let p, r be ExtReal; :: thesis: ( r <= p implies [.r,+infty.[ \ {p} = [.r,p.[ \/ ].p,+infty.[ )
p <= +infty by XXREAL_0:3;
hence ( r <= p implies [.r,+infty.[ \ {p} = [.r,p.[ \/ ].p,+infty.[ ) by Th314; :: thesis: verum