Question 1: Power function, over natural numbers

Recall the OCaml power function over natural numbers, shown below:

let rec power n x =

match n with

| 0 -> 1.0

| _ -> x *. power (n-1) x

Using induction over natural numbers show that

power n x = x^n.

Your proof must explicitly and clearly indicate the base case you prove, the inductive case you

prove and what the inductive hypothesis provides in the proof.

Each step in your proof must be accompanied by a justication describing why that step could be

taken.