proposition: Lemma lt_a_phi0_b_inv : forall a n b a', lt (cons a n b) (phi0 a') -> lt a a'.
proof: Proof. intros a n b a' H; destruct (lt_inv H); auto. destruct H0 as [H0 | H0]; decompose [and] H0. - abstract lia. - exfalso; eapply not_lt_zero; eassumption. 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)