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 Th311, XXREAL_0:12; :: thesis: verum