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(* 02110-1301 USA                                                     *)
(* Contribution to the Coq Library   V6.3 (July 1999)                    *)
(* ---                     Mult_compl.v                                 ----*)
(*                                                                          *)
(* Author: Pierre Casteran.                                                 *)
(*    LABRI, URA CNRS 1304,                                                 *)
(*    Departement d'Informatique, Universite Bordeaux I,                    *)
(*    33405 Talence CEDEX,                                                  *)
(*    e-mail:  casteran@labri.u-bordeaux.fr                                 *)
(* This file contains some lemmas on multiplication; it is an extension of the module Mult.v *)
(* multiplication is monotonous *)
(******************************************)
Hint Resolve mult_le_l: arith.
(* multiplication is strictly monotonous *)
(******************************************)
Hint Resolve mult_lt_l: arith.
(* same properties at right *)
(*****************************************)
Hint Resolve mult_le_r: arith.
(******************************************)
Hint Resolve mult_lt_r: arith.
(********************************************)
(************************************)
(************************************)
Hint Resolve mult_p_lt_qp mult_p_le_qp: arith.
(***********************************)
(************************************)
Hint Resolve mult_p_lt_pq mult_p_le_pq: arith.
(* exact quotient ******************)

Lemma quotient_positive : forall q n n0 : nat, n = q * n0 -> 0 < n -> 0 < q.