Prove2Me

`BookProof.NavierStokesFlow.FockOfFock.hFull_eq_hFock_oneParticle` (nu : ℝ) (hnu : 0 ≤ nu) (p q dr : Fin 3 → M → ℝ) (force : Fin 3 → ℝ) (cst : M → ℝ) (m : M) : (lagrangianFockData

Proved
BookProof.NavierStokesFlow.FockOfFock.hFull_eq_hFock_oneParticle

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNavierStokesFockEsa.

BookProof.NavierStokesFlow.FockOfFock.hFull_eq_hFock_oneParticle (nu : ℝ) (hnu : 0 ≤ nu) (p q dr : Fin 3 → M → ℝ) (force : Fin 3 → ℝ) (cst : M → ℝ) (m : M) : (lagrangianFockData nu hnu p q dr force cst).hFull (fockBasis (Finsupp.single m 1)) = hFockLag nu p q dr force cst (fockBasis (Finsupp.single m 1))

Formalization note: Lean 4 identifier BookProof.NavierStokesFlow.FockOfFock.hFull_eq_hFock_oneParticle.

Preamble
-- Generated from ChapterNavierStokesFockEsa.lean — theorem BookProof.NavierStokesFlow.FockOfFock.hFull_eq_hFock_oneParticle
import Mathlib
import Definitions.Def_ChapterNavierStokesFockEsa
import Definitions.Def_ChapterBRSTNilpotent
import Definitions.Def_ChapterFockOneParticleGap
import Definitions.Def_ChapterFockSecondQuantization
import Definitions.Def_ChapterNavierStokesFlow
import Definitions.Def_ChapterNavierStokesFockSpace
import Definitions.Def_ChapterNavierStokesLagrangianEsa
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
open BookProof.BRSTNilpotent
open BookProof.FockOneParticleGap
open BookProof.FockSecondQuantization
open BookProof.NavierStokesFlow.FockOfFock
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow.LagrangianEsa.LagrangianFullData
open BookProof.NavierStokesFlow


open MeasureTheory



open FullEsa LagrangianEsa

variable {M : Type*} [DecidableEq M]
variable {M : Type*} [DecidableEq M] {Ω : Type*} [MeasurableSpace Ω]
variable {J K : Type*} [DecidableEq J] [DecidableEq K]
Formal statement
theorem BookProof.NavierStokesFlow.FockOfFock.hFull_eq_hFock_oneParticle (nu : ℝ) (hnu : 0 ≤ nu) (p q dr : Fin 3 → M → ℝ)
    (force : Fin 3 → ℝ) (cst : M → ℝ) (m : M) :
    (lagrangianFockData nu hnu p q dr force cst).hFull (fockBasis (Finsupp.single m 1))
      = hFockLag nu p q dr force cst (fockBasis (Finsupp.single m 1)) := by sorry

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