Corollary 2

— If L is an algebraic and separable extension of a field K, the canonical mapping $\alpha : \Omega_P(K) \otimes_K L \to \Omega_P(L)$ is an isomorphism for every subfield P of K.

The mapping $\alpha$ is injective by Prop. 2 (V, p. 128) and Prop. 4, b); since $\Omega_K(L)$ reduces to 0 (Cor. 1) the exactness the sequence $(E_{P.K.L})$ implies that $\alpha$ is surjective.