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def definition def or abbrev

StabilityEstimate

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formal statement (Lean)

 191def StabilityEstimate (H : ℝ → ℝ) (T a : ℝ) (bounds : StabilityBounds H T) : Prop :=

proof body

Definition body.

 192  ∀ h : ℝ, 0 < h → h ≤ T →
 193  ∀ t : ℝ, |t| ≤ T - h →
 194  |H t - Real.cosh (Real.sqrt a * t)| ≤
 195    (δ_error bounds.ε bounds.B bounds.K h / a) * (Real.cosh (Real.sqrt a * |t|) - 1)
 196
 197/-- The ODE intermediate step: from the defect bound, we derive H'' - a·H is small.
 198
 199This is equation (7.3) in the paper:
 200  |H''(t) - a·H(t)| ≤ δ(h)  for |t| ≤ T - h -/

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