
theorem
  for A being non empty Interval st A is right_open_interval holds
  A = [.inf A,sup A.[
proof
  let A be non empty Interval;
  assume A is right_open_interval;
  then consider a being Real,b being R_eal such that
A1: A = [.a,b.[ by MEASURE5:def 4;
  reconsider a as R_eal by XXREAL_0:def 1;
A2: a <= b by A1,XXREAL_1:27;
  then sup A = b by A1,Th15;
  hence thesis by A1,A2,Th11;
end;
