let p be ExtReal; :: thesis: for r being Real holds ].r,+infty.] \ [.p,+infty.[ = ].r,p.[ \/ {+infty}
let r be Real; :: 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 Th319, XXREAL_0:3; :: thesis: verum