merge fixes/clarifications - fix several P to \p

[topbloke-formulae.git] / merge.tex

diff --git a/merge.tex b/merge.tex
index 555523648032b9548b6eea604d4a9292ff0e3bd2..f6a3e9304b5cc404dd8121d08b39cc95d642b3c8 100644 (file)
--- a/merge.tex
+++ b/merge.tex
@@ -59,7 +59,7 @@ branch without Topbloke's assistance, it is also forbidden to
 merge any Topbloke-controlled branch into any plain git branch.
 
 Given those conditions, Tip Merge and Merge Acyclic do not apply.
-And by Foreign Contents for Y, $\forall_{\p, D \in \py} D \not\le Y$
+And by Foreign Contents for (wlog) Y, $\forall_{\p, D \in \py} D \not\le Y$
 so then by No Replay $D \not\isin Y$
 so $\neg [ Y \haspatch \p ]$ so neither
 Merge Ends condition applies.
@@ -81,7 +81,7 @@ and calculate $\pendsof{C}{\pn}$.  So we will consider some
 putative ancestor $A \in \pn$ and see whether $A \le C$.
 
 By Exact Ancestors for C, $A \le C \equiv A \le L \lor A \le R \lor A = C$.
-But $C \in py$ and $A \in \pn$ so $A \neq C$.
+But $C \in \py$ and $A \in \pn$ so $A \neq C$.
 Thus $A \le C \equiv A \le L \lor A \le R$.
 
 By Unique Base of L and Transitive Ancestors,
@@ -100,7 +100,7 @@ That is, $\baseof{C} = \baseof{R}$.
 
 \subsubsection{For $R \in \pn$:}
 
-By Tip Merge condition on $R$ and since $M \le R$,
+By Tip Merge condition and since $M \le R$,
 $A \le \baseof{L} \implies A \le R$, so
 $A \le R \lor A \le \baseof{L} \equiv A \le R$.
 Thus $A \le C \equiv A \le R$.
@@ -163,22 +163,22 @@ Self Inpatch for $L$, $L \haspatch \p$, so $L=Y, R=X$.  By Tip Merge,
 $M=\baseof{L}$.  So by Base Acyclic $D \not\isin M$, i.e.
 $M \nothaspatch \p$.  And indeed $D \isin C$ and $D \le C$.  OK.
 
-Consider $D \neq C, M \nothaspatch P, D \isin Y$:
+Consider $D \neq C, M \nothaspatch \p, D \isin Y$:
 $D \le Y$ so $D \le C$.
 $D \not\isin M$ so by $\merge$, $D \isin C$.  OK.
 
-Consider $D \neq C, M \nothaspatch P, D \not\isin Y$:
+Consider $D \neq C, M \nothaspatch \p, D \not\isin Y$:
 $D \not\le Y$.  If $D \le X$ then
 $D \in \pancsof{X}{\py}$, so by Addition Merge Ends and
 Transitive Ancestors $D \le Y$ --- a contradiction, so $D \not\le X$.
 Thus $D \not\le C$.  By $\merge$, $D \not\isin C$.  OK.
 
-Consider $D \neq C, M \haspatch P, D \isin Y$:
+Consider $D \neq C, M \haspatch \p, D \isin Y$:
 $D \le Y$ so $D \in \pancsof{Y}{\py}$ so by Removal Merge Ends
 and Transitive Ancestors $D \in \pancsof{M}{\py}$ so $D \le M$.
 Thus $D \isin M$.  By $\merge$, $D \not\isin C$.  OK.
 
-Consider $D \neq C, M \haspatch P, D \not\isin Y$:
+Consider $D \neq C, M \haspatch \p, D \not\isin Y$:
 By $\merge$, $D \not\isin C$.  OK.
 
 $\qed$