Section DETERM_SEM.
Variable L: semantics.
Hypothesis DET: sem_deterministic L.
Ltac use_step_deterministic :=
match goal with
| [ S1: Step L _ ?t1 _, S2: Step L _ ?t2 _ |- _ ] =>
destruct (det_step L DET _ _ _ _ _ S1 S2) as [EQ1 EQ2]; subst
end.
(** Determinism for finite transition sequences. *)

Lemma star_step_diamond:
forall s0 t1 s1, Star L s0 t1 s1 ->
forall t2 s2, Star L s0 t2 s2 ->
exists t,
(Star L s1 t s2 /\ t2 = t1 ** t)
\/ (Star L s2 t s1 /\ t1 = t2 ** t).