Let $E$ be a well ordered chain semilattice of idempotent ( $E=\{e_{0}, e_{1}, ... , e_{n}, ... \}$ where $e_{i}\leq e_{j}$ if $i\leq j$).
Prove or disprove if $e_{k}e_{h}e_{m}=e_{h}e_{m}$ and $ e_{k}\neq e_{m}, e_{h}\neq e_{m}$. Then ether $e_{k}=id_{E}$ or $e_{k}=e_{h}$.
Thank you