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

theorem Th15:
  for A being Subset of R^1, a, b being Real st A = ]. a, b
  .[ & a <> b holds Cl A = [. a, b .]
proof
  let A be Subset of R^1, a, b be Real;
  assume that
A1: A = ]. a, b .[ and
A2: a <> b;
  Cl ]. a, b .[ = [. a, b .] by A2,JORDAN5A:26;
  hence thesis by A1,JORDAN5A:24;
end;
