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

theorem Th85: :: MEASURE5:15
  s <= r implies [.r,s.] c= {r} & [.r,s.] c= {s}
proof
  assume
A1: s <= r;
  thus [.r,s.] c= {r}
  proof
    let t;
    assume
A2: t in [.r,s.];
    then
A3: t <= s by Th1;
A4: r <= t by A2,Th1;
    t <= r by A1,A3,XXREAL_0:2;
    then r = t by A4,XXREAL_0:1;
    hence thesis by TARSKI:def 1;
  end;
  let t;
  assume
A5: t in [.r,s.];
  then r <= t by Th1;
  then
A6: s <= t by A1,XXREAL_0:2;
  t <= s by A5,Th1;
  then s = t by A6,XXREAL_0:1;
  hence thesis by TARSKI:def 1;
end;
