Section Alpha.
Definition alpha x t := 1/2 * (u0 (x + c * t) + u0 (x - c * t)).
Definition alpha20 x t := 1/2 * (Derive_n u0 2 (x + c * t) + Derive_n u0 2 (x - c * t)).
Definition alpha02 x t := c^2/2 * (Derive_n u0 2 (x + c * t) + Derive_n u0 2 (x - c * t)).
End Alpha.
Parameter u1 : R -> R.
Hypothesis Du1 : forall x, ex_derive (fun u => u1 u) x.

Lemma Cu1 : forall x, continuity_pt (fun u => u1 u) x.