reserve Y for non empty set;
reserve B for Subset of Y;

theorem
  for a,b,c being Function of Y,BOOLEAN
   holds a '&' b '&' c = a '&' (b '&' c)
proof
  let a,b,c be Function of Y,BOOLEAN;
  let x be Element of Y;
  thus (a '&' b '&' c).x = (a '&' b).x '&' c.x by MARGREL1:def 20
       .= a.x '&' b.x '&' c.x by MARGREL1:def 20
       .= a.x '&' (b.x '&' c.x)
       .= a.x '&' (b '&' c).x by MARGREL1:def 20
       .= (a '&' (b '&' c)).x by MARGREL1:def 20;
end;
