Let $E$ be an ordinary elliptic curve defined over a non-perfect field $K$ of characteristic $p$. If $P \in E(K)$ satisfies $P \not\in [p]E(K)$, is it true that its $p^m$-division points of $P$ are defined in inseparable $p^m$-degree extensions? Say, if $[p^m]P_m = P$, then $[K(P_m):K]_i \geq p^m$? Thanks in advance.