`BookProof.NavierStokesFlow.Carleman.tridiagOp_not_bounded` (c : ℕ → ℂ) (hc : ∀ C : ℝ, ∃ n, C < ‖c n‖) : ¬ ∃ C : ℝ, ∀ f : lpFiniteModes ℕ, ‖tridiagOp c f‖ ≤ C * ‖f‖

Proved

BookProof.NavierStokesFlow.Carleman.tridiagOp_not_bounded

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNavierStokesCarleman.

BookProof.NavierStokesFlow.Carleman.tridiagOp_not_bounded (c : ℕ → ℂ) (hc : ∀ C : ℝ, ∃ n, C < ‖c n‖) : ¬ ∃ C : ℝ, ∀ f : lpFiniteModes ℕ, ‖tridiagOp c f‖ ≤ C * ‖f‖

Formalization note: Lean 4 identifier BookProof.NavierStokesFlow.Carleman.tridiagOp_not_bounded.

Preamble

-- Generated from ChapterNavierStokesCarleman.lean — theorem BookProof.NavierStokesFlow.Carleman.tridiagOp_not_bounded
import Mathlib
import Definitions.Def_ChapterNavierStokesCarleman
import Definitions.Def_ChapterNavierStokesDeficiency
import Definitions.Def_ChapterNavierStokesEsa
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow.JacobiDeficiency
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow.Carleman


open scoped ENNReal



open LpNat DiagonalEsa FullEsa

Formal statement

theorem BookProof.NavierStokesFlow.Carleman.tridiagOp_not_bounded (c : ℕ → ℂ) (hc : ∀ C : ℝ, ∃ n, C < ‖c n‖) :
    ¬ ∃ C : ℝ, ∀ f : lpFiniteModes ℕ, ‖tridiagOp c f‖ ≤ C * ‖f‖ := by sorry

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