(* 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_Square.v                               *)
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Require Export Lib_Exp.
Definition Square (n : nat) := n * n.
intro.
unfold Square in |- *.
elim exp_2_n_plus_m.
rewrite plus_mult; reflexivity.
Qed.
Hint Resolve Square_exp_2.
unfold Square in |- *.
simpl in |- *.
intro; elim (mult_comm 1 n); simpl in |- *; auto with arith.
Qed.
Hint Resolve eq_Square_exp_n.
intros.
unfold Square in |- *.
apply le_mult_csts; assumption.
Qed.
Hint Resolve Square_inc.
intros.
unfold Square in |- *.
apply lt_mult_csts; assumption.
Qed.
Hint Resolve Square_strict_inc.

Lemma le_n_Square : forall n : nat, n <= Square n.