let r be ext-real number ; for s being real number holds ].r,+infty .[ \ ].s,+infty .[ = ].r,s.]
let s be real number ; ].r,+infty .[ \ ].s,+infty .[ = ].r,s.]
s in REAL
by XREAL_0:def 1;
hence
].r,+infty .[ \ ].s,+infty .[ = ].r,s.]
by Th197, XXREAL_0:9; verum