Prove2Me

`BookProof.FockFieldPerturbation.norm_annVec_le` (f : ℕ →₀ ℂ) (u : FockAlg) : ‖toLp (annVec f u)‖ ≤ l2norm f * Real.sqrt (numberQuad u)

Proved
BookProof.FockFieldPerturbation.norm_annVec_le

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFockFieldPerturbation.

BookProof.FockFieldPerturbation.norm_annVec_le (f : ℕ →₀ ℂ) (u : FockAlg) : ‖toLp (annVec f u)‖ ≤ l2norm f * Real.sqrt (numberQuad u)

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

Preamble
-- Generated from ChapterFockFieldPerturbation.lean — theorem BookProof.FockFieldPerturbation.norm_annVec_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.norm_annVec_le (f : ℕ →₀ ℂ) (u : FockAlg) :
    ‖toLp (annVec f u)‖ ≤ l2norm f * Real.sqrt (numberQuad u) := by sorry

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