`BookProof.FockCubicUnbounded.cubeA_apply` (k : ℕ) (x : FockAlg) : cubeA k x = creA k (creA k (creA k x)) + annA k (annA k (annA k x))

Proved

BookProof.FockCubicUnbounded.cubeA_apply

by leonardopedro · Oct 21, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFockCubicUnbounded.

BookProof.FockCubicUnbounded.cubeA_apply (k : ℕ) (x : FockAlg) : cubeA k x = creA k (creA k (creA k x)) + annA k (annA k (annA k x))

Formalization note: Lean 4 identifier BookProof.FockCubicUnbounded.cubeA_apply.

Preamble

-- Generated from ChapterFockCubicUnbounded.lean — theorem BookProof.FockCubicUnbounded.cubeA_apply
import Definitions.Def_ChapterFockOneParticleGap
import Definitions.Def_ChapterFockNumberPreservingGap
import Definitions.Def_ChapterFockFieldPerturbation
import Mathlib
import Definitions.Def_ChapterFockCubicUnbounded
import Definitions.Def_ChapterFockSecondQuantization
open BookProof.FockSecondQuantization
open BookProof.FockCubicUnbounded


noncomputable section


open BookProof.FockSecondQuantization BookProof.FockOneParticleGap
open BookProof.FockNumberPreservingGap BookProof.FockFieldPerturbation

Formal statement

theorem BookProof.FockCubicUnbounded.cubeA_apply (k : ℕ) (x : FockAlg) :
    cubeA k x = creA k (creA k (creA k x)) + annA k (annA k (annA k x)) := by sorry

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