reserve Y for non empty set;
reserve Y for non empty set;
reserve Y for non empty set;

theorem
  for a,b being Function of Y,BOOLEAN holds a 'or' b = a 'or' (
  'not' a '&' b)
proof
  let a,b be Function of Y,BOOLEAN;
    let x be Element of Y;
    (a 'or' ('not' a '&' b)).x =a.x 'or' ('not' a '&' b).x by BVFUNC_1:def 4
      .=a.x 'or' (('not' a).x '&' b.x) by MARGREL1:def 20
      .=(a.x 'or' ('not' a).x) '&' (a.x 'or' b.x) by XBOOLEAN:9
      .=(a.x 'or' 'not' a.x) '&' (a.x 'or' b.x) by MARGREL1:def 19
      .=TRUE '&' (a.x 'or' b.x) by XBOOLEAN:102
      .=a.x 'or' b.x 
      .=(a 'or' b).x by BVFUNC_1:def 4;
    hence thesis;
end;
