`BookProof.FockQuadratic.pairOp_commForm_le` (hω : ∀ i, 0 ≤ ω i) (g : ℂ) (P Q : Idx ι) (hPQ : deg P + deg Q ≤ 2) (x : maxDom (sig ω)) : |commForm (pairOp hω g P Q hPQ) (diagMax (si

Proved

BookProof.FockQuadratic.pairOp_commForm_le

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFockQuadraticEsa.

BookProof.FockQuadratic.pairOp_commForm_le (hω : ∀ i, 0 ≤ ω i) (g : ℂ) (P Q : Idx ι) (hPQ : deg P + deg Q ≤ 2) (x : maxDom (sig ω)) : |commForm (pairOp hω g P Q hPQ) (diagMax (sig ω)) x| ≤ (4 * ‖g‖ * (wsum ω P + wsum ω Q + 2)) * quadForm (diagMax (sig ω)) x

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

Preamble

-- Generated from ChapterFockQuadraticEsa.lean — theorem BookProof.FockQuadratic.pairOp_commForm_le
import Definitions.Def_ChapterFarisLavine
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
import Definitions.Def_ChapterNavierStokesDeficiency
import Definitions.Def_ChapterOperatorSeriesEsa
import Mathlib
import Definitions.Def_ChapterFockQuadraticEsa
import Definitions.Def_ChapterA3n
import Definitions.Def_ChapterFarisLavineCore
import Definitions.Def_ChapterNavierStokesHermiteFarisLavine
import Definitions.Def_ChapterNavierStokesIkebeKato
open BookProof.ChapterA3n
open BookProof.NavierStokesFlow.HermiteFarisLavine
open BookProof.NavierStokesFlow.IkebeKato
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.pairOp_commForm_le (hω : ∀ i, 0 ≤ ω i) (g : ℂ) (P Q : Idx ι)
    (hPQ : deg P + deg Q ≤ 2) (x : maxDom (sig ω)) :
    |commForm (pairOp hω g P Q hPQ) (diagMax (sig ω)) x|
      ≤ (4 * ‖g‖ * (wsum ω P + wsum ω Q + 2)) * quadForm (diagMax (sig ω)) x := by sorry

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