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

theorem
  r <= p implies [.r,+infty.[ \ {p} = [.r,p.[ \/ ].p,+infty.[
proof
  p <= +infty by XXREAL_0:3;
  hence thesis by Th314;
end;
