From eb70d3fc688d015e6fb846bebc2ca91db8c3745e Mon Sep 17 00:00:00 2001
From: Mallku2 <mallkuernesto@gmail.com>
Date: Wed, 12 Feb 2025 16:13:54 -0300
Subject: [PATCH] Minor changes in rule distinct_elim, nary_elim,
 distinct_elim, and source code docu. in doc.tex

---
 spec/doc.tex       |  2 +-
 spec/rule_list.tex | 21 +++++++++++----------
 2 files changed, 12 insertions(+), 11 deletions(-)

diff --git a/spec/doc.tex b/spec/doc.tex
index 9f59ddc..d16a68b 100644
--- a/spec/doc.tex
+++ b/spec/doc.tex
@@ -121,7 +121,7 @@
 }
 
 % These avoid the xltabular environment. While xltabular can break on pages
-% it seems to interact badly with the RuleDescription enviornment.
+% it seems to interact badly with the RuleDescription environment.
 \NewEnviron{AletheX}{%
 \renewcommand\spsep{\cline{2-4}}%
 \setlength{\arrayrulewidth}{0.8pt}%
diff --git a/spec/rule_list.tex b/spec/rule_list.tex
index d31df1a..a723588 100644
--- a/spec/rule_list.tex
+++ b/spec/rule_list.tex
@@ -1626,27 +1626,27 @@ This rule eliminates the $\lsymb{distinct}$ predicate. If called with one
 argument this predicate always holds:
 
 \begin{AletheXS}
-$i$. & \ctxsep & $\Gamma$ & $(\lsymb{distinct}\, t) ≈ \top$ & \currule \\
+$i$. & $\Gamma$ & \ctxsep & $(\lsymb{distinct}\, t) ≈ \top$ & \currule \\
 \end{AletheXS}
 
 If applied to terms of type $\lsymb{Bool}$ more than two terms can never be
 distinct, hence only two cases are possible:
 
 \begin{AletheXS}
-$i$. & \ctxsep & $\Gamma$ &
+$i$. & $\Gamma$ & \ctxsep &
 $(\lsymb{distinct}\,\varphi\,\psi) ≈ \neg (\varphi ≈ \psi)$ & \currule \\
 \end{AletheXS}
 and
 
 \begin{AletheXS}
-$i$. & \ctxsep & $\Gamma$ &
+$i$. & $\Gamma$ & \ctxsep &
 $(\lsymb{distinct}\,\varphi_1\,\varphi_2\,\varphi_3\,\dots) ≈ \bot$ & \currule \\
 \end{AletheXS}
 
 The general case is
 
 \begin{AletheXS}
-$i$. & \ctxsep & $\Gamma$ &
+$i$. & $\Gamma$ & \ctxsep &
 $(\lsymb{distinct}\,t_1\,\dots\, t_n) ≈
 \bigwedge_{i=1}^{n}\bigwedge_{j=i+1}^{n} t_i\;{\not≈}\;t_j$ & \currule \\
 \end{AletheXS}
@@ -1665,24 +1665,25 @@ application of the binary operator. It is never applied to $\land$ or $\lor$.
 Three cases are possible.
 If the operator $\circ$ is left associative, then the rule has the form
 \begin{AletheXS}
-$i$. & \ctxsep & $\Gamma$ & $\bigcirc_{i=1}^{n} t_i ≈ (\dots( t_1\circ  t_2) \circ  t_3)\circ \cdots  t_n)$
+$i$. & $\Gamma$ & \ctxsep & $\bigcirc_{i=1}^{n} t_i ≈ (\dots(( t_1\circ  t_2) \circ  t_3)\circ \cdots  t_n)$
  & \currule \\
 \end{AletheXS}
 
 If the operator $\circ$ is right associative, then the rule has the form
 
 \begin{AletheXS}
-$i$. & \ctxsep  & $\Gamma$ & $\bigcirc_{i=1}^{n} t_i ≈
-( t_1 \circ \cdots \circ ( t_{n-2} \circ ( t_{n-1} \circ  t_n)\dots)$ & \currule \\
+$i$. & $\Gamma$  & \ctxsep & $\bigcirc_{i=1}^{n} t_i ≈
+( t_1 \circ \cdots \circ ( t_{n-2} \circ ( t_{n-1} \circ  t_n))\dots)$ & \currule \\
 \end{AletheXS}
 
 If the operator is {\em chainable}, then it has the form
 
 \begin{AletheXS}
-$i$. & \ctxsep & $\Gamma$ & $\bigcirc_{i=1}^{n} t_i ≈
-( t_1\circ t_2) \land ( t_2 \circ  t_3) \land \cdots
-\land ( t_{n-1}\circ t_n)$ & \currule \\
+$i$. & $\Gamma$ & \ctxsep & $\bigcirc_{i=1}^{n} t_i ≈
+( t_1\circ t_2) \oplus ( t_2 \circ  t_3) \oplus \cdots
+\oplus ( t_{n-1}\circ t_n)$ & \currule \\
 \end{AletheXS}
+where $\oplus$ is the binary operator indicated to perform the chaining.
 \end{RuleDescription}
 
 \begin{RuleDescription}{bfun_elim}
-- 
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