theorem Th29:
  gO in the_Tree_of g implies ConwayRank(gO) c= ConwayRank(g)
proof
  assume
A1: gO in the_Tree_of g;
  per cases by A1,Th28;
    suppose gO = g;
      hence thesis;
    end;
    suppose
      ConwayRank(gO) in ConwayRank(g);
      hence thesis by ORDINAL1:def 2;
    end;
end;
