Definition cond_positivity (x:R) : bool :=
  match Rle_dec 0 x with
    | left _ => true
    | right _ => false
  end.

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