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

theorem Th17: :: MEASURE5:14
  [.r,r.] = {r}
proof
  let s;
  thus s in [.r,r.] implies s in {r}
  proof
    assume s in [.r,r.];
    then ex a st s = a & r <= a & a <= r;
    then s = r by XXREAL_0:1;
    hence thesis by TARSKI:def 1;
  end;
  assume s in {r};
  then
A1: s = r by TARSKI:def 1;
  reconsider s as Element of ExtREAL by XXREAL_0:def 1;
  s <= s;
  hence thesis by A1;
end;
