let p be ext-real number ; :: thesis: for q being real number st p <= q holds
].-infty ,q.] \ ].p,q.[ = ].-infty ,p.] \/ {q}
let q be real number ; :: thesis: ( p <= q implies ].-infty ,q.] \ ].p,q.[ = ].-infty ,p.] \/ {q} )
q in REAL by XREAL_0:def 1;
then -infty < q by XXREAL_0:12;
hence ( p <= q implies ].-infty ,q.] \ ].p,q.[ = ].-infty ,p.] \/ {q} ) by Th317; :: thesis: verum