proposition: Lemma head_lt : forall alpha alpha' n n' beta beta', lt alpha alpha' -> lt (cons alpha n beta) (cons alpha' n' beta').
proof: Proof. unfold lt. intros * H. rewrite compare_cons. now rewrite H. 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)