Equivalent forms of Jensen's diamond principle

Question

I try to prove that these four statements are equivalent:

1. $\Diamond$
2. There are $A_\alpha\subseteq \alpha\times\alpha$ for $\alpha<\omega_1$ s.t. for all $A\subset \omega_1\times\omega_1$, $\{\alpha<\omega_1:A\cap\alpha\times\alpha=A_\alpha\}$ is stationary.
3. There are $f_\alpha:\alpha\to\alpha$ $\alpha<\omega_1$ s.t. for each $f:\omega_1\to\omega_1$, $\{\alpha:f\upharpoonright\alpha=f_\alpha\}$ is stationary.
4. There are $f_\alpha:\alpha\to\alpha$ $\alpha<\omega_1$ s.t. for each $f:\omega_1\to\omega_1$, there is $\alpha>0$ such that $f\upharpoonright \alpha=f_\alpha$.

I prove that 1, 2 and 3 are equivalent and 3 implies 4, but I don't know how to prove the equivalence of 4 and 1. I try to prove that 4 implies 3 or $\lnot 2$ implies $\lnot 3$ however I have a struck. Thanks for any hints.