`BookProof.NavierStokesFlow.BilinearEsa.bilH_symmetricOn` (κ : J → ℝ) (hκ : ∀ j, 0 ≤ κ j) : SymmetricOn (lpFiniteModes (ℕ × J)) (bilH κ)

Proved

BookProof.NavierStokesFlow.BilinearEsa.bilH_symmetricOn

by leonardopedro · Oct 17, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNavierStokesBilinearEsa.

BookProof.NavierStokesFlow.BilinearEsa.bilH_symmetricOn (κ : J → ℝ) (hκ : ∀ j, 0 ≤ κ j) : SymmetricOn (lpFiniteModes (ℕ × J)) (bilH κ)

Formalization note: Lean 4 identifier BookProof.NavierStokesFlow.BilinearEsa.bilH_symmetricOn.

Preamble

-- Generated from ChapterNavierStokesBilinearEsa.lean — theorem BookProof.NavierStokesFlow.BilinearEsa.bilH_symmetricOn
import Mathlib
import Definitions.Def_ChapterNavierStokesBilinearEsa
import Definitions.Def_ChapterFarisLavineCore
import Definitions.Def_ChapterNavierStokesEsa
import Definitions.Def_ChapterNavierStokesHermiteFarisLavine
import Definitions.Def_ChapterNavierStokesIkebeKato
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow.BilinearEsa


open scoped ENNReal



open LpNat BookProof.FarisLavine IkebeKato HermiteFarisLavine

variable {J : Type*}

Formal statement

theorem BookProof.NavierStokesFlow.BilinearEsa.bilH_symmetricOn (κ : J → ℝ) (hκ : ∀ j, 0 ≤ κ j) :
    SymmetricOn (lpFiniteModes (ℕ × J)) (bilH κ) := by sorry

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