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(* as published by the Free Software Foundation; either version 2.1   *)
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(* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the      *)
(* GNU General Public License for more details.                       *)
(*                                                                    *)
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(* 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_1 :
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)
(Hg : g <> 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 c g Hg.