theorem Th27:
  x is Multiset of X iff x is Function of X,NAT
proof
A1: now
    let x be Function of X,NAT;
    dom x = X & rng x c= NAT by FUNCT_2:def 1;
    hence x is Element of Funcs(X,NAT) by FUNCT_2:def 2;
  end;
  x is Multiset of X iff x is Element of Funcs(X,NAT) by Th26;
  hence thesis by A1;
end;
