Section SIMU_DETERM_ONE.
Hypothesis simulation:
forall s1 t s1', Step L1 s1 t s1' ->
forall s2, match_states s1 s2 ->
exists s1'' s2', Star L1 s1' E0 s1'' /\ Step L2 s2 t s2' /\ match_states s1'' s2'.
End SIMU_DETERM_ONE.
End FORWARD_SIMU_DETERM_DIAGRAMS.
(** * Backward simulations between two transition semantics. *)
Definition safe (L: semantics) (s: state L) : Prop :=
forall s',
Star L s E0 s' ->
(exists r, final_state L s' r)
\/ (exists t, exists s'', Step L s' t s'').

Lemma star_safe:
forall (L: semantics) s s',
Star L s E0 s' -> safe L s -> safe L s'.