Structural Induction

Recall the ADTs defined in the previous lab:

• Tree
• FIFO
• Map

Prove the following properties are true, using structural induction:

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

2. $ \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 $ 2^{height(t)}-1$ nodes.