let p, r be ext-real number ; :: thesis: for s being real number st p <= r holds
[.r,s.] c= [.p,+infty .[
let s be real number ; :: thesis: ( p <= r implies [.r,s.] c= [.p,+infty .[ )
s in REAL by XREAL_0:def 1;
then s < +infty by XXREAL_0:9;
hence ( p <= r implies [.r,s.] c= [.p,+infty .[ ) by Th43; :: thesis: verum