Write hypothesis for inference rules with proof package

Question

I want to write inference rules like this one: where the hypothesis for C are not stated as a sequent depending on a set of hypothesis but with brackets []. This is as far as I got:

\documentclass[a4paper,11pt]{article}
\usepackage{proof}
\usepackage{amsmath,amssymb,amsthm,textcomp}

\begin{document}
\infer{C}{A \lor B & C & C}
\end{document}

How can I put on top of the Cs [A] and [B]

Answer 1

EDIT

In response to the new version of your question, proof also makes it pretty straightforward.

\documentclass{article}
\usepackage{proof}
\begin{document}
\infer{R}{%
    P \lor Q
    & \deduce{R}{[P]}
    & \deduce{R}{[Q]}
}
\end{document}

ebproof makes it pretty straightforward.

\documentclass{article}
\usepackage{ebproof}
\begin{document}
\[
  \begin{prooftree}
    \Hypo{P \lor Q}
    \Hypo {[P]}
    \Infer [rule style=no rule] 1 {R}
    \Hypo {[Q]}
    \Infer [rule style=no rule] 1 {R}
    \Infer3{R}
  \end{prooftree}
\]
\end{document}