docs: fix V being about any CMRA; fix V's timeless axiom

docs/logic.tex

@@ -270,7 +270,7 @@ In writing $\vctx, x:\type$, we presuppose that $x$ is not already declared in $
 	\infer{\vctx \proves \wtt{\melt}{\textlog{M}}}
 		{\vctx \proves \wtt{\ownGGhost{\melt}}{\Prop}}
 \and
-	\infer{\vctx \proves \wtt{\melt}{\textlog{M}}}
+	\infer{\vctx \proves \wtt{\melt}{\type} \and \text{$\type$ is a CMRA}}
 		{\vctx \proves \wtt{\mval(\melt)}{\Prop}}
 \and
 	\infer{\vctx \proves \wtt{\state}{\textlog{State}}}
@@ -464,7 +464,7 @@ A type $\type$ being \emph{inhabited} means that $ \proves \wtt{\term}{\type}$ i
 {\timeless{\ownGGhost\melt}}
 
 \infer
-{\text{$\melt$ is a discrete COFE element}}
+{\text{$\melt$ is an element of a discrete CMRA}}
 {\timeless{\mval(\melt)}}
 
 \infer{}

docs/model.tex

@@ -40,8 +40,8 @@ We introduce an additional logical connective $\ownM\melt$, which will later be
 	\Lam \melt. \setComp{n}{\begin{aligned}
             \All m, \meltB.& m \leq n \land  \melt\mtimes\meltB \in \mval_m \Ra {} \\
             & m \in \Sem{\vctx \proves \prop : \Prop}_\gamma(\meltB) \Ra {}\\& m \in \Sem{\vctx \proves \propB : \Prop}_\gamma(\melt\mtimes\meltB)\end{aligned}} \\
-        \Sem{\vctx \proves \ownM{\melt} : \Prop}_\gamma &\eqdef \Lam\meltB. \setComp{n}{\melt \mincl[n] \meltB}  \\
-        \Sem{\vctx \proves \mval(\melt) : \Prop}_\gamma &\eqdef \Lam\any. \setComp{n}{\melt \in \mval_n} \\
+        \Sem{\vctx \proves \ownM{\melt} : \Prop}_\gamma &\eqdef \Lam\meltB. \setComp{n}{\Sem{\vctx \proves \melt : \textlog{M}} \mincl[n] \meltB}  \\
+        \Sem{\vctx \proves \mval(\melt) : \Prop}_\gamma &\eqdef \Lam\any. \setComp{n}{\Sem{\vctx \proves \melt : \type} \in \mval_n} \\
 \end{align*}
 
 For every definition, we have to show all the side-conditions: The maps have to be non-expansive and monotone.