Global Instance finType_rsig: finTypeC (EqType rsig).Definition rsig_finType : finType := (@FinType (EqType rsig) finType_rsig).Definition halting_states : list (states T) :=
    List.filter (fun s => halt s) (elem (states T)).Definition not_halting_states : list (states T) :=
    List.filter (fun s => negb (halt s)) (elem (states T)).

Lemma not_halting (q: states T) : halt q = false <-> q el not_halting_states.