intros n; case n; auto.
intros H'; Contradict H'; auto.
intros n0 H'; rewrite inj_S; rewrite <- Zpred_succ; auto.
Qed.

Theorem Zle_abs : forall p : Z, (p <= Z_of_nat (Zabs_nat p))%Z.
intros p; case p; simpl in |- *; auto with zarith; intros q;
rewrite inject_nat_convert with (p := Zpos q);
auto with zarith.