`BookProof.FockCubicQuarticStability.quart_form_eq` (k : ℕ) (u : FockAlg) : (inner ℂ (toLp u) (toLp (quartA k u)) : ℂ).re = ‖toLp (annA k (annA k u))‖ ^ 2

Proved

BookProof.FockCubicQuarticStability.quart_form_eq

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFockCubicQuarticStability.

BookProof.FockCubicQuarticStability.quart_form_eq (k : ℕ) (u : FockAlg) : (inner ℂ (toLp u) (toLp (quartA k u)) : ℂ).re = ‖toLp (annA k (annA k u))‖ ^ 2

Formalization note: Lean 4 identifier BookProof.FockCubicQuarticStability.quart_form_eq.

Preamble

-- Generated from ChapterFockCubicQuarticStability.lean — theorem BookProof.FockCubicQuarticStability.quart_form_eq
import Definitions.Def_ChapterFockOneParticleGap
import Definitions.Def_ChapterFockNumberPreservingGap
import Definitions.Def_ChapterFockFieldPerturbation
import Definitions.Def_ChapterFockCubicUnbounded
import Mathlib
import Definitions.Def_ChapterFockCubicQuarticStability
import Definitions.Def_ChapterFockSecondQuantization
open BookProof.FockSecondQuantization
open BookProof.FockCubicQuarticStability


noncomputable section


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

Formal statement

theorem BookProof.FockCubicQuarticStability.quart_form_eq (k : ℕ) (u : FockAlg) :
    (inner ℂ (toLp u) (toLp (quartA k u)) : ℂ).re = ‖toLp (annA k (annA k u))‖ ^ 2 := by sorry

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