Notation match_states':=
  (fun (idx s1 : state L1) (s2 : state L2) => idx = s1 /\ match_states s1 s2).

Lemma simulation_forever_reactive: forall i s1 s2 T, Forever_reactive L1 s1 T -> match_states i s1 s2 -> Forever_reactive L2 s2 T.