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;
hence ( p <= q implies ].-infty,q.] \ ].p,s.[ = ].-infty,p.] \/ [.s,q.] ) by Th299, XXREAL_0:12; :: thesis: verum