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
  a 'nor' (a 'nor' b) = 'not' a '&' b
proof
  thus a 'nor' (a 'nor' b) = 'not' a '&' (a 'or' b) by Th38
    .= ('not' a '&' a) 'or' ('not' a '&' b) by BVFUNC_1:12
    .= O_el(Y) 'or' ('not' a '&' b) by BVFUNC_4:5
    .= 'not' a '&' b by BVFUNC_1:9;
end;
