reserve x,y,z, X,Y,Z for set,
  n for Element of NAT;
reserve A for set,
  D for non empty set,
  a,b,c,l,r for Element of D,
  o,o9 for BinOp of D,
  f,g,h for Function of A,D;
reserve G for non empty multMagma;

theorem Th30:
  chi(Y,X) is Multiset of X
proof
  rng chi(Y,X) c= {0,1};
  then
A1: rng chi(Y,X) c= NAT by XBOOLE_1:1;
  dom chi(Y,X) = X & carr(MultiSet_over X) = Funcs(X,NAT)
  by Th26,FUNCT_3:def 3;
  hence thesis by A1,FUNCT_2:def 2;
end;
