I am trying to understand section (3) of the Erratum to P. Scholze's "$p$-adic Hodge theory for rigid-analytic varieties" in detail. In particular, there is the following sentence on page two that I do not understand:

"But the map $$R_{i}^{+}[X_{1},\dots,X_{n}]/(X_{1},\dots,X_{n})^{r} \to \left(R_{i}^{+}\widehat{\otimes}_{W(\kappa)}R_{i}^{+}\right)/(\ker\theta_{i})^{r}$$ is injective, with cokernel killed by a power of $p$, where $\theta_{i} \colon R_{i}^{+}\widehat{\otimes}_{W(\kappa)}R_{i}^{+} \to R_{i}^{+}$ is the multiplication."

I would be grateful, if someone could clarify this for me please.