chiark / gitweb /
 author Ian Jackson Wed, 18 Apr 2012 20:34:13 +0000 (21:34 +0100) committer Ian Jackson Wed, 18 Apr 2012 20:34:13 +0000 (21:34 +0100)
 merge.tex patch | blob | history

index 48e7270..45b7f66 100644 (file)
--- a/merge.tex
+++ b/merge.tex
@@ -46,6 +46,13 @@ $L \in \pn$, $R \in \pry$, $M = \baseof{R}$.
\bigforall_{E \in \pendsof{X}{\py}} E \le Y
\right]
}\]
+$\eqn{ Suitable Tip }{ + \bigexists_T + \pendsof{J}{\p} = \{ T \} + \land + \forall_{E \in \pendsof{K}{\p}} T \ge E + , \text{where} \{J,K\} = \{L,R\} +}$
$\eqn{ Foreign Merges }{ \patchof{L} = \bot \implies \patchof{R} = \bot }$
@@ -258,6 +265,17 @@ 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. $\patchof{D} = \bot$.