a_1 \leq a_2 \leq a_3 \implies a_2 \leq a_3 \leq a_4 \implies \ldots \implies \\ a_n \leq a_{n+1} \leq a_{n+2} \implies a_{n+1} \leq a_{n+2} \leq a_{n+3} \implies\ldots