intros p q H'; rewrite H'.
CaseEq (nat_of_P q); simpl in |- *.
elim q; unfold nat_of_P in |- *; simpl in |- *; intros;
try discriminate.
absurd (0%Z = Zpos p0); auto.
red in |- *; intros H'0; try discriminate.
apply H; auto.
change (nat_of_P p0 = 0) in |- *.
generalize H0; rewrite ZL6; case (nat_of_P p0); simpl in |- *;
auto; intros; try discriminate.
intros n; rewrite <- nat_of_P_o_P_of_succ_nat_eq_succ.
intros H'0; apply f_equal with (f := Zpos).
apply nat_of_P_inj; auto.
Qed.
Hint Resolve inj_le inj_lt: zarith.

(* Specifications: *)
Theorem ZleLe : forall x y : nat, (Z_of_nat x <= Z_of_nat y)%Z -> x <= y.
intros x y H'.