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

theorem
  for a being Real holds Cl ]. -infty, a .[ = ]. -infty, a .]
proof
  let a be Real;
  reconsider A = ]. -infty, a .[ as Subset of R^1 by TOPMETR:17;
  Cl A = ]. -infty, a .] by Th50;
  hence thesis by JORDAN5A:24;
end;
