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RE: [mizar] Question about environments



Hi,

On Fri, 8 Jan 2010, James Smith wrote:

thanks kindly for your replies. I've spent the day sifting through them and
digging around the MML again. From a beginner's standpoint it does seem a
shame that the attributes natural, real, complex, etc are not equivalent to
Element of NAT, REAL, COMPLEX, etc without explicit reference.

The 'Element of' modes are mostly remnants of "the old way of writing in Mizar", and their use should be gradually eliminated in most cases, so the lack of automatic equivalence won't be that bad, afterall.

I wondered about these definitions at the time, but I'm pretty sure I
understand their utility now. Presumably they would become redundant if the
aforementioned equivalences were indeed set up?

They surely will when a bigger part of MML is revised to use 'real number' instead of 'Element of REAL' :-)

Moving on, given that the answer to my original question was an unequivocal
'no', I've changed the offending definition from...

definition
 let n be number;
 attr n is square means
  ex m being Nat st n = m^2;
::>                        *103
end;

If that is the only problem, you just need a reservation saying that natural numbers are also real numbers, so that the definition of ^2 can be matched - use XREAL_0 for that.

Best,

Adam

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