(* Proof by case analysis: 81 cases in 6 line :-) *)

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}.