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 A, Th317; :: thesis: verum