rename merge Ordering of L... to Ordering of Ingredients

[topbloke-formulae.git] / article.tex

diff --git a/article.tex b/article.tex
index 84b95b2958b0b59273d62f62ea4a63c7cb655d92..73453122e8a9dd7bf549c2df7a6f26edb44a85c5 100644 (file)
--- a/article.tex
+++ b/article.tex
@@ -498,11 +498,11 @@ Thus $D \le B$.
 
 \subsection{Unique Base}
 
-Not applicable. $\qed$
+Not applicable.
 
 \subsection{Tip Contents}
 
-Not applicable. $\qed$
+Not applicable.
 
 \subsection{Base Acyclic}
 
@@ -523,7 +523,17 @@ and $L \nothaspatch \p \implies B \nothaspatch P$.
 
 $\qed$.
 
-xxx unfinished
+\subsection{Foreign Inclusion}
+
+Consider some $D$ s.t. $\patchof{D} = \bot$.  $D \neq B$
+so $D \isin B \equiv D \isin L$.
+By Foreign Inclusion of $D$ in $L$, $D \isin L \equiv D \le L$.
+And by Exact Ancestors $D \le L \equiv D \le B$.
+So $D \isin B \equiv D \le B$.  $\qed$
+
+\subsection{Foreign Contents}
+
+Not applicable.
 
 \section{Create Tip}
 
@@ -557,7 +567,7 @@ R^+ \in \pry \land R^- = \baseof{R^+}
  L \haspatch \pry
 }\]
 
-\subsection{Ordering of ${L, R^+, R^-}$:}
+\subsection{Ordering of Ingredients:}
 
 By Unique Tip, $R^+ \le L$.  By definition of $\base$, $R^- \le R^+$
 so $R^- \le L$.  So $R^+ \le C$ and $R^- \le C$.
@@ -654,7 +664,7 @@ $\qed$
 
 \subsection{Foreign Contents}
 
-Not applicable. $\qed$
+Not applicable.
 
 \section{Merge}