reserve Y for non empty set;

theorem
  for a,b being Function of Y,BOOLEAN holds (a 'or' b)=I_el(Y) &
  'not' a=I_el(Y) implies b=I_el(Y)
proof
  let a,b be Function of Y,BOOLEAN;
  assume that
A1: (a 'or' b)=I_el(Y) and
A2: 'not' a=I_el(Y);
  for x being Element of Y holds b.x=TRUE
  proof
    let x be Element of Y;
    ('not' a).x= TRUE by A2,BVFUNC_1:def 11;
    then
A3: 'not' a.x = TRUE by MARGREL1:def 19;
    (a 'or' b).x= TRUE by A1,BVFUNC_1:def 11;
    then a.x 'or' b.x = TRUE by BVFUNC_1:def 4;
    hence thesis by A3;
  end;
  hence thesis by BVFUNC_1:def 11;
end;
