`BookProof.FockFieldPerturbation.annVec_apply` (f : ℕ →₀ ℂ) (x : FockAlg) : annVec f x = ∑ j ∈ f.support, ((starRingEnd ℂ) (f j)) • annA j x

Proved

BookProof.FockFieldPerturbation.annVec_apply

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFockFieldPerturbation.

BookProof.FockFieldPerturbation.annVec_apply (f : ℕ →₀ ℂ) (x : FockAlg) : annVec f x = ∑ j ∈ f.support, ((starRingEnd ℂ) (f j)) • annA j x

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

Preamble

-- Generated from ChapterFockFieldPerturbation.lean — theorem BookProof.FockFieldPerturbation.annVec_apply
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.annVec_apply (f : ℕ →₀ ℂ) (x : FockAlg) :
    annVec f x = ∑ j ∈ f.support, ((starRingEnd ℂ) (f j)) • annA j x := by sorry

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