lean_workbook_plus_19738

Let $n \in \mathbb{N}$ and $a_1, a_2, ..., a_{n+1} \in \mathbb{N}$ so that $a_1, a_2, ..., a_{n+1} < 2n$ ( and every two of these numbers are different). Prove that between this $n+1$ numers we can find $3$ , say $a,b,c$ , so that $a+b = c$ .