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

proof

given x being set such that A1: x in ].+infty ,p.[ ; :: thesis: contradiction
reconsider s = x as ext-real number by A1;
( +infty < s & s < p ) by A1, Th4;
hence contradiction by XXREAL_0:3; :: thesis: verum

end;

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