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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   *)
(* of the License, or (at your option) any later version.             *)
(*                                                                    *)
(* This program is distributed in the hope that it will be useful,    *)
(* 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.                       *)
(*                                                                    *)
(* You should have received a copy of the GNU Lesser General Public   *)
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(* 02110-1301 USA                                                     *)
Require Export Q_field.
intros n m; case m; case n; auto; intros n' m'; simpl in |- *;
rewrite Qpositive_mult_sym; auto.
Qed.
intros n m p; case p; case m; case n; auto; intros n' m' p'; simpl in |- *;
rewrite Qpositive_mult_assoc; auto.
Qed.
intros n; case n; auto.
Qed.
intros n; case n; simpl in |- *; auto; intros; rewrite Qpositive_mult_One;
auto.
Qed.

Theorem Q_opp_def : forall n : Q, Qplus n (Qopp n) = Zero.