strategy: traversal wip proofs

[topbloke-formulae.git] / merge.tex

diff --git a/merge.tex b/merge.tex
index 48e72702c780d17648ffe6ef5d5e5a6b1253fcce..465fcba55b4ac0962c881302e4b632a412c59014 100644 (file)
--- a/merge.tex
+++ b/merge.tex
@@ -10,8 +10,9 @@ Merge commits $L$ and $R$ using merge base $M$:
 \end{gather}
 We will occasionally use $X,Y$ s.t. $\{X,Y\} = \{L,R\}$.
 
-This can also be used for dependency re-insertion, by setting
-$L \in \pn$, $R \in \pry$, $M = \baseof{R}$.
+This can also be used for dependency re-insertion, by setting $L \in
+\pn$, $R \in \pry$, $M = \baseof{R}$, provided that the Conditions are
+satisfied; in particular, provided that $L \ge \baseof{R}$.
 
 \subsection{Conditions}
 \[ \eqn{ Ingredients }{
@@ -46,6 +47,13 @@ $L \in \pn$, $R \in \pry$, $M = \baseof{R}$.
     \bigforall_{E \in \pendsof{X}{\py}} E \le Y
    \right]
 }\]
+\[ \eqn{ Suitable Tip }{
+    \bigexists_T
+      \pendsof{J}{\py} = \{ T \}
+     \land
+      \forall_{E \in \pendsof{K}{\py}} T \ge E
+    , \text{where} \{J,K\} = \{L,R\}
+}\]
 \[ \eqn{ Foreign Merges }{
     \patchof{L} = \bot \implies \patchof{R} = \bot
 }\]
@@ -258,6 +266,17 @@ Therefore $D \isin C \equiv D \isin \baseof{C}$.  OK.
 
 $\qed$
 
+\subsection{Unique Tips}
+
+For $L \in \py$, trivially $\pendsof{C}{\py} = C$ so $T = C$ is
+suitable.
+
+For $L \not\in \py$, $\pancsof{C}{\py} = \pancsof{L}{\py} \cup
+\pancsof{R}{\py}$.  So $T$ from Suitable Tip is a suitable $T$ for
+Unique Tips.
+
+$\qed$
+
 \subsection{Foreign Inclusion}
 
 Consider some $D$ s.t. $\patchof{D} = \bot$.