Consider Case 3 (taken from slide 51 in Lecture-5-AVLTrees.pdf and shown below). On the left is t...

Consider Case 3 (taken from slide 51 in Lecture-5-AVLTrees.pdf and shown below). On the left is the subtree S' rooted at z that results from inserting key k into an AVL tree T. On the right is the subtree S rooted at node x which is the result of restructuring at node z in S'. Prove that the height of S is equal to the height of S, the subtree rooted at z prior to inserting key k.