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 Th8:
  (x in the_Options_of ConwayStar iff x = ConwayZero)
    & (x in the_LeftOptions_of ConwayStar iff x = ConwayZero)
    & (x in the_RightOptions_of ConwayStar iff x = ConwayZero)
proof
  the_LeftOptions_of ConwayStar = {ConwayZero}
    & the_RightOptions_of ConwayStar = {ConwayZero}
    by Def6,Def7;
  hence thesis by TARSKI:def 1;
end;
