`nat_diagonal_extraction`

proved

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module: IndisputableMonolith.NavierStokes.FourierExtraction
domain: NavierStokes
line: 159 · github
papers citing: none yet

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IndisputableMonolith.NavierStokes.FourierExtraction on GitHub at line 159.

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formal source

 156
 157/-- **Cantor diagonal extraction** for ℕ-indexed bounded sequences
 158in a proper metric space. Fully proved. -/
 159theorem nat_diagonal_extraction {X : Type*} [MetricSpace X] [ProperSpace X]
 160    (f : ℕ → ℕ → X) (c : X) (R : ℝ)
 161    (hf : ∀ n m, dist (f n m) c ≤ R) :
 162    ∃ (φ : ℕ → ℕ) (g : ℕ → X), StrictMono φ ∧
 163      ∀ m, Tendsto (fun n => f (φ n) m) atTop (𝓝 (g m)) :=
 164  ⟨D f c R hf, CL f c R hf, D_strictMono f c R hf, D_converges f c R hf⟩
 165
 166end IndisputableMonolith.NavierStokes.FourierExtraction

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