Definition same_ratio (a b c d e f g h : Z) :=
  (a * f)%Z = (b * e)%Z /\
  (b * g)%Z = (c * f)%Z /\
  (c * h)%Z = (d * g)%Z /\
  (a * g)%Z = (c * e)%Z /\ (a * h)%Z = (d * e)%Z /\ (b * h)%Z = (d * f)%Z.

Lemma Qquadratic_sign_tuple_equal : forall (l1 a1 b1 c1 d1 e1 f1 g1 h1 : Z) (x1 y1 : Qpositive) (l2 a2 b2 c2 d2 e2 f2 g2 h2 : Z) (x2 y2 : Qpositive), (l1, (a1, (b1, (c1, d1)), (e1, (f1, (g1, h1))), (x1, y1))) = (l2, (a2, (b2, (c2, d2)), (e2, (f2, (g2, h2))), (x2, y2))) -> l1 = l2 /\ (a1 = a2 /\ b1 = b2 /\ c1 = c2 /\ d1 = d2 /\ e1 = e2 /\ f1 = f2 /\ g1 = g2 /\ h1 = h2) /\ x1 = x2 /\ y1 = y2.