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

theorem
  'not' a '&' (a 'xor' b) = 'not' a '&' b
proof
  thus ('not' a) '&' (a 'xor' b) = ('not' a) '&' (('not' a '&' b) 'or' (a '&'
  'not' b)) by BVFUNC_4:9
    .= (('not' a) '&' ('not' a '&' b)) 'or' (('not' a) '&' (a '&' 'not' b))
  by BVFUNC_1:12
    .= ('not' a '&' 'not' a '&' b) 'or' (('not' a) '&' (a '&' 'not' b)) by
BVFUNC_1:4
    .= ('not' a '&' b) 'or' ('not' a '&' a '&' 'not' b) by BVFUNC_1:4
    .= ('not' a '&' b) 'or' (O_el(Y) '&' 'not' b) by BVFUNC_4:5
    .= ('not' a '&' b) 'or' O_el(Y) by BVFUNC_1:5
    .= 'not' a '&' b by BVFUNC_1:9;
end;
