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

theorem Th73:
  for X being compact Subset of R^1, X9 being Subset of REAL, x
  being Real st x in X9 & X9 = X holds lower_bound X9 <= x &
   x <= upper_bound X9
proof
  let X be compact Subset of R^1, X9 be Subset of REAL, x be Real;
  assume that
A1: x in X9 and
A2: X9 = X;
  X9 is bounded_above bounded_below by A2,Th72;
  hence thesis by A1,SEQ_4:def 1,def 2;
end;
