let r, p be ext-real number ; :: 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