reserve A for set, x,y,z for object,
  k for Element of NAT;
reserve n for Nat,
  x for object;
reserve V, C for set;

theorem Th16:
  V is finite & C is finite implies PFuncs (V, C) is finite
proof
  assume that
A1: V is finite and
A2: C is finite;
  PFuncs(V,C) c= bool [:V,C:] by Th15;
  hence thesis by A1,A2;
end;
