let p, q be ExtReal; :: thesis: for s being Real st p < q holds
].-infty,q.[ \ ].p,s.] = ].-infty,p.] \/ ].s,q.[
let s be Real; :: 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