(* 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 Zaux.
Require Export Qpositive.
Require Export Q_field.
Inductive fractionalAcc : Z -> Z -> Prop :=
| fractionalacc0 : forall m n : Z, m = n -> fractionalAcc m n
| fractionalacc1 :
forall m n : Z,
(0 < m)%Z ->
(m < n)%Z -> fractionalAcc m (n - m)%Z -> fractionalAcc m n
| fractionalacc2 :
forall m n : Z,
(0 < n)%Z ->
(n < m)%Z -> fractionalAcc (m - n)%Z n -> fractionalAcc m n.

Lemma fractionalacc_0 : forall m : Z, fractionalAcc m m.