Sequence of P-adic Integers has Convergent Subsequence/Proof 1

Lemma 1

 * there exists a sequence $\sequence{b_n}$ of $p$-adic digits:
 * for all $j \in \N$, there exists infinitely many $n \in \N$ such that the canonical expansion of $x_n$ begins with the $p$-adic digits $b_j, \dots, b_1, b_0$