### Explained formula worra

parent f42df3a1
 ... ... @@ -601,10 +601,16 @@ t_p)\bigwedge_{n\in N_i}\neg(s_n'\to t_n') \not\simeq \Empty$for all$i$in$I$. For such a$t$and any type$s$then we have: % \begin{equation} \worra t s = \dom t \wedge\bigvee_{i\in I}\left(\bigwedge_{\{P\subset P_i\alt s\leq \bigvee_{p \in P} \neg t_p\}}\left(\bigvee_{p \in P} \neg s_p\right) \right) \worra t s = \dom t \wedge\bigvee_{i\in I}\left(\bigwedge_{\{P\subseteq P_i\alt s\leq \bigvee_{p \in P} \neg t_p\}}\left(\bigvee_{p \in P} \neg s_p\right) \right) \end{equation} \beppe{Explain the formula?} The proof that this type satisfies \eqref{worra} is given in the Appendix~\ref{app:worra}. The formula considers only the positive arrows of each summand that forms$t$and states that, for each summand, whenever you take a subset$P$of its positive arrows that cannot yield results in$s$(since$s$does not overlap the intersection of the codomains of these arrows), then the success of the test cannot depend on these arrows and therefore the intersection of the domains of these arrows---i.e., the values that would precisely select that set of arrows---can be removed from$\dom t\$. The proof that this type satisfies \eqref{worra} is given in the Appendix~\ref{app:worra}. ... ...
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