proposition: Lemma plus_cons_cons_rw1 : forall a n b a' n' b', lt a a' -> cons a n b + cons a' n' b' = cons a' n' b'.
proof: Proof. simpl; destruct a. - destruct a'. + inversion 1. + intros * H. now apply compare_lt_iff in H as ->. - destruct a'; inversion 1. now apply compare_lt_iff in H as ->. 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)