let p, q be ext-real number ; :: thesis: for s being real number st p <= q holds
].-infty,q.] \ ].p,s.] = ].-infty,p.] \/ ].s,q.]
let s be real number ; :: 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 Th307, XXREAL_0:12; :: thesis: verum