let s be ext-real number ; for p being real number holds [.-infty,+infty.[ \ ].p,s.] = [.-infty,p.] \/ ].s,+infty.[
let p be real number ; [.-infty,+infty.[ \ ].p,s.] = [.-infty,p.] \/ ].s,+infty.[
p in REAL
by XREAL_0:def 1;
hence
[.-infty,+infty.[ \ ].p,s.] = [.-infty,p.] \/ ].s,+infty.[
by Th329, XXREAL_0:9; verum