erdos_1105_paths

For $n \geq k \geq 5$, let $\ell = \lfloor(k-1)/2\rfloor$ and $\epsilon = 1$ if $k$ odd, else $2$. Is $\mathrm{AR}(n, P_k) = \max\left(\binom{k-2}{2}+1,\; \binom{\ell-1}{2}+(\ell-1)(n-\ell+1)+\epsilon\right)$?

theorem erdos_1105_paths : answer(sorry) ↔
    ∀ (k n : ℕ), 5 ≤ k → k ≤ n →
    let ℓ

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