let r, s, p be ext-real number ; :: thesis: ( r <= s implies [.r,+infty .[ \ [.p,s.[ = [.r,p.[ \/ [.s,+infty .[ )
p <= +infty by XXREAL_0:3;
hence ( r <= s implies [.r,+infty .[ \ [.p,s.[ = [.r,p.[ \/ [.s,+infty .[ ) by Th302; :: thesis: verum