let p be ExtReal; :: thesis: ].+infty,p.[ = {}
for x being object holds not x in ].+infty,p.[

proof

given x being object such that A1: x in ].+infty,p.[ ; :: thesis: contradiction
reconsider s = x as ExtReal by A1;
+infty < s by A1, Th4;
hence contradiction by XXREAL_0:3; :: thesis: verum

end;

hence ].+infty,p.[ = {} ; :: thesis: verum