Centering of stacked bussproofs trees

Question

I like to stack proof rules build with bussproofs vertically. In order to use tags and labels I enclose the proof tress inside a equation, which is why I introduced the rawprooftree environment as suggested earlier in Numbering sequent proofs like equations. Directly enclosing bussproofs trees does not work.

However, the resulting stack is ugly, because the rules are not centered. How can I achieve that the proof trees are centered relative to each other?

The code is as follows:

\documentclass[fontsize=11pt,paper=a4,headsepline,footsepline,DIV=13,BCOR=12mm,bibliography=toc,chapterprefix=on]{scrbook}

\usepackage[T1]{fontenc}
\usepackage[ngerman,american]{babel}
\usepackage[utf8]{inputenc}

\usepackage{amsmath}
\usepackage{amsthm}
\usepackage{amssymb}

\usepackage{varwidth}

\usepackage{bussproofs} % sequent-calculus-style proofs

\usepackage{caption}
\captionsetup{format=plain, width=.9\textwidth}
\usepackage{subcaption}

\newenvironment{rawprooftree}
{\varwidth{.9\linewidth}\centering\leavevmode}
{\DisplayProof\endvarwidth}

\begin{document}
    \begin{figure}[h] 
        \centering
        \begin{small}
            \fbox{\begin{subfigure}[t]{.45\textwidth}%
                \begin{equation*}\tag{$\forall$R}\label{rule:forallR}%
                    \begin{rawprooftree}%
                        \def\defaultHypSeparation{\hskip .02in}%
                        \AxiomC{$\Gamma \vdash \varphi_x^y, \Delta$}%
                        \UnaryInfC{$\Gamma \vdash \forall x. \varphi, \Delta$}%
                    \end{rawprooftree}%
                \end{equation*}%
                \begin{equation*}\tag{CEL}\label{rule:CEL}%
                    \begin{rawprooftree}%
                        \def\defaultHypSeparation{\hskip .02in}%
                        \AxiomC{$\Gamma \vdash C(Q), \Delta$}%
                        \AxiomC{$P \leftrightarrow Q$}%
                        \BinaryInfC{$\Gamma \vdash C(P), \Delta$}%
                    \end{rawprooftree}%
                \end{equation*}%
            \end{subfigure}}%
        \end{small}
    \end{figure}
\end{document}

Answer 1

The problem is that 0.45\textwidth is too small.

Using 0.5\textwidth solves the issue (for the particular trees). Also the input can be vastly simplified. The varwidth is actually not necessary, at least in this application.

\documentclass[fontsize=11pt,paper=a4,headsepline,footsepline,DIV=13,BCOR=12mm,bibliography=toc,chapterprefix=on]{scrbook}

\usepackage[T1]{fontenc}
\usepackage[ngerman,american]{babel}
\usepackage[utf8]{inputenc}

\usepackage{amsmath}
\usepackage{amsthm}
\usepackage{amssymb}

\usepackage{bussproofs} % sequent-calculus-style proofs

\newenvironment{rawprooftree}{}{\DisplayProof}

\begin{document}

\begin{figure}[htp]
\centering\small

\fbox{\begin{minipage}{0.50\textwidth}
  \vspace*{-0.5\baselineskip}
  \begin{gather*}
    \tag{$\forall$R}\label{rule:forallR}
    \begin{rawprooftree}
      \def\defaultHypSeparation{\hskip .02in}
      \AxiomC{$\Gamma \vdash \varphi_x^y, \Delta$}
      \UnaryInfC{$\Gamma \vdash \forall x. \varphi, \Delta$}
    \end{rawprooftree}
  \\
    \tag{CEL}\label{rule:CEL}%
    \begin{rawprooftree}
      \def\defaultHypSeparation{\hskip .02in}
      \AxiomC{$\Gamma \vdash C(Q), \Delta$}
      \AxiomC{$P \leftrightarrow Q$}
      \BinaryInfC{$\Gamma \vdash C(P), \Delta$}
    \end{rawprooftree}
  \end{gather*}
  \vspace*{-0.5\baselineskip}
\end{minipage}}

\end{figure}

\end{document}