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