Section FORWARD_SIMULATIONS.
Context L1 L2 index order match_states (S: fsim_properties L1 L2 index order match_states).
End FORWARD_SIMULATIONS.

Theorem forward_simulation_behavior_improves:
forall L1 L2, forward_simulation L1 L2 ->
forall beh1, program_behaves L1 beh1 ->
exists beh2, program_behaves L2 beh2 /\ behavior_improves beh1 beh2.