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

theorem Th40:
  for A being Subset of R^1, a being Real st A = ]. -infty,
  a.] holds A is closed
proof
  let A be Subset of R^1, a be Real;
  assume
A1: A = ]. -infty,a.];
  ]. -infty,a.] is closed by Lm4;
  hence thesis by A1,JORDAN5A:23;
end;
