`BookProof.NavierStokesFlow.FockOfFock.dGamma_eq_sum_numberOp` (ω : M → ℝ) {n : Conf M} {S : Finset M} (hS : n.support ⊆ S) : dGamma ω (fockBasis n) = ∑ m ∈ S, ((ω m : ℝ) : ℂ) • nu

Proved

BookProof.NavierStokesFlow.FockOfFock.dGamma_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.dGamma_eq_sum_numberOp (ω : M → ℝ) {n : Conf M} {S : Finset M} (hS : n.support ⊆ S) : dGamma ω (fockBasis n) = ∑ m ∈ S, ((ω m : ℝ) : ℂ) • numberOp m (fockBasis n)

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

Preamble

-- Generated from ChapterNavierStokesFockEsa.lean — theorem BookProof.NavierStokesFlow.FockOfFock.dGamma_eq_sum_numberOp
import Mathlib
import Definitions.Def_ChapterNavierStokesFockEsa
import Definitions.Def_ChapterFockOneParticleGap
import Definitions.Def_ChapterFockSecondQuantization
import Definitions.Def_ChapterGhostField
import Definitions.Def_ChapterNavierStokesFockSpace
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
open BookProof.FockOneParticleGap
open BookProof.FockSecondQuantization
open BookProof.GhostField
open BookProof.NavierStokesFlow.FockOfFock
open BookProof.NavierStokesFlow


open MeasureTheory



open FullEsa LagrangianEsa

variable {M : Type*} [DecidableEq M]

Formal statement

theorem BookProof.NavierStokesFlow.FockOfFock.dGamma_eq_sum_numberOp (ω : M → ℝ) {n : Conf M} {S : Finset M} (hS : n.support ⊆ S) :
    dGamma ω (fockBasis n) = ∑ m ∈ S, ((ω m : ℝ) : ℂ) • numberOp m (fockBasis n) := by sorry

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