Prove that the following statements are equivalent.
1-) The Cartesian product of a non-empty family of non-empty sets is also non-empty, i.e, $\{A_i: i \in I\}, I\neq \emptyset, A_i \neq \emptyset \Rightarrow \Pi _{i \in I} A_i \neq \emptyset$
2-) all non-empty collection of non-empty sets admits function choice, i.e, $\tau \neq \emptyset , \forall A \in \tau , A \neq \emptyset \Rightarrow \exists f:\tau \to \bigcup \{A: A \in \tau\}$ where $A \to f(A) \in A$
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