Cut-elimination theorem

Have you ever played with paper and scissors, and cut out a bunch of little shapes? Sometimes you end up with a bunch of scraps of paper that you don't really need anymore. Cut-elimination theorem is a bit like that, but with math instead of paper.

In math, people use a lot of symbols and expressions to describe things. Sometimes, they use these symbols to come up with a proof, which is like a really detailed explanation that shows why something is true. Just like cutting out shapes from paper, people can also cut out parts of a proof that they don't need anymore.

The cut-elimination theorem says that no matter how many times you cut things out of a proof, you can always make it shorter and simpler. So if you keep cutting and cutting, eventually you'll get to the simplest possible proof for that thing.

It's kind of like taking away all the extra scraps of paper so that you're left with just the shapes you need. The cut-elimination theorem helps mathematicians get rid of all the unnecessary parts of a proof, so that they can see the real important stuff.