@@ -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.