Mathematical induction

Formally, assume $n\text{nat}$ means that $n$ is a natural number. To prove that whenever $n\text{nat}$, we have $𝒫(n)$, it's sufficient to show that:

1. $𝒫(\text{zero})$.

2. For every $n$ such that $n\text{nat}$, if $𝒫(n)$ then $𝒫(\text{succ}(n))$.