### validity persists

parent 7ada3cbb
 ... ... @@ -47,7 +47,7 @@ We collect here some important and frequently used derived proof rules. \end{defn} Of course, $\always\prop$ is persistent for any $\prop$. Furthermore, by the proof rules given above, $t = t'$ as well as $\ownGGhost{\mcore\melt}$ and $\knowInv\iname\prop$ are persistent. Furthermore, by the proof rules given in \Sref{sec:proof-rules}, $t = t'$ as well as $\ownGGhost{\mcore\melt}$, $\mval(\melt)$ and $\knowInv\iname\prop$ are persistent. Persistence is preserved by conjunction, disjunction, separating conjunction as well as universal and existential quantification. In our proofs, we will implicitly add and remove $\always$ from persistent assertions as necessary, and generally treat them like normal, non-linear assumptions. ... ...
 ... ... @@ -305,6 +305,7 @@ In writing $\vctx, x:\type$, we presuppose that $x$ is not already declared in $\end{mathparpagebreakable} \subsection{Proof rules} \label{sec:proof-rules} The judgment$\vctx \mid \pfctx \proves \prop$says that with free variables$\vctx$, proposition$\prop$holds whenever all assumptions$\pfctx$hold. We implicitly assume that an arbitrary variable context,$\vctx\$, is added to every constituent of the rules. ... ... @@ -516,6 +517,8 @@ This is entirely standard. { \knowInv\iname\prop \proves \always \knowInv\iname\prop} \and { \ownGGhost{\mcore\melt} \proves \always \ownGGhost{\mcore\melt}} \and { \mval(\melt) \proves \always \mval(\melt)} \end{mathpar} \paragraph{Laws of primitive view shifts.} ... ...
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