reserve x1, x2, x3, x4, x5, x6, x7 for set;

theorem
  for a being Real holds Cl ]. a,+infty .[ = [. a,+infty .[
proof
  let a be Real;
  reconsider A = ]. a,+infty .[ as Subset of R^1 by TOPMETR:17;
  Cl A = [. a,+infty .[ by Th48;
  hence thesis by JORDAN5A:24;
end;
