extend Self Tip Inpatch

[topbloke-formulae.git] / merge.tex

diff --git a/merge.tex b/merge.tex
index a34c9bcbac8753ae917462b975e7124aea784712..fd45642df697518317032ed9c9956c62baf7c1dd 100644 (file)
--- a/merge.tex
+++ b/merge.tex
@@ -220,8 +220,8 @@ $C \haspatch \p$ so by definition of $\haspatch$, $D \isin C \equiv D
 \subsubsection{For $D \not\in \py, R \not\in \py$:}
 
 $D \neq C$.  By Tip Contents of $L$,
-$D \isin L \equiv D \isin \baseof{L}$, and by Tip Merge condition,
-$D \isin L \equiv D \isin M$.  So by definition of $\merge$, $D \isin
+$D \isin L \equiv D \isin \baseof{L}$, so by Tip Merge condition,
+$D \isin L \equiv D \isin M$.  So by $\merge$, $D \isin
 C \equiv D \isin R$.  And $R = \baseof{C}$ by Unique Base of $C$.
 Thus $D \isin C \equiv D \isin \baseof{C}$.  OK.
 
@@ -233,14 +233,16 @@ By Tip Contents
 $D \isin L \equiv D \isin \baseof{L}$ and
 $D \isin R \equiv D \isin \baseof{R}$.
 
+Apply Tip Merge condition.
 If $\baseof{L} = M$, trivially $D \isin M \equiv D \isin \baseof{L}.$
 Whereas if $\baseof{L} = \baseof{M}$, by definition of $\base$,
 $\patchof{M} = \patchof{L} = \py$, so by Tip Contents of $M$,
 $D \isin M \equiv D \isin \baseof{M} \equiv D \isin \baseof{L}$.
 
-So $D \isin M \equiv D \isin L$ and by $\merge$,
+So $D \isin M \equiv D \isin L$ so by $\merge$,
 $D \isin C \equiv D \isin R$.  But from Unique Base,
-$\baseof{C} = R$ so $D \isin C \equiv D \isin \baseof{C}$.  OK.
+$\baseof{C} = \baseof{R}$.
+Therefore $D \isin C \equiv D \isin \baseof{C}$.  OK.
 
 $\qed$