Open Scope Z_scope.
(** Add [Z.to_euclidean_division_equations] to the end of [zify], just for this file. *)
Ltac zify ::= repeat (zify_nat; zify_positive; zify_N); zify_op; Z.to_euclidean_division_equations.

Lemma Z_zerop_or x : x = 0 \/ x <> 0. Proof. nia. Qed.
Lemma Z_eq_dec_or (x y : Z) : x = y \/ x <> y. Proof. nia. Qed.