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

A proof tree for the statement “\(b^* \matches bb\)”:

\[ \begin{prooftree} \AxiomC{} \LeftLabel{$\rlnm{Char}$} \UnaryInfC{$b \matches b$} \AxiomC{} \LeftLabel{$\rlnm{Char}$} \UnaryInfC{$b \matches b$} \AxiomC{} \LeftLabel{$\rlnm{StarB}$} \UnaryInfC{$b^* \matches \epsilon$} \LeftLabel{$\rlnm{StarS}$} \BinaryInfC{$b^* \matches b$} \LeftLabel{$\rlnm{StarS}$} \BinaryInfC{$b^* \matches bb$} \end{prooftree}
\]