Supermartingale with constant Expectation is a martingale
Fix $t\geq s$. Then $M_s-E[M_t\mid M_s]$ is a non-negative random variable. Its expectation is $$E[M_s]-E[E[M_t\mid M_s]]=E[M_s]-E[M_t]=0$$ by assumption.
A non-negative random variable $X$ with $0$ expectation is $0$ almost everywhere, since $$P(X\geq 2^{-n})\leq 2^nE X=0.$$