let p be ext-real number ; :: thesis: ].p,-infty.[ = {}
for x being set holds not x in ].p,-infty.[

proof

given x being set such that A1: x in ].p,-infty.[ ; :: thesis: contradiction
reconsider s = x as ext-real number by A1;
s < -infty by A1, Th4;
hence contradiction by XXREAL_0:5; :: thesis: verum

end;

hence ].p,-infty.[ = {} by XBOOLE_0:def 1; :: thesis: verum