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_9 : forall (a b c d : Z) (p xs : Qpositive) (H_Qhomographic_sg_denom_nonzero : Qhomographic_sg_denom_nonzero c d p), p = nR xs -> b <> 0%Z -> d <> 0%Z -> ~ inside_interval_1 (outside_interval a b) (outside_interval c d) -> inside_interval_2 (outside_interval a b) (outside_interval c d) -> Qhomographic_sign a b c d p H_Qhomographic_sg_denom_nonzero = ((-1)%Z, (a, (b, (c, d)), p)).