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 Th316; :: thesis: verum