intros z1 z2 H; apply Zsucc_lt_reg; rewrite <- Zsucc_pred; auto with zarith.
Qed.
Hint Resolve Zle_Zpred_Zlt: zarith.

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