theorem Th1:
 for x being object holds
  x in field R iff ex y being object st ([x,y] in R or [y,x] in R)
proof let x be object;
  x in (dom R \/ rng R) iff x in dom R or x in rng R by XBOOLE_0:def 3;
  hence thesis by RELAT_1:def 6,XTUPLE_0:def 12,def 13;
end;
