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. *)
Ltac use_star_step_diamond :=
match goal with
| [ S1: Star L _ ?t1 _, S2: Star L _ ?t2 _ |- _ ] =>
let t := fresh "t" in let P := fresh "P" in let EQ := fresh "EQ" in
destruct (star_step_diamond _ _ _ S1 _ _ S2)
as [t [ [P EQ] | [P EQ] ]]; subst
end.
Ltac use_nostep :=
match goal with
| [ S: Step L ?s _ _, NO: Nostep L ?s |- _ ] => elim (NO _ _ S)
end.
Ltac use_star_step_triangle :=
match goal with
| [ S1: Star L _ ?t1 _, S2: Star L _ ?t2 ?s2, NO: Nostep L ?s2 |- _ ] =>
let t := fresh "t" in let P := fresh "P" in let EQ := fresh "EQ" in
destruct (star_step_triangle _ _ _ _ _ S1 S2 NO)
as [t [P EQ]]; subst
end.
(** Determinism for infinite transition sequences. *)

Lemma star2_final_not_forever_silent:
forall s t1 s1 t2 s2,
Star L s t1 s1 -> Nostep L s1 ->
Star L s t2 s2 -> Forever_silent L s2 ->
False.