Prove2Me

`BookProof.FockQuadratic.pairOp_symmetricOn` (hω : ∀ i, 0 ≤ ω i) (g : ℂ) (P Q : Idx ι) (hPQ : deg P + deg Q ≤ 2) : SymmetricOn (maxDom (sig ω)) (pairOp hω g P Q hPQ)

Proved
BookProof.FockQuadratic.pairOp_symmetricOn

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFockQuadraticEsa.

BookProof.FockQuadratic.pairOp_symmetricOn (hω : ∀ i, 0 ≤ ω i) (g : ℂ) (P Q : Idx ι) (hPQ : deg P + deg Q ≤ 2) : SymmetricOn (maxDom (sig ω)) (pairOp hω g P Q hPQ)

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

Preamble
-- Generated from ChapterFockQuadraticEsa.lean — theorem BookProof.FockQuadratic.pairOp_symmetricOn
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_ChapterNavierStokesIkebeKato
open BookProof.ChapterA3n
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_symmetricOn (hω : ∀ i, 0 ≤ ω i) (g : ℂ) (P Q : Idx ι)
    (hPQ : deg P + deg Q ≤ 2) : SymmetricOn (maxDom (sig ω)) (pairOp hω g P Q hPQ) := by sorry

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