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

theorem
  for f being non empty constant ext-natural-valued Function
  ex N st for x being object st x in dom f holds f.x = N
proof
  let f be non empty constant ext-natural-valued Function;
  consider R being ExtReal such that
    A1: for x being object st x in dom f holds f.x = R by VALUED_0:14;
  set x = the Element of dom f;
  f.x = R & f.x is ext-natural by A1;
  then reconsider N = R as ExtNat;
  take N;
  thus thesis by A1;
end;
