theorem
  (gO in the_LeftOptions_of g or gO in the_RightOptions_of g)
    implies ConwayRank(gO) in ConwayRank(g)
proof
  assume gO in the_LeftOptions_of g or gO in the_RightOptions_of g;
  then gO in the_Options_of g by XBOOLE_0:def 3;
  hence thesis by Th14;
end;
