`BookProof.FockQuadratic.hopOp_pairing` (hω : ∀ i, 0 ≤ ω i) {P Q : Idx ι} (hPQ : deg P + deg Q ≤ 2) (hQP : deg Q + deg P ≤ 2) (x y : maxDom (sig ω)) : (inner ℂ (hopOp hω P Q hPQ x

Proved

BookProof.FockQuadratic.hopOp_pairing

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFockQuadraticEsa.

BookProof.FockQuadratic.hopOp_pairing (hω : ∀ i, 0 ≤ ω i) {P Q : Idx ι} (hPQ : deg P + deg Q ≤ 2) (hQP : deg Q + deg P ≤ 2) (x y : maxDom (sig ω)) : (inner ℂ (hopOp hω P Q hPQ x : L2I (Idx ι)) (y : L2I (Idx ι)) : ℂ) = inner ℂ (x : L2I (Idx ι)) (hopOp hω Q P hQP y : L2I (Idx ι))

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

Preamble

-- Generated from ChapterFockQuadraticEsa.lean — theorem BookProof.FockQuadratic.hopOp_pairing
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_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.hopOp_pairing (hω : ∀ i, 0 ≤ ω i) {P Q : Idx ι} (hPQ : deg P + deg Q ≤ 2)
    (hQP : deg Q + deg P ≤ 2) (x y : maxDom (sig ω)) :
    (inner ℂ (hopOp hω P Q hPQ x : L2I (Idx ι)) (y : L2I (Idx ι)) : ℂ)
      = inner ℂ (x : L2I (Idx ι)) (hopOp hω Q P hQP y : L2I (Idx ι)) := by sorry

View graph