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 Th34:
  the_Options_of g c= the_Tree_of g
proof
  the_Options_of g c= the_proper_Tree_of g by Th33;
  hence thesis by XBOOLE_1:1;
end;
