# Spaced proof review as a way to understand key insights in a proof

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One time I completely forgot the trick for how to even get started proving Löb's theorem. (That's sort of a good thing because I wasn't just relying on a memorized trick!) Eventually I remembered that Löb's theorem had something to do with the Santa Claus sentence, which I wrote down as "If this sentence is true, then Santa Claus exists". So then I realized I wanted something like $T \vdash L \leftrightarrow (L \to \varphi)$. But then I remembered that actually it's not just the bare sentence, but there was a provability predicate somewhere. And that's when I remembered that we are supposed to diagonalize $\mathrm{Bew}(x) \to \varphi$. So, $T \vdash L \leftrightarrow (\Box L \to \varphi)$. Previously, I think it was somewhat mysterious to me why I should diagonalize that particular formula (like, where that formula even comes from).