Commit 6b839469 by Ralf Jung

### some more intuition for SProp

parent 04d3ee68
Pipeline #334 passed with stage
 ... ... @@ -28,9 +28,12 @@ One way to understand this definition is to re-write it a little. We start by defining the COFE of \emph{step-indexed propositions}: For every step-index, we proposition either holds or does not hold. \begin{align*} \SProp \eqdef{}& \psetdown{\mathbb{N}} \\ \eqdef{}& \setComp{\prop \in \pset{\mathbb{N}}}{ \All n, m. n \geq m \Ra n \in \prop \Ra m \in \prop } \\ \prop \nequiv{n} \propB \eqdef{}& \All m \leq n. m \in \prop \Lra m \in \propB \eqdef{}& \setComp{X \in \pset{\mathbb{N}}}{ \All n, m. n \geq m \Ra n \in X \Ra m \in X } \\ X \nequiv{n} Y \eqdef{}& \All m \leq n. m \in X \Lra m \in Y \end{align*} 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}. 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. \begin{align*} \UPred(\monoid) \cong{}& \monoid \monra \SProp \\ ... ...
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