(** The order tactic enriched with some knowledge of 0,1,2 *)

(** The difference between integers and natural numbers is that for every integer there is a predecessor, which is not true for natural numbers. However, for both classes, every number that is bigger than some other number has a predecessor. The proof of this fact by regular induction does not go through, so we need to use strong (course-of-value) induction. *)
Theorem lt_exists_pred :
forall z n, z < n -> exists k, n == S k /\ z <= k.