proposition: Lemma head_lt_cons : forall a n b, lt a (cons a n b).
proof: Proof. induction a; auto with T1. 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)