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

theorem
  ].-infty,s.[ = {g : g<s}
proof
  thus ].-infty,s.[ c= {g : g<s}
  proof
    let x be Real;
    assume
A1: x in ].-infty,s.[;
A2: x < s by A1,Th4;
    thus thesis by A2;
  end;
  let x be object;
  assume x in {g : g<s};
  then consider g such that
A3: x = g and
A4: g < s;
  g in REAL by XREAL_0:def 1;
  then -infty < g by XXREAL_0:12;
  hence thesis by A3,A4,Th4;
end;
