`BookProof.NavierStokesFlow.FockOfFock.numberDensityOp_eq_sum_numberOp` (dens : M → Ω → ℝ) (ξ : Ω) {n : Conf M} {S : Finset M} (hS : n.support ⊆ S) : numberDensityOp dens ξ (fockBa

Proved

BookProof.NavierStokesFlow.FockOfFock.numberDensityOp_eq_sum_numberOp

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNavierStokesFockEsa.

BookProof.NavierStokesFlow.FockOfFock.numberDensityOp_eq_sum_numberOp (dens : M → Ω → ℝ) (ξ : Ω) {n : Conf M} {S : Finset M} (hS : n.support ⊆ S) : numberDensityOp dens ξ (fockBasis n) = ∑ m ∈ S, ((dens m ξ : ℝ) : ℂ) • numberOp m (fockBasis n)

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

Preamble

-- Generated from ChapterNavierStokesFockEsa.lean — theorem BookProof.NavierStokesFlow.FockOfFock.numberDensityOp_eq_sum_numberOp
import Mathlib
import Definitions.Def_ChapterNavierStokesFockEsa
import Definitions.Def_ChapterFockSecondQuantization
import Definitions.Def_ChapterGhostField
import Definitions.Def_ChapterNavierStokesFockSpace
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
open BookProof.FockSecondQuantization
open BookProof.GhostField
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_eq_sum_numberOp (dens : M → Ω → ℝ) (ξ : Ω) {n : Conf M} {S : Finset M}
    (hS : n.support ⊆ S) :
    numberDensityOp dens ξ (fockBasis n)
      = ∑ m ∈ S, ((dens m ξ : ℝ) : ℂ) • numberOp m (fockBasis n) := by sorry

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