Prove2Me

`BookProof.NavierStokesFlow.FullEsa.latticeAdvectionCLM_mem_finiteModes` (v : Fin 15 → LinfZ) (nu : ℝ) (i : Fin 3) {f : L2Z} (hf : f ∈ finiteModes) : latticeAdvectionCLM v nu i f ∈

Proved
BookProof.NavierStokesFlow.FullEsa.latticeAdvectionCLM_mem_finiteModes

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNavierStokesFullEsa.

BookProof.NavierStokesFlow.FullEsa.latticeAdvectionCLM_mem_finiteModes (v : Fin 15 → LinfZ) (nu : ℝ) (i : Fin 3) {f : L2Z} (hf : f ∈ finiteModes) : latticeAdvectionCLM v nu i f ∈ finiteModes

Formalization note: Lean 4 identifier BookProof.NavierStokesFlow.FullEsa.latticeAdvectionCLM_mem_finiteModes.

Preamble
-- Generated from ChapterNavierStokesFullEsa.lean — theorem BookProof.NavierStokesFlow.FullEsa.latticeAdvectionCLM_mem_finiteModes
import Mathlib
import Definitions.Def_ChapterNavierStokesFullEsa
import Definitions.Def_ChapterContinuityUnitary
import Definitions.Def_ChapterContinuityUnitaryInfinite
import Definitions.Def_ChapterNavierStokesEsa
import Definitions.Def_ChapterNavierStokesFlow
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
open BookProof.ChapterContinuityUnitary
open BookProof.ChapterContinuityUnitaryInfinite
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.latticeAdvectionCLM_mem_finiteModes (v : Fin 15 → LinfZ) (nu : ℝ) (i : Fin 3)
    {f : L2Z} (hf : f ∈ finiteModes) : latticeAdvectionCLM v nu i f ∈ finiteModes := by sorry

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