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_equal_strong : forall (a1 a2 b1 b2 c1 c2 d1 d2 : Z) (p1 p2 : Qpositive) (H_ok_1 : Qhomographic_sg_denom_nonzero c1 d1 p1) (H_ok_2 : Qhomographic_sg_denom_nonzero c2 d2 p2), a1 = a2 -> b1 = b2 -> c1 = c2 -> d1 = d2 -> p1 = p2 -> Qhomographic_sign a1 b1 c1 d1 p1 H_ok_1 = Qhomographic_sign a2 b2 c2 d2 p2 H_ok_2.