lean_workbook_plus_55065

Given a sequence $a_1,a_2,...,a_{99}$ of one-digit numbers with the poperty that if for some $n$ we have $a_n = 1$ , then $a_{n + 1}\neq 2$ ; and if for some $n$ we have $a_n = 3$ , then $a_{n + 1}\neq 4$ . Prove that exist two number $k,l\in\{1,2,...,98\}$ such that $a_k = a_l$ and $a_{k + 1} = a_{l + 1}$ .