Lemma 31.13.8. Let $X$ be a scheme. Let $D, D'$ be two effective Cartier divisors on $X$. If $D \subset D'$ (as closed subschemes of $X$), then there exists an effective Cartier divisor $D''$ such that $D' = D + D''$.

**Proof.**
Omitted.
$\square$

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