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_LeftOptions_of -g iff -gO in the_RightOptions_of g)
    & (gO in the_LeftOptions_of g iff -gO in the_RightOptions_of -g)
    & (gO in the_RightOptions_of -g iff -gO in the_LeftOptions_of g)
    & (gO in the_RightOptions_of g iff -gO in the_LeftOptions_of -g)
proof
  g = -(-g) & gO = -(-gO) by Th40;
  hence thesis by Th39;
end;
