`BookProof.FockFieldPerturbation.fieldVec_unbounded` (k : ℕ) (C : ℝ) : ∃ u : FockAlg, ‖toLp u‖ = 1 ∧ C ≤ ‖toLp (fieldVec (Finsupp.single k 1) u)‖

Proved

BookProof.FockFieldPerturbation.fieldVec_unbounded

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFockFieldPerturbation.

BookProof.FockFieldPerturbation.fieldVec_unbounded (k : ℕ) (C : ℝ) : ∃ u : FockAlg, ‖toLp u‖ = 1 ∧ C ≤ ‖toLp (fieldVec (Finsupp.single k 1) u)‖

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

Preamble

-- Generated from ChapterFockFieldPerturbation.lean — theorem BookProof.FockFieldPerturbation.fieldVec_unbounded
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.fieldVec_unbounded (k : ℕ) (C : ℝ) :
    ∃ u : FockAlg, ‖toLp u‖ = 1 ∧ C ≤ ‖toLp (fieldVec (Finsupp.single k 1) u)‖ := by sorry

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