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(* 02110-1301 USA                                                     *)
Unset Standard Proposition Elimination Names.
(** 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.
Local Open Scope Z_scope.
(** Results *)

Lemma divide_left : forall a b c : Z, (a | b) -> (a | b * c).