`BookProof.NavierStokesFlow.BilinearEsa.bilH_not_bounded` (κ : J → ℝ) (hunb : ∀ C : ℝ, ∃ j, C < κ j) (C : ℝ) : ∃ x : lpFiniteModes (ℕ × J), ‖((x : lpFiniteModes (ℕ × J)) :...

Proved

BookProof.NavierStokesFlow.BilinearEsa.bilH_not_bounded

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNavierStokesBilinearEsa.

BookProof.NavierStokesFlow.BilinearEsa.bilH_not_bounded (κ : J → ℝ) (hunb : ∀ C : ℝ, ∃ j, C < κ j) (C : ℝ) : ∃ x : lpFiniteModes (ℕ × J), ‖((x : lpFiniteModes (ℕ × J)) : L2I (ℕ × J))‖ = 1 ∧ C < ‖bilH κ x‖

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

Preamble

-- Generated from ChapterNavierStokesBilinearEsa.lean — theorem BookProof.NavierStokesFlow.BilinearEsa.bilH_not_bounded
import Mathlib
import Definitions.Def_ChapterNavierStokesBilinearEsa
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_not_bounded (κ : J → ℝ) (hunb : ∀ C : ℝ, ∃ j, C < κ j) (C : ℝ) :
    ∃ x : lpFiniteModes (ℕ × J),
      ‖((x : lpFiniteModes (ℕ × J)) : L2I (ℕ × J))‖ = 1 ∧ C < ‖bilH κ x‖ := by sorry

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