proposition: Lemma nf_cons_inv a n b : nf (cons a n b) -> nf a /\ nf b /\ lt b (phi0 a).
proof: Proof. unfold nf; cbn; destruct b. - repeat split; auto with T1. - intro H; red in H; repeat rewrite andb_true_iff in H; decompose [and] H; repeat split; auto. apply bool_decide_eq_true in H1; red in H1. red; cbn; destruct (compare b1 a); try discriminate. trivial. 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)