let p, r be ExtReal; :: thesis: for s being Real st p < r holds
[.r,s.] c= ].p,+infty.[
let s be Real; :: 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 Th47; :: thesis: verum