let p be ext-real number ; :: thesis: for b being real number holds ].-infty,b.] /\ ].p,+infty.[ = ].p,b.]
let b be real number ; :: thesis: ].-infty,b.] /\ ].p,+infty.[ = ].p,b.]
A1: b in REAL by XREAL_0:def 1;
-infty <= p by XXREAL_0:5;
hence ].-infty,b.] /\ ].p,+infty.[ = ].p,b.] by A1, Th159, XXREAL_0:9; :: thesis: verum