if the following are true:

• ((length of stack tree) - 1) - index = back_i
• the element at index back_i of stack tree = node (value, cs)
• elements of numbers that are not in tree tree = new_elements
• result of storing (node (value, new_elements)) at index back_i of stack tree = updated

then result of adding numbers to tree tree as children of the node at backwards index index = result of pushing values new_elements to tree updated