strong principle of mathematical induction

Formally, to prove that $P(n)$ holds for $n\ge n_0$ via strong induction:

1. Base Case: Prove $P(m)$ for all $m$ such that $n_0\le m\le n_k$, where $n_k\ge n_0$.
2. Induction Hypothesis: Let $n\ge n_k$ be arbitrary but fixed, and assume that $P(m)$ holds for $n_0\le m\le n$.
3. Induction Step: Assuming the induction hypothesis, show that $P(n+1)$ holds.