Tube lemma

Okay kiddo, listen up! Imagine you have a big map of a city with lots of different streets and buildings. Now imagine you need to draw a line on the map that goes from one side of the city to the other side, but you can only draw the line on certain streets.

The tube lemma is like a special trick that helps you draw that line more easily. It says that if you have a bunch of smaller lines on your map that all start in one place and end in another place, then you can connect all of those lines with a big tube-shaped line, kind of like a tunnel, that also goes from the starting place to the ending place.

This can be really helpful because instead of trying to figure out all the different paths you could take to get from the starting place to the ending place, you can just draw the big tube-shaped line and know that it will work!

So that's the tube lemma, it's like a special shortcut that helps you draw lines on a map more easily. Pretty cool, huh?