theorem Th1:
  x in dom tan implies cos.x<>0
proof
  assume x in dom tan;
  then x in dom sin /\ (dom cos \ cos"{0}) by RFUNCT_1:def 1;
  then x in dom cos \ cos"{0} by XBOOLE_0:def 4;
  then x in dom (cos^) by RFUNCT_1:def 2;
  hence thesis by RFUNCT_1:3;
end;
