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 Th305; :: thesis: verum