Prove2Me

`BookProof.NavierStokesFlow.FockOfFock.numberDensityOp_basis` (dens : M → Ω → ℝ) (ξ : Ω) (n : Conf M) : numberDensityOp dens ξ (fockBasis n) = ((confDensity dens n ξ : ℝ) : ℂ) • fo

Proved
BookProof.NavierStokesFlow.FockOfFock.numberDensityOp_basis

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNavierStokesFockEsa.

BookProof.NavierStokesFlow.FockOfFock.numberDensityOp_basis (dens : M → Ω → ℝ) (ξ : Ω) (n : Conf M) : numberDensityOp dens ξ (fockBasis n) = ((confDensity dens n ξ : ℝ) : ℂ) • fockBasis n

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

Preamble
-- Generated from ChapterNavierStokesFockEsa.lean — theorem BookProof.NavierStokesFlow.FockOfFock.numberDensityOp_basis
import Mathlib
import Definitions.Def_ChapterNavierStokesFockEsa
import Definitions.Def_ChapterFockSecondQuantization
import Definitions.Def_ChapterNavierStokesFockSpace
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
open BookProof.FockSecondQuantization
open BookProof.NavierStokesFlow.FockOfFock
open BookProof.NavierStokesFlow


open MeasureTheory



open FullEsa LagrangianEsa

variable {M : Type*} [DecidableEq M]
variable {M : Type*} [DecidableEq M] {Ω : Type*} [MeasurableSpace Ω]
Formal statement
theorem BookProof.NavierStokesFlow.FockOfFock.numberDensityOp_basis (dens : M → Ω → ℝ) (ξ : Ω) (n : Conf M) :
    numberDensityOp dens ξ (fockBasis n) = ((confDensity dens n ξ : ℝ) : ℂ) • fockBasis n := by sorry

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