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 = (a 'or' b) '&' (a
  'or' 'not' b)
proof
  let a,b be Function of Y,BOOLEAN;
    let x be Element of Y;
    ((a 'or' b) '&' (a 'or' 'not' b)).x =(a 'or' (b '&' 'not' b)).x by
BVFUNC_1:11
      .=(a 'or' O_el(Y)).x by BVFUNC_4:5
      .=a.x by BVFUNC_1:9;
    hence thesis;
end;
