From de463fdc28ca9e32627818f508509d870c8a948b Mon Sep 17 00:00:00 2001
From: Chloe Brown <chloe.brown.00@outlook.com>
Date: Tue, 6 May 2025 16:00:11 +0100
Subject: Change signature of `\casetm`.

---
 sec/lang.ltx | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

(limited to 'sec/lang.ltx')

diff --git a/sec/lang.ltx b/sec/lang.ltx
index 3b0134a..1ad22d4 100644
--- a/sec/lang.ltx
+++ b/sec/lang.ltx
@@ -104,7 +104,7 @@ unrepresentable in some models of System~T}.
     \begin{prooftree}
       \hypo{\judgement{\Gamma}{t}{\sum_i A_i}}
       \hypo{\rangeover{\judgement{\Gamma, x_i : A_i}{t_i}{B}}{i}}
-      \infer2{\judgement{\Gamma}{\casetm{t}{x_i}{t_i}{i}}{B}}
+      \infer2{\judgement{\Gamma}{\casetm{t}{\tuple{i,x_i}}{t_i}{i}}{B}}
     \end{prooftree}
     \\\\
     \multicolumn{2}{c}{
@@ -156,7 +156,7 @@ derivation \(\jdgmnt{ty}{\Psi}{A}\), with our chosen variable \(X \in \Psi\).
   \maptm{X}{A \to B} &\coloneq \lambda f, x. x \\
   \maptm{X}{\prod_i A_i} &\coloneq \lambda f, x. \tuple{\rangeover{\maptm{X}{A_i}~f~x.i}{i}} \\
   \maptm{X}{\sum_i A_i} &\coloneq
-    \lambda f, x. \casetm{x}{x_i}{\tuple{i, \maptm{X}{A_i}~f~x_i}}{i} \\
+    \lambda f, x. \casetm{x}{\tuple{i,x_i}}{\tuple{i, \maptm{X}{A_i}~f~x_i}}{i} \\
   \maptm{X}{\mu Y. A} &\coloneq
   \lambda f, x.
     \dofold{x}{y}{\roll~(\maptm{X}{\sub{A}{Y/\mu Y. \sub{A}{X/C}}}~f~y)}
@@ -193,7 +193,7 @@ do not accidentally depend on an equation that does not hold.
   \begin{align*}
     (\lambda x. t)~u &\coloneq \sub{t}{x/u}
     &
-    \casetm{\tuple{k, t}}{x_i}{u_i}{i} &\coloneq \sub{u_k}{x_k/t}
+    \casetm{\tuple{k, t}}{\tuple{i,x_i}}{u_i}{i} &\coloneq \sub{u_k}{x_k/t}
     \\
     \tuple{\rangeover{t_i}{i}}.k &\coloneq t_k
     &
-- 
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