Definition trace (state: Type): Type := stream (state * MetaState state).Identity Coercion trace_stream: trace >-> stream.Definition singleton_trace {state: Type} s ms: trace state :=
  fin_stream ((s, ms) :: nil).

Lemma singleton_trace_n_stream {state: Type}: forall (s: state) ms, is_n_stream 1 (singleton_trace s ms).