proposition: Lemma succ_cons alpha n beta : beta <> zero -> nf (cons alpha n beta) -> succ (cons alpha n beta) = cons alpha n (succ beta).
proof: Proof. destruct alpha; cbn. - intros H H0; destruct H; apply nf_of_finite with n; auto. - reflexivity. 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)