theorem Th19:
  dom(P*R) c= dom P
proof
  let x be object;
  assume x in dom(P*R);
  then consider y being object such that
A1: [x,y] in P*R by XTUPLE_0:def 12;
  ex z st [x,z] in P & [z,y] in R by A1,Def6;
  hence thesis by XTUPLE_0:def 12;
end;
