:: Built-in Concepts
:: by Andrzej Trybulec
::
:: Received January 1, 1989
:: Copyright (c) 1990-2021 Association of Mizar Users

:: This article documents a part of the Mizar axiomatics - it shows how
:: the primitives of set theory are introduced in the Mizar Mathematical
:: Library.
:: Please note that the notions defined here are not subject to standard
:: verification, so the Mizar verifier and other utilities may report
:: errors when processing this article.

definition

mode object -> object ;

end;

definition

mode set -> object ;

end;

definition

let x, y be object ;
pred x = y;
reflexivity
errorfrm ;
symmetry
errorfrm ;

end;

notation

let x, y be object ;
antonym x <> y for x = y;

end;

definition

let x be object ;
let X be set ;
pred x in X;

end;