# Proof of contention of the wait-free consensus algorithm

I know that this is a known theorem but I can't find its proof. The theorem is:

The write-contention of any $n$-process wait-free consensus algorithm (implemented from any read-modify-write operations) is $n$.

Can someone link me to a proof or an explanation?

For (wait-free) binary consensus, the critical-state argument says that there must exist a state S of the system such that both decisions are still possible starting from S, but for every immediate successor S' of S the decision is determined. Thus we can partition the processors into two teams $\Pi_0$ and $\Pi_1$ such that a step of a processor from team $\Pi_0$ from S eventually results in decision 0 while a step of a processor from team $\Pi_1$ from S eventually results in the decision 1.
Now suppose that, in S, the next step of processor $p_0$ is to modify object $O_1$, and the next step of processor $p_1$ is to modify object $O_2\neq O_1$. Wlog we can assume $p_0\in\Pi_0$ and $p_1\in\Pi_1$. Since $O_2\neq O_1$, the steps of $p_0$ and $p_1$ commute and lead to the same state S'' regardless of their order. Moreover, since $p_0\in\Pi_0$, the consensus decision from S'' is 0. However, since $p_1\in\Pi_1$, the consensus decision from S'' is also 1, which is a contradiction.