`BookProof.FockFieldPerturbation.numberQuad_eq_sum` {u : FockAlg} {K : Finset ℕ} (hK : modes u ⊆ K) : numberQuad u = ∑ k ∈ K, ‖toLp (annA k u)‖ ^ 2

Proved

BookProof.FockFieldPerturbation.numberQuad_eq_sum

by leonardopedro · Oct 17, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFockFieldPerturbation.

BookProof.FockFieldPerturbation.numberQuad_eq_sum {u : FockAlg} {K : Finset ℕ} (hK : modes u ⊆ K) : numberQuad u = ∑ k ∈ K, ‖toLp (annA k u)‖ ^ 2

Formalization note: Lean 4 identifier BookProof.FockFieldPerturbation.numberQuad_eq_sum.

Preamble

-- Generated from ChapterFockFieldPerturbation.lean — theorem BookProof.FockFieldPerturbation.numberQuad_eq_sum
import Definitions.Def_ChapterFockNumberPreservingGap
import Definitions.Def_ChapterFockInteractionStability
import Mathlib
import Definitions.Def_ChapterFockFieldPerturbation
import Definitions.Def_ChapterFockOneParticleGap
import Definitions.Def_ChapterFockSecondQuantization
open BookProof.FockOneParticleGap
open BookProof.FockSecondQuantization
open BookProof.FockFieldPerturbation


noncomputable section


open BookProof.FockSecondQuantization BookProof.FockOneParticleGap
open BookProof.FockNumberPreservingGap BookProof.FockInteractionStability

Formal statement

theorem BookProof.FockFieldPerturbation.numberQuad_eq_sum {u : FockAlg} {K : Finset ℕ} (hK : modes u ⊆ K) :
    numberQuad u = ∑ k ∈ K, ‖toLp (annA k u)‖ ^ 2 := by sorry

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