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 [.s,+infty.[ = {g : s<=g}
proof
  let s be Real;
  thus [.s,+infty.[ c= {g : s<=g}
  proof
    let x be Real;
    assume x in [.s,+infty.[;
    then
A1: s <= x by Th3;
    thus thesis by A1;
  end;
  let x be object;
  assume x in {g : s<=g};
  then consider g such that
A2: x = g and
A3: s <= g;
  g in REAL by XREAL_0:def 1;
  then g < +infty by XXREAL_0:9;
  hence thesis by A2,A3,Th3;
end;
