
theorem
  for A being non empty Interval st A is closed_interval holds
    A = [.inf A,sup A.]
proof
  let A be non empty Interval;
  assume A is closed_interval;
  then consider a,b being Real such that
A1: A = [.a,b.] by MEASURE5:def 3;
A2: a <= b by A1,XXREAL_1:29;
  reconsider b as R_eal by XXREAL_0:def 1;
  sup A = b by A1,A2,XXREAL_2:29;
  hence thesis by A1,A2,XXREAL_2:25;
end;
