Commit 5b489445 authored by Ralf Jung's avatar Ralf Jung

validity persists

parent 7ada3cbb
...@@ -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.
......
...@@ -305,6 +305,7 @@ In writing $\vctx, x:\type$, we presuppose that $x$ is not already declared in $ ...@@ -305,6 +305,7 @@ In writing $\vctx, x:\type$, we presuppose that $x$ is not already declared in $
\end{mathparpagebreakable} \end{mathparpagebreakable}
\subsection{Proof rules} \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. 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. 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. ...@@ -516,6 +517,8 @@ This is entirely standard.
{ \knowInv\iname\prop \proves \always \knowInv\iname\prop} { \knowInv\iname\prop \proves \always \knowInv\iname\prop}
\and \and
{ \ownGGhost{\mcore\melt} \proves \always \ownGGhost{\mcore\melt}} { \ownGGhost{\mcore\melt} \proves \always \ownGGhost{\mcore\melt}}
\and
{ \mval(\melt) \proves \always \mval(\melt)}
\end{mathpar} \end{mathpar}
\paragraph{Laws of primitive view shifts.} \paragraph{Laws of primitive view shifts.}
......
Markdown is supported
0% or
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment