proposition: Theorem le_lt_trans : forall a b c, a <= b -> b < c -> a < c.
proof: Proof. destruct 1. subst b;auto. intros;eapply lt_trans;eauto. Qed.
imports: Arith Omega Compare_dec Relations Wellfounded Tools More_nat Wf_nat AccP not_decreasing ArithRing term rpo List