Ltac coinductive_case CIH :=
    apply W_tl; simpl in *; auto;
    apply CIH; simpl in *; auto.

Lemma InputLock_eventually_MsgLock : forall c s, lb_step_execution lb_step_async s -> weak_fairness lb_step_async label_silent s -> now (occurred (InputLock c)) s -> eventually (now (occurred (MsgLock c))) s.