add context closure

LaTeX/lfmt.tex

@@ -17,9 +17,10 @@
     \textbf{Variables} & \(x,y,z,\dots\) & & \\
     \textbf{Sorts} & \(s\) & \(\defn\) & \(\ttype{} ~|~ \tkind\) \\
     \textbf{Terms} & \(A,B,t,u\) & \(\defn\) & \(x~|~s~|~\tpi{x}{A}{B} ~|~\tabs{x}{A}{u} ~|~ \tapp{t}{u} \)\\
+    \textbf{Relations} & \(\mathcal{R}\) & & \\
     \textbf{Context} & \(\Gamma\) & \(\defn\) & \(\emptyset~|~\Gamma, x:A~|~\Gamma, \mathcal{R}\)\\
     \textbf{Typing Judgment} & & & \(\Gamma \vdash t : A\)\\
-    \textbf{Typing context well-formed} & & & \(\vdash \wf{\Gamma}\) \\
+    \textbf{Typing context well-formed} & & & \(\phantom{\Gamma} \vdash \wf{\Gamma}\) \\
     \textbf{Relation well-formed} & & & \(\Gamma \vdash \wf{\mathcal{R}}\) \\
   \end{tabular}
   \caption{\lfmt{}}
@@ -48,7 +49,7 @@
 \end{definition}
 
 \begin{definition}
-  We define \(\conv_{\beta\Gamma}\) as the reflexive, symmetric, and transitive closure of \(\beta\) and \(\bigcup_{\mathcal{R} \in \Gamma} \mathcal{R}\).
+  We define \(\conv_{\beta\Gamma}\) as the reflexive, symmetric, transitive closure of \(\beta\) and \(\bigcup_{\mathcal{R} \in \Gamma} \mathcal{R}\) and closed by context.
 \end{definition}
 
 \begin{rules}{typing}{Typing rules}