(* 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 Qquadratic.
Functional Scheme Qquadratic_Qpositive_to_Q_ind :=
Induction for Qquadratic_Qpositive_to_Q Sort Prop.

Lemma Qquadratic_Qpositive_to_Q_3 :
forall (a b c d e f g h : Z) (p1 p2 : Qpositive)
(H_Qquadratic_sg_denom_nonzero : Qquadratic_sg_denom_nonzero e f g h p1 p2)
(He : e <> 0%Z),
same_ratio a b c d e f g h ->
Qquadratic_Qpositive_to_Q a b c d e f g h p1 p2
H_Qquadratic_sg_denom_nonzero = fraction_encoding a e He.