I am not sure how to prove complete induction:

P(n) is a statement of variables n. If

(i) P(1), P(2),...,P(m) are true and

(ii)$\displaystyle k\in\mathbb{Z}, \ k\geq m$ if P(i) is true $\displaystyle \forall i\in\mathbb{N}, \ 1\leq i\leq k$ then P(k+1) is true.

How do I prove this?