intros z1 z2; rewrite (Zminus_diag_reverse z2); auto with zarith.
Qed.
Hint Resolve Zle_Zminus_ZERO Zlt_Zminus_ZERO: zarith.

Theorem Zle_Zpred_Zpred :
forall z1 z2 : Z, (z1 <= z2)%Z -> (Zpred z1 <= Zpred z2)%Z.