reserve x for set,
  p,q,r,s,t,u for ExtReal,
  g for Real,
  a for Element of ExtREAL;

theorem
  p < q & [.p,q.[ = [.r,s.[ implies p = r & q = s
proof
  assume that
A1: p < q and
A2: [.p,q.[ = [.r,s.[;
A3: r <= p by A1,A2,Th55;
A4: q <= s by A1,A2,Th55;
  r < q by A1,A3,XXREAL_0:2;
  then
A5: r < s by A4,XXREAL_0:2;
  then
A6: p <= r by A2,Th55;
  s <= q by A2,A5,Th55;
  hence thesis by A3,A4,A6,XXREAL_0:1;
end;
