Now, now Spikey; the lad was just asking a simple question.
Yes the cabin will have to climb (if you are to keep your windows and other pressure hull fittings in place) as dictated to by the outflow/safety valves. How much it climbs though, will depend on what the max. press. diff. of the airframe is. With a high diff. you might climb the 4000' and find the cabin has only gone up by 1800'.
