theorem
  for p being Real holds
  r < s implies ].r,+infty.[ \ ].p,s.] = ].r,p.] \/ ].s,+infty.[
proof
  let p be Real;
  p in REAL by XREAL_0:def 1;
  then p < +infty by XXREAL_0:9;
  hence thesis by Th305;
end;
