pseudomerge: add some $\qed$s

[topbloke-formulae.git] / pseudomerge.tex

diff --git a/pseudomerge.tex b/pseudomerge.tex
index 27b2e528525bef39cd8a2bfe8556389cac0ff5c7..7ee7ffbbdc25e2c1140983173f4f0b8ddb5aca52 100644 (file)
--- a/pseudomerge.tex
+++ b/pseudomerge.tex
@@ -45,7 +45,7 @@ $\isforeign{D} \implies \big[ D \le C \equiv D \le L \big]$.
 Trivial by Foreign Unaffected and the definition of $\pends$
 }
 
-It might seem that bare git commits might also be psuedo-merges ---
+It might seem that foreign commits might also be psuedo-merges ---
 e.g., merges made directly with {\tt git merge -s ours}.  However, by
 our definition of $\has$, these are considered simply as normal merges
 (\autoref{commit-merge}).
@@ -57,11 +57,11 @@ $A = L$ always satisfies the $\exists$.  $\qed$
 
 \subsection{Unique Base}
 
-Not applicable, by Base Only.
+Not applicable, by Base Only.  $\qed$
 
 \subsection{Tip Contents}
 
-Not applicable, by Base Only.
+Not applicable, by Base Only.  $\qed$
 
 \subsection{Base Acyclic}
 
@@ -88,7 +88,15 @@ Explicitly dealt with by our Unique Tips condition.
 
 \subsection{Foreign Inclusion}
 
-True by Foreign Identical, and Foreign Inclusion of $L$.
+We need to consider $D \in \foreign$.
+
+For $D = C$: $D \has C$, $D \le C$; OK.
+
+For $D \neq C$: $D \has C \equiv D \has L$ by construction.
+$D \has L \equiv D \le L$ by Foreign Inclusion of $L$.
+$D \neq C$ so this $D \le L \equiv D \le C$.
+
+$\qed$
 
 \subsection{Foreign Ancestry}
 
@@ -109,3 +117,5 @@ For $D = R \in \set R, R \in \foreign$, or $R \in \pqy$: $D \not\in
 \pdn$ so Bases' Children does not apply.
 
 Other possibilities for $D \in \set R$ are excluded by Ingredients.
+
+$\qed$