Let $\mathfrak{X}$ be an admissible formal scheme and $x\in X:=\mathfrak{X}^{\textup{an}}$. Let $V$ be the closure of $\{\red(x)\}$ in the special fibre $\tilde{\mathfrak{X}}$. Then $V$ is proper if and only if the morphism $\tilde{X_{x}}\rightarrow\boldsymbol{P}_{\widetilde{\mathscr{H}(x)}/\tilde{K}}$ is bijective.