intros z; case z.
3: intros p H'; Contradict H'; auto with zarith.
replace (Zsucc 0) with (Z_of_nat 1).
intros H'; rewrite absolu_INR; simpl in |- *; auto.
simpl in |- *; auto.
intros p H'; rewrite <- Zpos_succ_morphism; simpl in |- *; auto with zarith.
unfold nat_of_P in |- *; rewrite Pmult_nat_succ_morphism; auto.
Qed.
Hint Resolve Zlt_le_succ: zarith.

Theorem Zlt_next :
forall n m : Z, (n < m)%Z -> m = Zsucc n \/ (Zsucc n < m)%Z.