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

theorem
  for s being Real holds ].-infty,s.] = {g : g<=s}
proof
  let s be Real;
  thus ].-infty,s.] c= {g : g<=s}
  proof
    let x be Real;
    assume x in ].-infty,s.];
    then
A1: x <= s by Th2;
    thus thesis by A1;
  end;
  let x be object;
  assume x in {g : g<=s};
  then consider g such that
A2: x = g and
A3: g <= s;
  g in REAL by XREAL_0:def 1;
  then -infty < g by XXREAL_0:12;
  hence thesis by A2,A3,Th2;
end;
