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def definition def or abbrev

symmetric_second_diff_limit_hypothesis

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formal statement (Lean)

 859def symmetric_second_diff_limit_hypothesis (H : ℝ → ℝ) (t : ℝ) : Prop :=

proof body

Definition body.

 860  H 0 = 1 → Continuous H → (∀ t u, H (t+u) + H (t-u) = 2 * H t * H u) →
 861    HasDerivAt (deriv H) 1 0 → Filter.Tendsto (fun u => (H (t+u) + H (t-u) - 2 * H t) / u^2) (nhds 0) (nhds (H t))
 862
 863end Constructive
 864
 865/-! ## Aczél's Theorem and the ODE Derivation
 866
 867These results close the five regularity hypothesis gaps in `washburn_uniqueness`.
 868After adding the single Aczél axiom, all five `_hypothesis` defs become provable, and
 869a clean no-hypothesis version of the uniqueness theorem follows.
 870-/
 871
 872/-- The `dAlembert_continuous_implies_smooth_hypothesis` holds for every H,
 873    as a direct consequence of the Aczél axiom. -/

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