
theorem Th13:
  for A being non empty Interval, b being ExtReal st ex a being
  ExtReal st a <= b & A = ].a,b.] holds b = sup A
proof
  let A be non empty Interval, IT be ExtReal;
  given a being ExtReal such that
A1: a <= IT and
A2: A = ].a,IT.];
  a <> IT by A2;
  then a < IT by A1,XXREAL_0:1;
  hence thesis by A2,XXREAL_2:30;
end;
