let r be ext-real number ; :: thesis: for s being real number holds [.r,+infty .[ \ ].s,+infty .[ = [.r,s.]
let s be real number ; :: thesis: [.r,+infty .[ \ ].s,+infty .[ = [.r,s.]
s in REAL by XREAL_0:def 1;
hence [.r,+infty .[ \ ].s,+infty .[ = [.r,s.] by Th196, XXREAL_0:9; :: thesis: verum