let q be ext-real number ; :: thesis: for p being real number st p <= q holds
].-infty ,q.] \ {p} = ].-infty ,p.[ \/ ].p,q.]
let p be real number ; :: thesis: ( p <= q implies ].-infty ,q.] \ {p} = ].-infty ,p.[ \/ ].p,q.] )
p in REAL by XREAL_0:def 1;
then -infty < p by XXREAL_0:12;
hence ( p <= q implies ].-infty ,q.] \ {p} = ].-infty ,p.[ \/ ].p,q.] ) by Th315; :: thesis: verum