reserve A,X,X1,X2,Y,Y1,Y2 for set, a,b,c,d,x,y,z for object;
reserve P,P1,P2,Q,R,S for Relation;

theorem
  P c= R implies field P c= field R
proof
  assume P c= R;
  then dom P c= dom R & rng P c= rng R by XTUPLE_0:8,9;
  hence thesis by XBOOLE_1:13;
end;
