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

theorem
  for a being Real holds ].-infty,p.[ /\ [.a,+infty.[ = [.a,p.[
proof
  let a be Real;
  a in REAL by XREAL_0:def 1;
  then -infty < a by XXREAL_0:12;
  hence thesis by Th154,XXREAL_0:3;
end;
