proposition: Theorem le_phi0 : forall a n b, leq lt (phi0 a) (cons a n b).
proof: Proof. induction n. - intro; apply le_tail; auto with T1. - intros b. apply lt_incl_le. apply le_lt_trans with (cons a n b). + apply IHn. + auto with T1 arith. 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)