intros p0 H'; unfold nat_of_P in |- *; simpl in |- *; rewrite ZL6.
generalize H'; case (nat_of_P p0); auto.
intros p0 H'; unfold nat_of_P in |- *; simpl in |- *; rewrite ZL6.
generalize H'; case (nat_of_P p0); simpl in |- *; auto.
unfold nat_of_P in |- *; simpl in |- *; auto with arith.
Qed.
Hint Resolve convert_not_O: zarith arith.
Hint Resolve Zlt_le_weak Zle_not_gt Zgt_irrefl Zlt_irrefl Zle_not_lt
Zlt_not_le Zlt_asym inj_lt inj_le: zarith.

Theorem inj_abs :
forall x : Z, (0 <= x)%Z -> Z_of_nat (Zabs_nat x) = x.