“All your proof are belong to us“
The first way we learn to do proofs is by induction. Proofs by induction are done in three steps. First, we establish a base case. Next we assume a hypothesis, and finally, we prove the inductive step. As an example let us consider the fact that the sum $0+1+2+ \ldots+n$ is $n(n+1)/2$. The three steps are:
Base case: consider the series $0+1$, the sum is $1$, and the formula is $1(2)/2$.