proposition: Lemma T1is_succ_def alpha (Halpha : nf alpha) : T1is_succ alpha -> {beta | nf beta /\ alpha = succ beta}.
proof: Proof. intro H; destruct (zero_limit_succ_dec Halpha) as [[H0 | H0] | H0]. - subst alpha; discriminate. - rewrite succ_not_limit in H0; trivial. discriminate. - exact H0. Defined.
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)