Functional Scheme Qquadratic_Qpositive_to_Q_ind :=
Induction for Qquadratic_Qpositive_to_Q Sort Prop.

(* Specifications: *)
Lemma Qquadratic_Qpositive_to_Q_0 :
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)
(Hh : h <> 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 d h Hh.
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.
Lemma Qquadratic_Qpositive_to_Q_2 :
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)
(Hf : f <> 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 b f Hf.
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.