reserve Y for non empty set;

theorem
  for a being Function of Y,BOOLEAN holds a 'or' 'not' a = I_el(Y)
proof
  let a be Function of Y,BOOLEAN;
  let x be Element of Y;
  thus (a 'or' 'not' a).x = a.x 'or' ('not' a).x by BVFUNC_1:def 4
     .= a.x 'or' 'not' a.x by MARGREL1:def 19
     .= TRUE by XBOOLEAN:102
     .= I_el(Y).x by BVFUNC_1:def 11;
end;
