let s be ExtReal; :: thesis: for p being Real st p <= s holds
[.p,+infty.[ \ ].p,s.] = {p} \/ ].s,+infty.[
let p be Real; :: 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 Th323, XXREAL_0:9; :: thesis: verum