(** Proof independence of Qquadratic_Qpositive_to_Qpositive: *)
Scheme quadraticAcc_ind_dep := Induction for quadraticAcc Sort Prop.

(* Specifications: *)
Lemma Qquadratic_Qpositive_to_Qpositive_equal :
forall (a b c d e f g h : Z) (p1 p2 : Qpositive)
(hyp1 hyp2 : quadraticAcc a b c d e f g h p1 p2),
Qquadratic_Qpositive_to_Qpositive a b c d e f g h p1 p2 hyp1 =
Qquadratic_Qpositive_to_Qpositive a b c d e f g h p1 p2 hyp2.
Lemma Qquadratic_Qpositive_to_Qpositive_equal_strong :
forall (a1 a2 b1 b2 c1 c2 d1 d2 e1 e2 f1 f2 g1 g2 h1 h2 : Z)
(x1 x2 y1 y2 : Qpositive)
(hyp1 : quadraticAcc a1 b1 c1 d1 e1 f1 g1 h1 x1 y1)
(hyp2 : quadraticAcc a2 b2 c2 d2 e2 f2 g2 h2 x2 y2),
a1 = a2 ->
b1 = b2 ->
c1 = c2 ->
d1 = d2 ->
e1 = e2 ->
f1 = f2 ->
g1 = g2 ->
h1 = h2 ->
x1 = x2 ->
y1 = y2 ->
Qquadratic_Qpositive_to_Qpositive a1 b1 c1 d1 e1 f1 g1 h1 x1 y1 hyp1 =
Qquadratic_Qpositive_to_Qpositive a2 b2 c2 d2 e2 f2 g2 h2 x2 y2 hyp2.