Definition Zdivide_dec:
  forall (p q: Z), p > 0 -> { (p|q) } + { ~(p|q) }.

(* Specifications: *)
Lemma Zdivide_interval: forall a b c, 0 < c -> 0 <= a < b -> (c | a) -> (c | b) -> 0 <= a <= b - c.
Lemma Zdivide_interval: forall a b c, 0 < c -> 0 <= a < b -> (c | a) -> (c | b) -> 0 <= a <= b - c.