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(* modify it under the terms of the GNU Lesser General Public License *)
(* as published by the Free Software Foundation; either version 2.1   *)
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(* but WITHOUT ANY WARRANTY; without even the implied warranty of     *)
(* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the      *)
(* GNU General Public License for more details.                       *)
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(* Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA *)
(* 02110-1301 USA                                                     *)
Require Export MiscRsa.
(******************************************************************************)
Inductive divides : nat -> nat -> Prop :=
dividesDef : forall a b q : nat, b = q * a -> divides a b.
intros a; apply dividesDef with (q := 1); auto with arith.
Qed.

Lemma divides_div :
forall x y : nat, 0 < y -> divides y x -> exists q : _, is_div x y q 0.