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 outside_square_9 : forall a b c d : Z, (outside_square a b c d < -2)%Z -> (c <= 0)%Z.