Can I use one variation template parameter when creating a new one?

I am writing a hoist that is supposed to hoist a variable arity function into some std :: vectors which is like a SQL table with an index. I want to apply the f parameter to every set of elements that have the same id across all vectors. I had a problem with the template output and I overtook it here (minus the iterator logic). I wrote what I think is a reasonable recursive affair, but boilerplate inference considers it not viable.

// Simple container type
template <typename T>
struct A {
  T x;
  T y;
  T z;
};

// Wrapper type to differentiate an extracted value from a container
// in template deduction
template <typename T>
struct B {
  T value;
};

// Base case. All A<Ts> have been extracted to B<Ts>.
template <typename F, typename... Ts>
void lift (F f, B<Ts> ...bs) {
  // Call f with extracted values
  f(bs.value...);
}

// Recursive case
template <typename F, typename T, typename... Ts, typename Us>
void lift (F f, A<T> a, A<Ts> ...as, B<Us> ...bs) {
  // Copy a value from the beheaded container A<T>.
  B<T> b = {a.x};
  // Append this B<T> to args and continue beheading A<Ts>.
  lift(f, as..., bs..., b);
}

// Test function
template <typename... Ts>
struct Test {
  void operator () (Ts...) {}
};

int main () {

  B<int> b = {1};
  // No errors for the base case
  lift(Test<>());
  lift(Test<int, int>(), b, b);

  // error: no matching function for call to 'lift'
  // The notes refer to the recursive case
  A<int> a = {1,0,0};
  lift(Test<int>(), a); // note: requires at least 3 arguments, but 2 were provided
  lift(Test<int>(), a, a); // note: requires 2 arguments, but 3 were provided
  lift(Test<int>(), a, a, b); // note: requires 2 arguments, but 4 were provided
}

      

        
        
        
      

    

What's wrong with this code?

Ignoring that everything is passed by value here for read / write convenience. Why doesn't it compile?