\[ \newcommand{\tr}{\Rightarrow} \newcommand{\trs}{\tr^{\!\ast}} \newcommand{\rlnm}[1]{\mathsf{(#1)}} \newcommand{\rred}[1]{\xrightarrow{#1}} \newcommand{\rreds}[1]{\mathrel{\xrightarrow{#1}\!\!^*}} \newcommand{\cl}{\mathsf{Cl}} \newcommand{\pow}{\mathcal{P}} \newcommand{\matches}{\mathrel{\mathsf{matches}}} \newcommand{\kw}[1]{\mathsf{#1}} \]

A proof tree for the statement “$(0+1)(0+1) \matches 10$”:

\[ \begin{prooftree} \AxiomC{} \LeftLabel{$\rlnm{Char}$} \UnaryInfC{$1 \matches 1$} \LeftLabel{$\rlnm{ChoiceR}$} \UnaryInfC{$0+1 \matches 1$} \AxiomC{} \LeftLabel{$\rlnm{Char}$} \UnaryInfC{$0 \matches 0$} \LeftLabel{$\rlnm{ChoiceL}$} \UnaryInfC{$0+1 \matches 0$} \LeftLabel{$\rlnm{Concat}$} \BinaryInfC{$(0+1)(0+1) \matches 10$} \end{prooftree} \]