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 Th16:
  not g in the_Options_of g
proof
  assume not thesis;
  then ConwayRank(g) in ConwayRank(g) by Th14;
  hence contradiction;
end;
