This definition varies slightly from the original one in~\cite{catlogic}.
\begin{defn}[Chain]
Given some set $\cofe$ and an indexed family $({\nequiv{n}}\subseteq\cofe\times\cofe)_{n \in\mathbb{N}}$ of equivalence relations, a \emph{chain} is a function $c : \mathbb{N}\to\cofe$ such that $\All n, m. n \leq m \Ra c (m)\nequiv{n} c (n)$.
\end{defn}
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@@ -94,7 +95,8 @@ Note that the composition of non-expansive (bi)functors is non-expansive, and th
\All n, \melt, \meltB_1, \meltB_2.&\omit\rlap{$\melt\in\mval_n \land\melt\nequiv{n}\meltB_1\mtimes\meltB_2\Ra{}$}\\
% Given a set $X$, we define a monoid such that at most one $x \in X$ can be owned.
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@@ -373,8 +374,6 @@ We obtain the following frame-preserving updates:
% \subsection{STS with tokens monoid}
% \label{sec:stsmon}
% \ralf{This needs syncing with the Coq development.}
% Given a state-transition system~(STS) $(\STSS, \ra)$, a set of tokens $\STSS$, and a labeling $\STSL: \STSS \ra \mathcal{P}(\STST)$ of \emph{protocol-owned} tokens for each state, we construct a monoid modeling an authoritative current state and permitting transitions given a \emph{bound} on the current state and a set of \emph{locally-owned} tokens.
% The construction follows the idea of STSs as described in CaReSL \cite{caresl}.
% \subsection{STSs with interpretation}\label{sec:stsinterp}
% Building on \Sref{sec:stsmon}, after constructing the monoid $\STSMon{\STSS}$ for a particular STS, we can use an invariant to tie an interpretation, $\pred : \STSS \to \Prop$, to the STS's current state, recovering CaReSL-style reasoning~\cite{caresl}.