proposition: Lemma lt_a_phi0_b_intro : forall a n b, nf (cons a n b) -> b <_phi0 a.
proof: Proof. intros a n b H; unfold nf in H; cbn in H. destruct b. - constructor. - red in H. repeat rewrite andb_true_iff in H. destruct H as ((_, _), Hlt). apply bool_decide_eq_true in Hlt. now right. 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)