CoInductive possible_traceinf: world -> traceinf -> Prop :=
  | possible_traceinf_cons: forall w1 ev w2 T,
      possible_event w1 ev w2 ->
      possible_traceinf w2 T ->
      possible_traceinf w1 (Econsinf ev T).CoInductive possible_traceinf: world -> traceinf -> Prop :=
  | possible_traceinf_cons: forall w1 ev w2 T,
      possible_event w1 ev w2 ->
      possible_traceinf w2 T ->
      possible_traceinf w1 (Econsinf ev T).Definition possible_behavior (w: world) (b: program_behavior) : Prop :=
  match b with
  | Terminates t r => exists w', possible_trace w t w'
  | Diverges t => exists w', possible_trace w t w'
  | Reacts T => possible_traceinf w T
  | Goes_wrong t => exists w', possible_trace w t w'
  end.

(* Specifications: *)
Lemma possible_traceinf'_traceinf: forall w T, possible_traceinf' w T -> possible_traceinf w T.
Lemma possible_traceinf'_traceinf: forall w T, possible_traceinf' w T -> possible_traceinf w T.