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

Correct Instantiation



\[\begin{prooftree}\AxiomC{$a \matches a$}\AxiomC{$b^* \matches bbb$}\LeftLabel{$\rlnm{Concat}$}\BinaryInfC{$ab^* \matches abbb$}\end{prooftree}\]



\[\begin{prooftree}\AxiomC{$a+b \matches b$}\AxiomC{$a+b \matches a$}\LeftLabel{$\rlnm{Concat}$}\BinaryInfC{$(a+b)(a+b) \matches ba$}\end{prooftree}\]



\[\begin{prooftree}\AxiomC{$abc \matches abc$}\AxiomC{$(b + \epsilon) \matches \epsilon$}\LeftLabel{$\rlnm{Concat}$}\BinaryInfC{$(abc)(b + \epsilon) \matches abcb$}\end{prooftree}\]