theorem
  field(P \/ R) = field P \/ field R
proof
  thus field(P \/ R) = dom P \/ dom R \/ rng(P \/ R) by XTUPLE_0:23
    .= dom P \/ dom R \/ (rng P \/ rng R) by XTUPLE_0:27
    .= dom P \/ dom R \/ rng P \/ rng R by XBOOLE_1:4
    .= field P \/ dom R \/ rng R by XBOOLE_1:4
    .= field P \/ field R by XBOOLE_1:4;
end;
