Inductive forward_simulation (L1 L2: semantics) : Prop :=
  Forward_simulation (index: Type)
                     (order: index -> index -> Prop)
                     (match_states: index -> state L1 -> state L2 -> Prop)
                     (props: fsim_properties L1 L2 index order match_states).Inductive forward_simulation (L1 L2: semantics) : Prop :=
  Forward_simulation (index: Type)
                     (order: index -> index -> Prop)
                     (match_states: index -> state L1 -> state L2 -> Prop)
                     (props: fsim_properties L1 L2 index order match_states).

Lemma forward_simulation_star_wf: forward_simulation L1 L2.