\apply t s & = &\bigvee_{i\in I}\left(\bigvee_{\{Q\subsetneq P_i\alt s\not\leq\bigvee_{q\in Q}s_q\}}\left(\bigwedge_{p\in P_i\setminus Q}t_p\right)\right)\hspace*{1cm}\makebox[0cm][l]{(for $s\leq\dom{t}$)}\\[4mm]
%\worra t s & = & \dom t \wedge\bigvee_{i\in I}\left(\bigwedge_{\{P \subseteq P_i\alt s \leq \bigvee_{p \in P} \neg t_p\}} \left(\bigvee_{p \in P} \neg s_p \right)\right)\\[4mm]
\worra t s & = &\left\{\left(\bigwedge_{p\in P_i}(s_p\to t_p)\bigwedge_{n\in N_i}\neg(s_n'\to t_n'),\ \dom t \wedge\bigwedge_{\{P \subseteq P_i\alt s \leq\bigvee_{p \in P}\neg t_p\}}\left(\bigvee_{p \in P}\neg s_p \right)\right)\ |\ i\in I\right\}
\worra t s & = &\dom t \wedge\bigvee_{i\in I}\left(\bigwedge_{\{P \subseteq P_i\alt s \leq\bigvee_{p \in P}\neg t_p\}}\left(\bigvee_{p \in P}\neg s_p \right)\right)\\[4mm]
%\worra t s & = & \left\{\left(\bigwedge_{p\in P_i}(s_p\to t_p)\bigwedge_{n\in N_i}\neg(s_n'\to t_n'),\ \dom t \wedge\bigwedge_{\{P \subseteq P_i\alt s \leq \bigvee_{p \in P} \neg t_p\}} \left(\bigvee_{p \in P} \neg s_p \right)\right)\ |\ i\in I\right\}
\end{eqnarray*}
The elements of $\Gamma\avdash\Gammap\ct e:S$ mean:
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@@ -212,16 +212,16 @@ The elements of $\Gamma\avdash\Gammap\ct e:S$ mean: