I am watching "[Modal logic 1.2 - truth trees for system K](https://www.youtube.com/watch?v=fkS7cE8PA5I)" presented through [Kane B's channel](https://www.youtube.com/user/kanebaker91/videos).

The standard propositional truth tree diagrams are not a problem. Where I am having trouble is opening worlds in the tree diagram and closing branches with these opened worlds. I don't see why I am justified in closing a whole branch if some worlds in that branch do not have a contradiction in them.

At about 14:00 in the video the presenter states, "If we derive a contradiction in either of these worlds the whole branch closes." 

Shouldn't we close all worlds prior to closing the whole branch? 

Here is a screenshot of the tree:

[![enter image description here](https://i.stack.imgur.com/JPOwl.png)](https://i.stack.imgur.com/JPOwl.png)

I don't see why stacking the worlds justifies the step. Creating world "w2" was not permitted without the stacking.