reserve N,M,K for ExtNat;

theorem ThSubset:
  for X being set holds X is ext-natural-membered iff X c= ExtNAT
proof
  let X be set;
  hereby
    assume A1: X is ext-natural-membered;
    now
      let x be object;
      assume x in X;
      then x is ext-natural by A1;
      hence x in ExtNAT;
    end;
    hence X c= ExtNAT by TARSKI:def 3;
  end;
  assume X c= ExtNAT;
  hence thesis;
end;
