(** Proof independence of Qquadratic_Qpositive_to_Qpositive: *)

Scheme quadraticAcc_ind_dep := Induction for quadraticAcc Sort Prop.

Lemma Qquadratic_Qpositive_to_Qpositive_3_OO : forall (a b c d e f g h : Z) (p1 p2 : Qpositive) (hyp : quadraticAcc a b c d e f g h p1 p2), ~ quadratic_top_more a b c d e f g h -> ~ quadratic_top_more e f g h a b c d -> forall xs : Qpositive, p1 = dL xs -> forall ys : Qpositive, p2 = dL ys -> forall hyp_rec : quadraticAcc (a + b + c + d) (b + d) (c + d) d (e + f + g + h) (f + h) (g + h) h xs ys, Qquadratic_Qpositive_to_Qpositive a b c d e f g h p1 p2 hyp = Qquadratic_Qpositive_to_Qpositive (a + b + c + d) (b + d) (c + d) d (e + f + g + h) (f + h) (g + h) h xs ys hyp_rec.