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

theorem :: INTEGRA1:6 ??
  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,Th50;
A4: q <= s by A1,A2,Th50;
  r <= q by A1,A3,XXREAL_0:2;
  then
A5: r <= s by A4,XXREAL_0:2;
  then
A6: p <= r by A2,Th50;
  s <= q by A2,A5,Th50;
  hence thesis by A3,A4,A6,XXREAL_0:1;
end;
