Ok I will have to disagree with the previous 2 posts. If a previous controller for example tells you to descend FL280 and to cross a point FL310 or below, and then transfers you to me, and I then give you continuous descent to FL150, I would still expect you to meet the previous restriction because it hasn't been specifically cancelled. If I give an amended clearance that clearly precludes you from meeting that restriction, ie. Stop descent FL330, then obviously restriction is cancelled.
Just my opinion a restriction to cross, just like an ATC requirement is only cancelled through specific cancellation not just because you have been given an onwards subsequent clearance. We have a standard height restriction on one of our major inbound routes to Dubai, and if we had to reiterate the restriction to every inbound flight when we further descent we would go under in a second. Just my opinion.