`BookProof.FockInteractionStability.interaction_form_bound` [InnerProductSpace ℂ E] (V : E →L[ℂ] E) (x : E) : |(inner ℂ x (V x) : ℂ).re| ≤ ‖V‖ * ‖x‖ ^ 2

Proved

BookProof.FockInteractionStability.interaction_form_bound

by leonardopedro · Oct 6, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFockInteractionStability.

BookProof.FockInteractionStability.interaction_form_bound [InnerProductSpace ℂ E] (V : E →L[ℂ] E) (x : E) : |(inner ℂ x (V x) : ℂ).re| ≤ ‖V‖ * ‖x‖ ^ 2

Formalization note: Lean 4 identifier BookProof.FockInteractionStability.interaction_form_bound.

Preamble

-- Generated from ChapterFockInteractionStability.lean — theorem BookProof.FockInteractionStability.interaction_form_bound
import Definitions.Def_ChapterFockSecondQuantization
import Definitions.Def_ChapterFockOneParticleGap
import Definitions.Def_ChapterFockNumberPreservingGap
import Definitions.Def_ChapterFarisLavine
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
import Mathlib
import Definitions.Def_ChapterFockInteractionStability
open BookProof.FockInteractionStability

variable {E : Type*} [NormedAddCommGroup E]


noncomputable section


open BookProof.FockSecondQuantization BookProof.FockOneParticleGap
open BookProof.FockNumberPreservingGap
open BookProof.FarisLavine BookProof.NavierStokesFlow

Formal statement

theorem BookProof.FockInteractionStability.interaction_form_bound [InnerProductSpace ℂ E] (V : E →L[ℂ] E) (x : E) :
    |(inner ℂ x (V x) : ℂ).re| ≤ ‖V‖ * ‖x‖ ^ 2 := by sorry

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