\begin{multicols}{2}
\begin{enumerate}
\item[] $(\neg \Rightarrow) \quad \dfrac{\Gamma \Rightarrow \Delta, \psi}{\Gamma , \neg\psi \Rightarrow \Delta}$
\item[] $(\Rightarrow \neg) \quad \dfrac{\Gamma, \psi \Rightarrow \Delta}{\Gamma \Rightarrow \Delta, \neg\psi}$
\item[] $(\lor \Rightarrow) \quad \dfrac{\Gamma, \psi \Rightarrow \Delta \quad \Gamma, \vartheta \Rightarrow \Delta}{\Gamma, \psi \lor \vartheta \Rightarrow \Delta}$
\item[] $(\Rightarrow \lor) \quad \dfrac{\Gamma \Rightarrow \Delta, \psi, \vartheta}{\Gamma \Rightarrow \Delta, \psi \lor \vartheta}$
\item[] $(\land \Rightarrow) \quad \dfrac{\Gamma, \psi, \vartheta \Rightarrow \Delta}{\Gamma, \psi \land \vartheta \Rightarrow \Delta}$
\item[] $(\Rightarrow \land) \quad \dfrac{\Gamma \Rightarrow \Delta, \psi \quad \Gamma \Rightarrow \Delta, \vartheta}{\Gamma \Rightarrow \Delta, \psi \land \vartheta}$
\item[] $(\rightarrow \Rightarrow) \quad \dfrac{\Gamma \Rightarrow \Delta , \psi \quad \Gamma, \vartheta \Rightarrow \Delta}{\Gamma, \psi \rightarrow \vartheta \Rightarrow \Delta}$
\item[] $(\Rightarrow \rightarrow) \quad \dfrac{\Gamma, \psi \Rightarrow \Delta, \vartheta}{\Gamma \Rightarrow \Delta, \psi \rightarrow \vartheta}$
\item[] $(=) \quad \dfrac{\Gamma, t = t \Rightarrow \Delta}{\Gamma \Rightarrow \Delta}$
\item[] $(S \Rightarrow) \quad \dfrac{\Gamma, \psi(t) \Rightarrow \Delta}{\Gamma, t \overset{.}{=} t', \psi(t') \Rightarrow \Delta}$
\item[] $(\Rightarrow S) \quad \dfrac{\Gamma \Rightarrow \Delta, \psi(t)}{\Gamma, t \overset{.}{=} t' \Rightarrow \Delta, \psi(t')}$
\item[] $(\exists \Rightarrow) \quad \dfrac{\Gamma, \psi(c) \Rightarrow \Delta}{\Gamma, \exists x \psi(x) \Rightarrow \Delta}$
\item[] $(\Rightarrow \exists) \quad \dfrac{\Gamma \Rightarrow \Delta, \psi(t)}{\Gamma \Rightarrow \Delta, \exists x\psi(x)}$
\item[] $(\forall \Rightarrow) \quad \dfrac{\Gamma, \psi(t) \Rightarrow \Delta}{\Gamma, \forall x\psi(x) \Rightarrow \Delta}$
\item[] $(\Rightarrow \forall) \quad \dfrac{\Gamma \Rightarrow \Delta, \psi(c)}{\Gamma \Rightarrow \Delta, \forall x\psi(x)}$
\end{enumerate}
\end{multicols} |
