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

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