Definition outside_square (a b c d : Z) :=
  (Z.sgn a + Z.sgn b + Z.sgn c + Z.sgn d)%Z.

Lemma three_integers_dec_inf : forall a b c : Z, {a = 0%Z /\ b = 0%Z /\ c = 0%Z} + {~ (a = 0%Z /\ b = 0%Z /\ c = 0%Z)}.