reserve a,b,x,y,z,z1,z2,z3,y1,y3,y4,A,B,C,D,G,M,N,X,Y,Z,W0,W00 for set,
  R,S,T, W,W1,W2 for Relation,
  F,H,H1 for Function;

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;
