reserve N,M,K for ExtNat;
reserve X for ext-natural-membered set;

theorem ThEx:
  for X being non empty ext-natural-membered set ex N st N in X
proof
  let X be non empty ext-natural-membered set;
  consider x being ExtReal such that
    A1: x in X by MEMBERED:8;
  reconsider N = x as ext-natural ExtReal by A1;
  take N;
  thus thesis by A1;
end;
