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 Th303; :: thesis: verum