@@ -47,7 +47,7 @@ We collect here some important and frequently used derived proof rules.

...

@@ -47,7 +47,7 @@ We collect here some important and frequently used derived proof rules.

\end{defn}

\end{defn}

Of course, $\always\prop$ is persistent for any $\prop$.

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.

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.

In our proofs, we will implicitly add and remove $\always$ from persistent assertions as necessary, and generally treat them like normal, non-linear assumptions.