(** Divisibility *)

Inductive divide (a b : Z) : Prop :=
    divide_intro : forall q : Z, b = (q * a)%Z -> divide a b.(** Divisibility *)

Inductive divide (a b : Z) : Prop :=
    divide_intro : forall q : Z, b = (q * a)%Z -> divide a b.Notation "( x | y )" := (divide x y) (at level 0) : Z_scope.

Lemma divide_plus : forall a b c : Z, (a | b) -> (a | c) -> (a | b + c).