proposition: Lemma plus_left_absorb : forall a n b c, lt c (phi0 a) -> c + cons a n b = cons a n b.
proof: Proof. cbn; destruct c. - reflexivity. - intro H. simpl. apply lt_inv_strong in H as [Hlt | Heqa Hlt | Heqa Heqn Hlt]. + now apply compare_lt_iff in Hlt as ->. + now apply compare_eq_iff in Heqa as ->. + now apply not_lt_zero in Hlt. 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)