(** Intermediate Value Theorem on an Interval (Proof mainly taken from Reals.Rsqrt_def) and its corollary *)

Lemma IVT_interv : forall (f : R -> R) (x y : R),
(forall a, x <= a <= y -> continuity_pt f a) ->
x < y ->
f x < 0 ->
0 < f y ->
{z : R | x <= z <= y /\ f z = 0}.