`BookProof.NavierStokesFlow.FullEsa.latticeFullData_hamiltonian_apply` (v : Fin 15 → LinfZ) (nu : ℝ) (x : (latticeFullData v nu).D) : ((latticeFullData v nu).hamiltonian x : L2Z) =

Proved

BookProof.NavierStokesFlow.FullEsa.latticeFullData_hamiltonian_apply

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNavierStokesFullEsa.

BookProof.NavierStokesFlow.FullEsa.latticeFullData_hamiltonian_apply (v : Fin 15 → LinfZ) (nu : ℝ) (x : (latticeFullData v nu).D) : ((latticeFullData v nu).hamiltonian x : L2Z) = latticeFullHamiltonianCLM v nu (x : L2Z)

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

Preamble

-- Generated from ChapterNavierStokesFullEsa.lean — theorem BookProof.NavierStokesFlow.FullEsa.latticeFullData_hamiltonian_apply
import Mathlib
import Definitions.Def_ChapterNavierStokesFullEsa
import Definitions.Def_ChapterContinuityUnitary
import Definitions.Def_ChapterContinuityUnitaryInfinite
import Definitions.Def_ChapterNavierStokesCanonicalVector
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
open BookProof.ChapterContinuityUnitary
open BookProof.ChapterContinuityUnitaryInfinite
open BookProof.NavierStokesFlow.CanonicalVector
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.latticeFullData_hamiltonian_apply (v : Fin 15 → LinfZ) (nu : ℝ)
    (x : (latticeFullData v nu).D) :
    ((latticeFullData v nu).hamiltonian x : L2Z) = latticeFullHamiltonianCLM v nu (x : L2Z) := by sorry

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