`BookProof.FockCubicUnbounded.quartA_single_confAt` (k m : ℕ) (z : ℂ) : quartA k (Finsupp.single (confAt k m) z) = Finsupp.single (confAt k m) ((((m : ℝ) * ((m : ℝ) - 1) : ℝ) : ℂ)

Proved

BookProof.FockCubicUnbounded.quartA_single_confAt

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFockCubicUnbounded.

BookProof.FockCubicUnbounded.quartA_single_confAt (k m : ℕ) (z : ℂ) : quartA k (Finsupp.single (confAt k m) z) = Finsupp.single (confAt k m) ((((m : ℝ) * ((m : ℝ) - 1) : ℝ) : ℂ) * z)

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

Preamble

-- Generated from ChapterFockCubicUnbounded.lean — theorem BookProof.FockCubicUnbounded.quartA_single_confAt
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.quartA_single_confAt (k m : ℕ) (z : ℂ) :
    quartA k (Finsupp.single (confAt k m) z)
      = Finsupp.single (confAt k m) ((((m : ℝ) * ((m : ℝ) - 1) : ℝ) : ℂ) * z) := by sorry

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