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

theorem Th41:
  for A being Subset of R^1, a being Real st A = [. a,
  +infty .[ holds A is closed
proof
  let A be Subset of R^1, a be Real;
  assume
A1: A = [. a,+infty .[;
  [. a,+infty .[ is closed by Lm5;
  hence thesis by A1,JORDAN5A:23;
end;
