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;
hence ( p <= q implies ].-infty ,q.] \ [.p,q.[ = ].-infty ,p.[ \/ {q} ) by Th319, XXREAL_0:12; :: thesis: verum