`BookProof.FockQuadratic.norm_hopT` (P Q : Idx ι) (x : Idx ι → ℂ) (b : Idx ι) : ‖hopT P Q x b‖ = amp P Q b * ‖x (tgt P Q b)‖ * ‖x b‖

Proved

BookProof.FockQuadratic.norm_hopT

by leonardopedro · Oct 5, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFockQuadraticEsa.

BookProof.FockQuadratic.norm_hopT (P Q : Idx ι) (x : Idx ι → ℂ) (b : Idx ι) : ‖hopT P Q x b‖ = amp P Q b * ‖x (tgt P Q b)‖ * ‖x b‖

Formalization note: Lean 4 identifier BookProof.FockQuadratic.norm_hopT.

Preamble

-- Generated from ChapterFockQuadraticEsa.lean — theorem BookProof.FockQuadratic.norm_hopT
import Definitions.Def_ChapterFarisLavine
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
import Definitions.Def_ChapterNavierStokesIkebeKato
import Definitions.Def_ChapterNavierStokesDeficiency
import Definitions.Def_ChapterOperatorSeriesEsa
import Mathlib
import Definitions.Def_ChapterFockQuadraticEsa
import Definitions.Def_ChapterA3n
import Definitions.Def_ChapterNavierStokesHermiteFarisLavine
open BookProof.ChapterA3n
open BookProof.NavierStokesFlow.HermiteFarisLavine
open BookProof.FockQuadratic

variable {ι : Type*}
variable {ω : ι → ℝ}


open scoped ENNReal


open BookProof.FarisLavine BookProof.NavierStokesFlow BookProof.NavierStokesFlow.IkebeKato
open BookProof.NavierStokesFlow.LpNat BookProof.OperatorSeries

noncomputable section

Formal statement

theorem BookProof.FockQuadratic.norm_hopT (P Q : Idx ι) (x : Idx ι → ℂ) (b : Idx ι) :
    ‖hopT P Q x b‖ = amp P Q b * ‖x (tgt P Q b)‖ * ‖x b‖ := by sorry

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