let p, q be ext-real number ; :: thesis: for s being real number st p <= q holds
].-infty ,q.[ \ [.p,s.[ = ].-infty ,p.[ \/ [.s,q.[
let s be real number ; :: thesis: ( p <= q implies ].-infty ,q.[ \ [.p,s.[ = ].-infty ,p.[ \/ [.s,q.[ )
s in REAL by XREAL_0:def 1;
then -infty < s by XXREAL_0:12;
hence ( p <= q implies ].-infty ,q.[ \ [.p,s.[ = ].-infty ,p.[ \/ [.s,q.[ ) by Th301; :: thesis: verum