theorem Th64:
  for F being closed Subset-Family of T holds F c= BorelSets T
proof
  let F be closed Subset-Family of T;
  F c= BorelSets T
  proof
    let x be object;
    assume
A1: x in F;
    then reconsider xx = x as Subset of T;
    xx is closed by A1,TOPS_2:def 2;
    hence thesis by Def3;
  end;
  hence thesis;
end;
