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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeNov 20th 2011

I felt that we needed an entry titled proof. I added something, but maybe somebody else feels like turning it into a genuine entry.

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeSep 5th 2012
• (edited Sep 5th 2012)

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.

• CommentRowNumber3.
• CommentAuthorTobyBartels
• CommentTimeSep 6th 2012

Your definition of formal proof only works in a specific context, so I generalised it and then noted its implications for that context.

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeSep 6th 2012

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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