theorem Th6:
  g = ConwayZero iff the_Options_of g = {}
proof
  hereby
    assume g = ConwayZero;
    then the_LeftOptions_of g = {} & the_RightOptions_of g = {};
    hence the_Options_of g = {};
  end;
  hereby
    reconsider w = g as strict left-right by Th4;
    assume the_Options_of g = {};
    then the_LeftOptions_of g = {} & the_RightOptions_of g = {};
    then the LeftOptions of w = {} & the RightOptions of w = {}
      by Def6,Def7;
    hence g = ConwayZero;
  end;
end;
