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 Th4:
  g is strict left-right
proof
  consider alpha such that
A1: g in ConwayDay(alpha) by Def3;
  ex w being strict left-right st w = g &
    for x st x in (the LeftOptions of w) \/ (the RightOptions of w)
      ex beta st beta in alpha & x in ConwayDay(beta) by A1,Th1;
  hence thesis;
end;
