Added missing steps and fixed typos.

src/fa/tvs/metric.tex

@@ -76,7 +76,7 @@
     $(4) \Rightarrow (1)$: By \autoref{definition:tvs-pseudonorm-topology}, for each $r > 0$, $\rho^{-1}([0, r)) \in \cn_E(0)$. Thus for any $x, y \in E$, if $x - y \in \rho^{-1}([0, r))$, then $\abs{\rho(x) - \rho(y)} \le r$. Therefore $\rho \in UC(E; [0, \infty))$.
 \end{proof}
 
-\begin{lemma}[{{\cite[Theorem I.6.1]{SchaeferWolff}}}]
+\begin{lemma}[]
 \label{lemma:tvs-sequence-pseudonorm}
     Let $E$ be a vector space over $K \in \RC$, $\seq{U_n} \subset 2^E$ such that
     \begin{enumerate}
@@ -89,7 +89,7 @@
     \]
 
 \end{lemma}
-\begin{proof}
+\begin{proof}[Proof {{\cite[Theorem I.6.1]{SchaeferWolff}}}.]
     For each $H \subset \natp$ finite, let
     \[
     U_H = \sum_{n \in H}V_n \quad \rho_H = \sum_{n \in H}2^{-n}