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

Lemma InputLock_Lock : forall s c, lb_step_execution lb_step_async s -> now (occurred (InputLock c)) s -> next (fun s => In (mkPacket (Client c) Server Lock) (nwPackets (evt_a (hd s)))) s.