proposition: Lemma nf_cons_iff a n b : nf (cons a n b) <-> nf a /\ nf b /\ lt b (phi0 a).
proof: Proof. split. - apply nf_cons_inv. - intros [H1 [H2 H3]]; destruct b. + now apply single_nf. + apply cons_nf; eauto with T1. destruct (lt_inv H3); trivial. decompose [or and] H. * lia. * exfalso; eapply not_lt_zero; eauto. 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)