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_Options_of g implies the_Tree_of gO c= the_proper_Tree_of g
proof
  assume
A1: gO in the_Options_of g;
  the_Options_of g c= the_proper_Tree_of g by Th33;
  hence thesis by Th35,A1;
end;
