`BookProof.NavierStokesFlow.AffineFiber.affH_not_bounded` {κ c : ℝ} (hκ : 0 < κ) (hc : 0 ≤ c) (C : ℝ) : ∃ n : ℕ, ‖(basisState κ c n : L2I ℕ)‖ = 1 ∧ C < ‖(affH hκ.le hc...

Proved

BookProof.NavierStokesFlow.AffineFiber.affH_not_bounded

by leonardopedro · Oct 9, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNavierStokesAffineFiberEsa.

BookProof.NavierStokesFlow.AffineFiber.affH_not_bounded {κ c : ℝ} (hκ : 0 < κ) (hc : 0 ≤ c) (C : ℝ) : ∃ n : ℕ, ‖(basisState κ c n : L2I ℕ)‖ = 1 ∧ C < ‖(affH hκ.le hc (basisState κ c n) : L2I ℕ)‖

Formalization note: Lean 4 identifier BookProof.NavierStokesFlow.AffineFiber.affH_not_bounded.

Preamble

-- Generated from ChapterNavierStokesAffineFiberEsa.lean — theorem BookProof.NavierStokesFlow.AffineFiber.affH_not_bounded
import Mathlib
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
import Definitions.Def_ChapterNavierStokesHermiteFarisLavine
import Definitions.Def_ChapterNavierStokesIkebeKato
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow.AffineFiber


open scoped ENNReal



open LpNat BookProof.FarisLavine IkebeKato HermiteFarisLavine ShiftHamiltonian

variable {ι : Type*}

variable {F : Type*} [NormedAddCommGroup F] [InnerProductSpace ℂ F] {D : Submodule ℂ F}
variable (P : PairShift ι)

Formal statement

theorem BookProof.NavierStokesFlow.AffineFiber.affH_not_bounded {κ c : ℝ} (hκ : 0 < κ) (hc : 0 ≤ c) (C : ℝ) :
    ∃ n : ℕ, ‖(basisState κ c n : L2I ℕ)‖ = 1
      ∧ C < ‖(affH hκ.le hc (basisState κ c n) : L2I ℕ)‖ := by sorry

View graph