# Base change of horizontal divisor in semi-stable curves

Let $$X\rightarrow Spec(O_K)$$ be a semi-stable curve, where $$K$$ is an algebraic number field. Let $$D$$ be a horizontal divisor and finite extension $$K'\supset K$$ contains the splitting field of the function field of $$D$$.

Then how do we know that $$D':=D\times_{Spec(O_K)}Spec(O_{K'})$$ is a section of $$X'=X\times_{Spec(O_K)}Spec(O_{K'})$$?