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I felt that we needed an entry titled proof. I added something, but maybe somebody else feels like turning it into a genuine entry.
I used to be very unhappy with the entry proof. Now I read Robert Harper’s little exposition Extensionality, Intensionality, and Brouwer’s Dictum and now I am happy. I moved some of this into the entry.
Your definition of formal proof only works in a specific context, so I generalised it and then noted its implications for that context.
Okay, thanks.
I remember I was wondering about this point re Gödel’s theorem when reading in Martin-Löf’s lecture notes the piece where he emphasizes in great length that
true $\Leftrightarrow$ has a proof
which is of course the whole point of all of constructivism/ type theory. Still, put this way a Gödel-alarm bell tends to go off.
So it’s good to know how to switch that alarm off:
true $\Leftarrow$ has formal proof
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