
theorem
  for A being non empty Interval st A is open_interval
     holds A = ].inf A,sup A.[
proof
  let A be non empty Interval;
  assume A is open_interval;
  then consider a,b being R_eal such that
A1: A = ].a,b.[ by MEASURE5:def 2;
  sup A = b by A1,XXREAL_1:28,XXREAL_2:32;
  hence thesis by A1,XXREAL_1:28,XXREAL_2:28;
end;
