Fixpoint Qquadratic_sign (a b c d e f g h : Z) (p1 p2 : Qpositive) {struct p1} :
  forall (H_Qquadratic_sg_denom_nonzero : Qquadratic_sg_denom_nonzero e f g h p1 p2),
  Z * (Z * (Z * (Z * Z)) * (Z * (Z * (Z * Z))) * (Qpositive * Qpositive)).Scheme Qquadratic_sg_denom_nonzero_inv_dep :=
  Induction for Qquadratic_sg_denom_nonzero Sort Prop.

Lemma Qquadratic_sign_nRdL_nRdL_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), p1 <> One -> p2 <> One -> b = 0%Z /\ c = 0%Z /\ d = 0%Z -> ~ (f = 0%Z /\ g = 0%Z /\ h = 0%Z) -> ~ (2 < outside_square e f g h)%Z -> (outside_square e f g h < -2)%Z -> Qquadratic_sign a b c d e f g h p1 p2 H_Qquadratic_sg_denom_nonzero = ((- Z.sgn a)%Z, (a, (b, (c, d)), (e, (f, (g, h))), (p1, p2))).