proposition: Lemma prec_transitive : transitive A prec.
proof: Proof. intros s1 s2 s3;destruct s1, s2, s3; simpl; intros; trivial; contradiction. Qed.
imports: Coq(Arith Lia Compare_dec Relations Wellfounded Wf_nat List Bool Eqdep_dec Ensembles ArithRing Logic) hydras(More_Arith Restriction DecPreOrder rpo.term rpo.rpo Epsilon0.T1)