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 Th11:
  g in ConwayDay(alpha) &
    (x in the_LeftOptions_of g or x in the_RightOptions_of g)
    implies x in ConwayDay(alpha)
proof
  (x in the_LeftOptions_of g or x in the_RightOptions_of g)
    implies x in the_Options_of g by XBOOLE_0:def 3;
  hence thesis by Th10;
end;
