Prove2Me

`BookProof.FockFieldPerturbation.sum_sq_annA_le` (u : FockAlg) (S : Finset ℕ) : ∑ k ∈ S, ‖toLp (annA k u)‖ ^ 2 ≤ numberQuad u

Proved
BookProof.FockFieldPerturbation.sum_sq_annA_le

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFockFieldPerturbation.

BookProof.FockFieldPerturbation.sum_sq_annA_le (u : FockAlg) (S : Finset ℕ) : ∑ k ∈ S, ‖toLp (annA k u)‖ ^ 2 ≤ numberQuad u

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

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


noncomputable section


open BookProof.FockSecondQuantization BookProof.FockOneParticleGap
open BookProof.FockNumberPreservingGap BookProof.FockInteractionStability
Formal statement
theorem BookProof.FockFieldPerturbation.sum_sq_annA_le (u : FockAlg) (S : Finset ℕ) :
    ∑ k ∈ S, ‖toLp (annA k u)‖ ^ 2 ≤ numberQuad u := by sorry

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