X-Git-Url: http://www.chiark.greenend.org.uk/ucgi/~ian/git?a=blobdiff_plain;f=simple.tex;h=ffd2d8d0ca378f2c58e48ac0f33bb792e4d26f45;hb=294a235fb0c1167d1101866cb35f41ddfabc287b;hp=ae6fc5551fd797dedeeeced6423cf5708b0d0f05;hpb=b1adf56763bea8bb31f2b2113b0718be0dd0bc3a;p=topbloke-formulae.git

diff --git a/simple.tex b/simple.tex
index ae6fc55..ffd2d8d 100644
--- a/simple.tex
+++ b/simple.tex
@@ -56,7 +56,6 @@ $$
 \end{cases}
 $$
 \proofstarts
-~
 
 Firstly, if $L \haspatch \p$, $\exists_{F \in \py} F \le L$
 and this $F$ is also $\le C$
@@ -79,23 +78,31 @@ Ancestors: $ D \le C \equiv D \le L $.
 
 Contents: $ D \isin C \equiv D \isin L \lor f $
 so $ D \isin C \equiv D \isin L $, i.e. $ C \zhaspatch P $.
+OK.
 
 \subsubsection{For $L \nothaspatch \p$:}
 
 Firstly, $C \not\in \py$ since if it were, $L \in \py$.
 Thus $D \neq C$.
 
-Now by contents of $L$, $D \notin L$, so $D \notin C$.
+Now by $\nothaspatch$, $D \not\isin L$ so $D \not\isin C$.
 OK.
 
 $\qed$
 
+\subsection{Unique Tips:}
+
+Single Parent Unique Tips applies.  $\qed$
+
 \subsection{Foreign Inclusion:}
 
 Simple Foreign Inclusion applies.  $\qed$
 
-\subsection{Foreign Contents:}
+\subsection{Foreign Ancestry:}
+
+Only relevant if $\isforeign{C}$, and in that case Totally
+Foreign Ancestry applies. $\qed$
 
-Only relevant if $\patchof{C} = \bot$, and in that case Totally
-Foreign Contents applies. $\qed$
+\subsection{Bases' Children:}
 
+Trivial.