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 Th18:
  (x in the_LeftOptions_of g or x in the_RightOptions_of g)
    implies x is ConwayGame-like left-right
proof
  assume x in the_LeftOptions_of g or x in the_RightOptions_of g;
  then x in the_Options_of g by XBOOLE_0:def 3;
  hence thesis by Th17;
end;
