Corollary 2

Let $A$ be a Krull domain, $K$ its field of fractions and $(v_t)_{t \in I}$ a family of valuations with the properties of Definition 3. Then every essential valuation of $A$ is equivalent to one of the $v_t$.

Let $P$ be an extremal divisor of $A$ and $p$ the corresponding divisorial ideal. By Corollary 1, Proposition 5, Lemma 1 and assertion (1) in the proof of Theorem 2, no. 3, there exists $t \in I$ such that the ring $A_t$ of $v_t$ contains the ring $A$, of $v_P$. As $v_t$ and $v_P$ are of height 1, they are therefore equivalent (Chapter VI, § 4, no. 5, Proposition 6).