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;
