Proof: By Proposition 5.13, there is a very affine open subset $U$ of $X$ such that ${\rm supp}(\alpha)\subset{U^{\rm an}}$ and such that $\alpha$ is given on ${U^{\rm an}}$ by a superform $\alpha_{U}\in A^{2n-1}_{c}({\rm Trop}(U))$. Then $U$ is a very affine chart of integration for $d^{\prime}\alpha$ and $d^{\prime\prime}\alpha$ and the claim follows from Proposition 3.5. $\square$