(* This program is free software; you can redistribute it and/or      *)
(* 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   *)
(* License along with this program; if not, write to the Free         *)
(* Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA *)
(* 02110-1301 USA                                                     *)
Require Export Qpositive_le.
Require Export Qpositive_plus_mult.
(* These tactics were originally in a different file, but moved here *)
Ltac make_fraction w p q Heq := elim (interp_non_zero w); intros p (q, Heq).
Ltac expand a b c d p q Heq Heq1 Heq2 :=
elim (construct_correct2' c a b);
[ intros d; elim (interp_non_zero (Qpositive_c a b c)); intros p (q, Heq);
rewrite Heq; unfold fst, snd in |- *; intros (Heq1, Heq2)
| try (simpl in |- *; auto with arith; fail)
| try (simpl in |- *; auto with arith; fail)
| auto ].

Theorem Qpositive_le_add :
forall w w' w'' : Qpositive,
Qpositive_le w w' ->
Qpositive_le (Qpositive_plus w w'') (Qpositive_plus w' w'').