(* This code is copyrighted by its authors; it is distributed under  *)
(* the terms of the LGPL license (see LICENSE and description files) *)
(* Contribution to the Coq Library   V6.3 (July 1999)                    *)
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(*                                                                          *)
(*                   Solange Coupet-Grimal & Line Jakubiec                  *)
(*                                                                          *)
(*                                                                          *)
(*              Laboratoire d'Informatique de Marseille                     *)
(*               CMI-Technopole de Chateau-Gombert                          *)
(*                   39, Rue F. Joliot Curie                                *)
(*                   13453 MARSEILLE Cedex 13                               *)
(*           e-mail:{Solange. Coupet,Line. Jakubiec}@lim.univ-mrs.fr          *)
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(*                                Coq V5.10                                 *)
(*                              May 30th 1996                               *)
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(*                            Lib_Div_Even_Odd.v                            *)
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Require Export Lib_Mult.
(****************************** even/odd *********************************)
Inductive even (n : nat) : Prop :=
even_intro : forall q : nat, n = 2 * q -> even n.
Inductive odd (n : nat) : Prop :=
odd_intro : forall q : nat, n = 2 * q + 1 -> odd n.
(************************* quotients and divisors ***********************)

Lemma no_zero_div :
forall n m : nat, 0 < n -> forall q : nat, n = m * q -> 0 < q.