proposition: Lemma nat_lt_cons : forall (n:nat) a p b , rpo (nat_2_term n) (Term ord_cons (a::p::b::nil)).
proof: Proof. induction n;simpl. constructor 2. simpl; trivial. destruct 1. constructor 2. simpl; trivial. inversion_clear 1. subst s';apply IHn. case H0. Qed.
imports: Arith Omega Compare_dec Relations Wellfounded Tools More_nat Wf_nat AccP not_decreasing ArithRing term rpo List