Hi Bill,
>Freek's miz3 code in the miz3 dox 1201.3601-1.pdf
>solving the drinker's paradox on p 13--14 is perhaps designed to show
>various features of miz3, but it is more than twice as long as needed:
It's mainly intended to be as close as possible to the
Jaśkowsky/Fitch-style natural deduction proof that's right
before it, to show off the similarity of the proof styles.
That one you _can't_ make significantly shorter, because only
the basic natural deduction intro and elim rules are allowed.
But if you want to be short, then
let DRINKER = thm `;
let P be A->bool;
thus ?x. P x ==> !y. P y`;;
already works. Getting a short proof, or even a proof
that mimics how a human would understand this, was not
the primary aim of the example. And yes, showing off the
various miz3 proof steps _was_ one of its aims.
If you like to see a _really_ involved proof of this
statement, then look at
http://www.cs.ru.nl/~freek/notes/drinker.miz
Now that's a silly version, as Mizar also can prove this
without any help. But this one would also work in a minimal
logic version of Mizar :-)
Freek
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