reserve x,y,y1,y2,z,e,s for set;
reserve alpha,beta,gamma for Ordinal;
reserve n,m,k for Nat;
reserve g,g0,g1,g2,gO,gL,gR,gLL,gLR,gRL,gRR for ConwayGame;

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;
