What are some important results of type theory?

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It would be great to have an overview of some of the most important results in type theory.

What are in your opinion some of the most important results/widely applicable results in type theory everyone should know about?

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Maybe the question is a bit inappropriate. But I would like to say that a part of type theory is the use of computer-assisted proof, for example, the LEAN system. In my case it is the only approach I have had to this area. I recommend This question in MO.