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    $\begingroup$ Normal forms are overrated. $\endgroup$
    – Andrej Bauer
    Commented Feb 8, 2022 at 22:18
  • $\begingroup$ @GuyCoder I don't see why this technical concept would appear here. A lot of systems use normal forms for one reason or another, but this is an irrelevant detail from the perspective of this question. $\endgroup$
    – Gilles 'SO- stop being evil'
    Commented Feb 9, 2022 at 11:00
  • $\begingroup$ I like this answer, but could you modify it a little bit? I never meant to imply that proof assistants can only prove tautologies. They prove lots of different things by deriving tautologies. What's proven is whatever hypothesis we started with. Am I right in believing all this, or do the aspects of perfectoid spaces, etc. address this belief of mine too? If so, could you please elaborate on that? $\endgroup$
    – prash
    Commented Feb 9, 2022 at 15:11
  • $\begingroup$ Your question implies that proof assistant only prove logical statements (which you phrased in a slightly unfortunate way mentioning "tautologies"). In reality they are used to define all sorts of elaborate concepts and construct complicated mathematical objects, which is the point of my first paragraph. I have modified it to better reflect the sentiment. $\endgroup$
    – Andrej Bauer
    Commented Feb 9, 2022 at 16:13
  • $\begingroup$ Is this better? $\endgroup$
    – Andrej Bauer
    Commented Feb 9, 2022 at 16:15