
theorem
  for A being non empty Interval st A is left_open_interval holds
   A = ].inf A,sup A.]
proof
  let A be non empty Interval;
  assume A is left_open_interval;
  then consider a being R_eal,b being Real such that
A1: A = ].a,b.] by MEASURE5:def 5;
A2: a <= b by A1,XXREAL_1:26;
  reconsider b as R_eal by XXREAL_0:def 1;
  sup A = b by A2,A1,Th13;
  hence thesis by A1,XXREAL_1:26,XXREAL_2:27;
end;
