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 inside_square_1_inf : forall o1 o2 : Z, inside_square_1 o1 o2 -> {(2 < o1)%Z /\ (2 < o2)%Z} + {(o1 < -2)%Z /\ (o2 < -2)%Z}.