theorem
  [a,b] in R implies a in field R & b in field R
proof
  assume
A1: [a,b] in R;
  then a in dom R by XTUPLE_0:def 12;
  hence a in field R by XBOOLE_0:def 3;
  b in rng R by A1,XTUPLE_0:def 13;
  hence thesis by XBOOLE_0:def 3;
end;
