(** * Some results about the sign function. *)

Notation Zsgn_Zmult := Z.sgn_mul (only parsing).Notation Zsgn_Zopp := Z.sgn_opp (only parsing).Notation Zsgn_pos := Z.sgn_pos_iff (only parsing).Notation Zsgn_neg := Z.sgn_neg_iff (only parsing).Notation Zsgn_null := Z.sgn_null_iff (only parsing).

Lemma Zsgn_spec x : 0 < x /\ Z.sgn x = 1 \/ 0 = x /\ Z.sgn x = 0 \/ 0 > x /\ Z.sgn x = -1.