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Re: [mizar] I am trying to figure out...



Hi Adem,

On Sat, 24 Oct 2009, Ozyavas, Adem wrote:

There are two user-defined sets A and B. The first theorem to be proved is:

   for a,A being set st a being Element of A holds a in A;      ::Q1

It holds if (and only if) A is non-empty.

and the second:

  for f being Function of A,B holds dom f = A;                ::Q2

For Q2 I tried to use

definition
 let X,Y;
 let R be Relation of X,Y;
 attr R is quasi_total means
:: FUNCT_2:def 1

 X = dom R if Y = {} implies X = {}
 otherwise R = {};
end;

and looked into the theorems in FUNCT_2 article. The hypothesis "Y = {} implies X = {}" seems a lot of work and I was wondering if there is another way.

As in the former case, the statement is clearly accepted if Y is non-empty. The condition is formulated in this form just to allow defining functions from X to Y even in a slightly more general situation.

Best,

Adam Naumowicz

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Dept. of Programming and Formal Methods  Fax: +48(85)7457662
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