1.	Proof by induction
Definition of a leaf as a refresher:
Leaf- a node with no children

Mathematical theorem:
L(I) = I+1; where I denotes the amount internal nodes


Basis Step:
A tree with only one vertex is considered to have one internal node with no children
Thus L(0) holds

Inductive hypothesis:
Imagine a tree with n internal nodes, now remove two sibling leaves at any random node.
Let that sub-tree be T’

Then that sub-tree has n-1 internal nodes.
As a result let y = L(I) = I+1
By algebraic manipulation that implies L(I-1) = I
Hence by inspecting the following formula manipulation one can see that adding two leaves implies increasing the internal node count by 1. As a result the theorem holds because deducting one internal node implies that we remove two leaves.  Hence the inverse holds where adding an internal node yields two new leaves.
 L (n) = I+2-1  I+1