# 1.10 Recursive Definition

## Counting Cases

If for a structural induction proof, there are 3 base cases and 4 different constructors, how many cases (i.e. specific $$P(x)$$'s) must be considered?

Exercise 1

Explanation

Each of the base cases must be proved, as well as each of the constructors $$P(c(x))$$, assuming $$P(x)$$ is true.

3+4 gives 7.