proposition: Lemma nf_LT_iff : forall alpha n beta, nf (cons alpha n beta) <-> nf alpha /\ nf beta /\ beta t1< phi0 alpha.
proof: Proof. split. intros H. repeat split; eauto with T1. apply lt_a_phi0_b_phi0. eapply lt_a_phi0_b_intro; eauto. intro H; decompose [and] H. apply nf_intro; eauto. apply lt_a_phi0_b_phi0R. destruct H3; tauto. Qed.
imports: Coq(Arith Max Bool Lia Compare_dec Relations Ensembles Wellfounded Bool RelationClasses Operators_Properties ArithRing Logic.Eqdep_dec) hydras(More_Arith Restriction DecPreOrder) hydras(OrdNotations)