how to display very large tree (+ standalone vs. bussproofs)

Question

I am looking at different options to typeset proof trees, and be helped by What is the best package out there to typeset proof trees?

A question I don't see any hint therein is about whether there are tools to display very large proof trees (hundreds of nodes). I am speculating/dreaming about a tool to navigate a proof tree up and down (kind of what we do with google maps). Is there anything you may think of which could be suitable for doing that? How would you go to get something workable?

-------- second update

Thanks to cfr, I learnt about varwidth (without which it seems we get error messages: Something's wrong--perhaps a missing \item. \begin{prooftree}, why so?). Still, for a large number of proof steps, I get a cropped proof tree. I understand I may adjust the border's value, by trial and error. Question is: is there a way to ask latex to calculate the best value, for each given proof tree? Or at least, is there a way to know such value somehow in advance? (for the example below, border=125pt is good enough)

\documentclass[border=10pt,varwidth]{standalone}
\usepackage{bussproofs}
\begin{document}
\begin{prooftree}
\AxiomC{A}
\UnaryInfC{B}
\AxiomC{C}
\BinaryInfC{D}
\AxiomC{E}
\AxiomC{F}
\BinaryInfC{G}
\UnaryInfC{H}
\BinaryInfC{J}
\AxiomC{A}
\UnaryInfC{B}
\AxiomC{C}
\BinaryInfC{D}
\AxiomC{E}
\AxiomC{F}
\BinaryInfC{G}
\UnaryInfC{H}
\BinaryInfC{J}
\BinaryInfC{JJ}
\AxiomC{A}
\UnaryInfC{B}
\AxiomC{C}
\BinaryInfC{D}
\AxiomC{E}
\AxiomC{F}
\BinaryInfC{G}
\UnaryInfC{H}
\BinaryInfC{J}
\AxiomC{A}
\UnaryInfC{B}
\AxiomC{C}
\BinaryInfC{D}
\AxiomC{E}
\AxiomC{F}
\BinaryInfC{G}
\UnaryInfC{H}
\BinaryInfC{J}
\BinaryInfC{JJ}
\BinaryInfC{JJJ}
\end{prooftree}
\end{document}

Answer 1

Following Steven B. Segletes's solution, we can simply add varwidth:

\documentclass[border=10pt,varwidth]{standalone}
\usepackage{bussproofs}
\begin{document}
  \begin{prooftree}
    \AxiomC{A}
    \UnaryInfC{B}
    \AxiomC{C}
    \BinaryInfC{D}
    \AxiomC{E}
    \AxiomC{F}
    \BinaryInfC{G}
    \UnaryInfC{H}
    \BinaryInfC{J}
  \end{prooftree}
\end{document}