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

theorem Th39:
  for A being Subset of R^1, a,b being ExtReal st A = ]. a
  ,b .[ holds A is open
proof
  let A be Subset of R^1, a,b be ExtReal;
  ]. a,b .[ is open by Lm6;
  hence thesis by Th38;
end;
