====== Structural Induction ======

Recall the ADTs defined in the previous lab:
  * ''Tree''
  * ''FIFO''
  * ''Map''

Prove the following properties are true, using structural induction:

1. $math[\forall t\in \texttt{Tree}. size(t) \geq height(t)]

2. $math[\forall t \in \texttt{Tree}. flatten(mirror(t)) = reverse(flatten(t))]

Find a proper formulation and prove the following properties:

1. Merging (using the strategy from ''Mergesort'') two sorted lists produces a sorted list.

2. A complete binary tree always has $math[2^{height(t)}-1] nodes.