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 r < +infty by XXREAL_0:9;
hence ].r,+infty .] \ ].p,+infty .[ = ].r,p.] \/ {+infty } by Th317, XXREAL_0:3; :: thesis: verum