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_nR_4 : forall (a b c d : Z) (p xs : Qpositive) (H_Qhomographic_sg_denom_nonzero : Qhomographic_sg_denom_nonzero c (c + d) xs) (H_Qhomographic_sg_denom_nonzero_nR : Qhomographic_sg_denom_nonzero c d (nR 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 (nR xs) H_Qhomographic_sg_denom_nonzero_nR = Qhomographic_sign a (a + b) c (c + d) xs H_Qhomographic_sg_denom_nonzero.