(* 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 positive_fraction_encoding.
Definition outside_interval (a b : Z) := (Z.sgn a + Z.sgn b)%Z.
Definition inside_interval_1 (o1 o2 : Z) :=
(0 < o1)%Z /\ (0 < o2)%Z \/ (o1 < 0)%Z /\ (o2 < 0)%Z.
Definition inside_interval_2 (o1 o2 : Z) :=
(0 < o1)%Z /\ (o2 < 0)%Z \/ (o1 < 0)%Z /\ (0 < o2)%Z.

Lemma inside_interval_1_dec_inf :
forall o1 o2 : Z, {inside_interval_1 o1 o2} + {~ inside_interval_1 o1 o2}.