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 Th17:
  x in the_Options_of g implies x is ConwayGame-like left-right
proof
  consider alpha such that
A1: g in ConwayDay(alpha) by Def3;
  assume x in the_Options_of g;
  then x in ConwayDay(alpha) by Th10,A1;
  hence thesis by Th4;
end;
