Inference justification labels for sequent calculus proofs in bussproofs

Question

I'm working through Computability and Logic and need to construct proofs the same way they do in the book. However, I can't find anything about how to give inference justifications that are on the same lines as premises in the sequent-style proof. What I can do is this :

But what I need to do is this:

Answer 1

Not exactly clear what you want. How about

\documentclass{article}

\usepackage{amsmath}
\usepackage{amssymb}

\begin{document}
\begin{align}
  \{A\}        & \implies \{A\} \tag{R0}        \\
  \{A,{\sim}A\} & \implies \varnothing \tag{R2a} \\
  \Gamma       & \implies \varnothing \tag{R1}.
\end{align}
\end{document}

Answer 2

Seeing bussproofs in your question now, perhaps you want to use a proofs package, and I think the prooftreespackage does what you want except the nice alignment of the implications. But the package is suitable to write proofs.

\documentclass{article}

\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{prooftrees}
\forestset{line numbering=false}

\begin{document}
\begin{prooftree}
  {
    to prove={}
  }
  [
      \{ A \} \Rightarrow \{ A \}, just=(R0)
      [
          {\{A, \neg A\} \Rightarrow \varnothing}, just=(R2a)
          [
             \Gamma   \Rightarrow \varnothing, just=(R1)
             ]]]
\end{prooftree}
\end{document}