let s be ext-real number ; :: thesis: for p being real number st p <= s holds
[.p,+infty.[ \ ].p,s.[ = {p} \/ [.s,+infty.[
let p be real number ; :: thesis: ( p <= s implies [.p,+infty.[ \ ].p,s.[ = {p} \/ [.s,+infty.[ )
p in REAL by XREAL_0:def 1;
hence ( p <= s implies [.p,+infty.[ \ ].p,s.[ = {p} \/ [.s,+infty.[ ) by Th321, XXREAL_0:9; :: thesis: verum