Compact way to write inference rule with bussproofs

Question

I have the following inference rule

That I need to write with the package bussproofs and use it in the mathjax.

Mathjax support the bussproofs

I have no idea how to reproduce the following inference rule with the same form, like <A, []> -> []

To write these rules I used the proof but it is not available on mathjax

Answer 1

The following should set your proof in bussproofs and work in MathJax:

\newcommand\inf[2]{$\langle#1,[]\rangle\rightarrow #2$}

\begin{prooftree}
  \AXC{}\RL{num}
  \UIC{\inf{1}{1}}
  \AXC{}\RL{var}
  \UIC{\inf{x}{0}}\RL{gt}
  \BIC{\inf{x>1}{false}}
  \AXC{}\RL{skip}
  \UIC{\inf{skip()}{[]}}\RL{if}
  \BIC{\inf{if(x>1)then(x:=10)else(skip())}{[]}}
\end{prooftree}

Note, that the \inf macro sets your inference rules.