(** Proof independence of Qquadratic_Qpositive_to_Qpositive: *)

Scheme quadraticAcc_ind_dep := Induction for quadraticAcc Sort Prop.

Lemma Qquadratic_Qpositive_to_Qpositive_3_II : 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 = nR xs -> forall ys : Qpositive, p2 = nR ys -> forall hyp_rec : quadraticAcc a (a + b) (a + c) (a + b + c + d) e (e + f) (e + g) (e + f + g + h) xs ys, Qquadratic_Qpositive_to_Qpositive a b c d e f g h p1 p2 hyp = Qquadratic_Qpositive_to_Qpositive a (a + b) (a + c) (a + b + c + d) e (e + f) (e + g) (e + f + g + h) xs ys hyp_rec.