
theorem Th11:
  for A being non empty Interval, a being ExtReal st
   ex b being ExtReal st a <= b & A = [.a,b.[ holds a = inf A
proof
  let A be non empty Interval, IT be ExtReal;
  given b being ExtReal such that
A1: IT <= b and
A2: A = [.IT,b.[;
  IT <> b by A2;
  then IT < b by A1,XXREAL_0:1;
  hence thesis by A2,XXREAL_2:26;
end;
