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_4 : forall (a b c d : Z) (p xs : Qpositive) (H_Qhomographic_sg_denom_nonzero : Qhomographic_sg_denom_nonzero (c + d) d xs) (H_Qhomographic_sg_denom_nonzero_dL : Qhomographic_sg_denom_nonzero c d (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 (dL xs) H_Qhomographic_sg_denom_nonzero_dL = Qhomographic_sign (a + b) b (c + d) d xs H_Qhomographic_sg_denom_nonzero.