The Principle of Induction:
Goal: Collection of statements $ P_0,P_1...P_i $ that we want to prove. Idea: Prove $ P_0 $ explicitly. Design a crank/elevator that proves the following Since $ P_0 $ has been proven to be true, it shows that there is at least one$ P_i $ which is true. We have to show that $ P_{i+1} $ is also true. Then, induction guarantees that every $ P_i $ is true.
