.latticeLagData_hFull_apply (v : Fin 3 → LinfZ) (w : LinfZ) (fr : Fin 3 → ℝ) {nu : ℝ}
    (hnu : 0 ≤ nu) (x : (latticeLagData v w fr hnu).D) :
    ((latticeLagData v w fr hnu).hFull x : L2Z) = latticeLagCLM v w fr nu (x : L2Z) := by sorry

View graph