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I’m older than Morgyn but I’m obsessed with the massive little brother energy I give off half the time
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this is a post to remind me to post about path induction in HoTT now that I’m feeling at least a bit better. posting this proto-post so that it’s, like, a Real Post I can come back to
gist of what I want to say: the reason it “works” is because, like with other inductive types, you never have to actually compute with what path induction gives you until it matches the constructor (refl)! it doesn’t do anything magical to actually get from something defined on refl to something defined on all paths, it just says “yeah, you can formally generalize from these circumstances” and defers computation until you’re actually back in those circumstances
