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(* 02110-1301 USA                                                     *)
(* Contribution to the Coq Library   V6.3 (July 1999)                    *)
(* ---                              euclid.v                          ----- *)
(*                                                                          *)
(* Author: Pierre Casteran.                                                 *)
(*    LABRI, URA CNRS 1304,                                                 *)
(*    Departement d'Informatique, Universite Bordeaux I,                    *)
(*    33405 Talence CEDEX,                                                  *)
(*    e-mail:  casteran@labri.u-bordeaux.fr                                 *)
(* Some lemmas about qb+r  ... (useful with euclidean division) *)
(***************************************************)
Hint Resolve lt_b_qbr: arith.
(****************************************************)
Hint Resolve lt_q_qbr: arith.
(****************************************************)
Hint Resolve lt_q_qbr': arith.

Lemma le_q_qbr : forall b q r : nat, 0 < b -> q <= q * b + r.