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;
hence ( p <= r implies [.r,s.] c= [.p,+infty.[ ) by Th43, XXREAL_0:9; :: thesis: verum