reserve Y for non empty set,
  a,b,c,d for Function of Y,BOOLEAN;

theorem
  a = (b 'imp' a) '&' ('not' b 'imp' a)
proof
  a=(a 'or' b) '&' (a 'or' 'not' b) by BVFUNC_6:80
    .=(a 'or' 'not' 'not' b) '&' (b 'imp' a) by BVFUNC_4:8
    .=('not' b 'imp' a) '&' (b 'imp' a) by BVFUNC_4:8;
  hence thesis;
end;
