@@ -32,7 +32,7 @@ We start by defining the COFE of \emph{step-indexed propositions}: For every ste
...
@@ -32,7 +32,7 @@ We start by defining the COFE of \emph{step-indexed propositions}: For every ste
X \nequiv{n} Y \eqdef{}&\All m \leq n. m \in X \Lra m \in Y
X \nequiv{n} Y \eqdef{}&\All m \leq n. m \in X \Lra m \in Y
\end{align*}
\end{align*}
Notice that with this notion of $\SProp$ is already hidden in the validity predicate $\mval_n$ of a CMRA:
Notice that with this notion of $\SProp$ is already hidden in the validity predicate $\mval_n$ of a CMRA:
We could equivalently require every CRMA to define $\mval_{-}(-) : \monoid\nfn\SProp$, replacing \ruleref{cmra-valid-ne} and \ruleref{cmra-valid-mono}.
We could equivalently require every CMRA to define $\mval_{-}(-) : \monoid\nfn\SProp$, replacing \ruleref{cmra-valid-ne} and \ruleref{cmra-valid-mono}.
Now we can rewrite $\UPred(\monoid)$ as monotone step-indexed predicates over $\monoid$, where the definition of a ``monotone'' function here is a little funny.
Now we can rewrite $\UPred(\monoid)$ as monotone step-indexed predicates over $\monoid$, where the definition of a ``monotone'' function here is a little funny.