Fixpoint Qhomographic_sign (a b c d : Z) (p : Qpositive) {struct p} :
  forall (H_Qhomographic_sg_denom_nonzero : Qhomographic_sg_denom_nonzero c d p),
  Z * (Z * (Z * (Z * Z)) * Qpositive).Scheme Qhomographic_sg_denom_nonzero_inv_dep :=
  Induction for Qhomographic_sg_denom_nonzero Sort Prop.

Lemma Qhomographic_sign_dL_3 : forall (a b c d : Z) (p xs : Qpositive) (H_Qhomographic_sg_denom_nonzero : Qhomographic_sg_denom_nonzero c d p), p = dL xs -> b = 0%Z -> d <> 0%Z -> ~ (0 < outside_interval c d)%Z -> (outside_interval c d < 0)%Z -> Qhomographic_sign a b c d p H_Qhomographic_sg_denom_nonzero = ((- Z.sgn a)%Z, (a, (b, (c, d)), p)).