let p be ext-real number ; :: thesis: for r being real number holds ].r,+infty .] \ [.p,+infty .[ = ].r,p.[ \/ {+infty }
let r be real number ; :: thesis: ].r,+infty .] \ [.p,+infty .[ = ].r,p.[ \/ {+infty }
r in REAL by XREAL_0:def 1;
then A: ( r < +infty & p <= +infty ) by XXREAL_0:3, XXREAL_0:9;
thus ].r,+infty .] \ [.p,+infty .[ = ].r,p.[ \/ {+infty } by Th319, A; :: thesis: verum