Lemma 13.1. Assuming that:

$M ∕ L ∕ K$ finite separable extensions of local fields

Then

(i) $f_{M ∕ K} = f_{L ∕ K} f_{M ∕ L}$
(ii) $e_{M ∕ K} = e_{L ∕ K} f_{M ∕ L}$