Definition boule_of_interval x y (h : x < y) :
{c :R & {r : posreal | c - r = x /\ c + r = y}}.
Definition boule_in_interval x y z (h : x < z < y) :
{c : R & {r | Boule c r z /\  x < c - r /\ c + r < y}}.

(* Specifications: *)
Lemma Ball_in_inter : forall c1 c2 r1 r2 x,
Boule c1 r1 x -> Boule c2 r2 x ->
{r3 : posreal | forall y, Boule x r3 y -> Boule c1 r1 y /\ Boule c2 r2 y}.
Lemma Boule_center : forall x r, Boule x r x.
Definition CVU (fn:nat -> R -> R) (f:R -> R) (x:R)
(r:posreal) : Prop :=
forall eps:R,
0 < eps ->
exists N : nat,
(forall (n:nat) (y:R),
(N <= n)%nat -> Boule x r y -> Rabs (f y - fn n y) < eps).