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 forever_reactive_inv2:
forall s t1 s1, Star L s t1 s1 ->
forall t2 s2 T1 T2,
Star L s t2 s2 ->
t1 <> E0 -> t2 <> E0 ->
Forever_reactive L s1 T1 ->
Forever_reactive L s2 T2 ->
exists s', exists t, exists T1', exists T2',
t <> E0 /\
Forever_reactive L s' T1' /\
Forever_reactive L s' T2' /\
t1 *** T1 = t *** T1' /\
t2 *** T2 = t *** T2'.