move merge X and Y def up

[topbloke-formulae.git] / article.tex

diff --git a/article.tex b/article.tex
index 0018429e2a80618059f63b2189d3a4103d3b8994..a0adacbdee9b8d02bb1f2421f8158b1a43b505b2 100644 (file)
--- a/article.tex
+++ b/article.tex
@@ -81,7 +81,8 @@
 \newcommand{\Largenexists}{\mathop{\hbox{\Large$\nexists$}}}
 
 \newcommand{\qed}{\square}
-\newcommand{\proof}[1]{{\it Proof.} #1 $\qed$}
+\newcommand{\proofstarts}{{\it Proof:}}
+\newcommand{\proof}[1]{\proofstarts #1 $\qed$}
 
 \newcommand{\gathbegin}{\begin{gather} \tag*{}}
 \newcommand{\gathnext}{\\ \tag*{}}
@@ -262,7 +263,7 @@ XXX proof TBD.
 
 \subsection{No Replay for Merge Results}
 
-If we are constructing $C$, given
+If we are constructing $C$, with,
 \gathbegin
   \mergeof{C}{L}{M}{R}
 \gathnext
@@ -270,7 +271,7 @@ If we are constructing $C$, given
 \gathnext
   R \le C
 \end{gather}
-No Replay is preserved.  {\it Proof:}
+No Replay is preserved.  \proofstarts
 
 \subsubsection{For $D=C$:} $D \isin C, D \le C$.  OK.
 
@@ -424,7 +425,7 @@ Merge Results applies. $\qed$
 \subsection{Desired Contents}
 
 \[ D \isin C \equiv [ D \notin \pry \land D \isin L ] \lor D = C \]
-{\it Proof.}
+\proofstarts
 
 \subsubsection{For $D = C$:}
 
@@ -473,6 +474,7 @@ Merge commits $L$ and $R$ using merge base $M$ ($M < L, M < R$):
 \gathnext
  \mergeof{C}{L}{M}{R}
 \end{gather}
+We will occasionally use $X,Y$ s.t. $\{X,Y\} = \{L,R\}$.
 
 \subsection{Conditions}
 
@@ -530,8 +532,6 @@ $\qed$
 Need to determine $C \haspatch P$ based on $L,M,R \haspatch P$.
 This involves considering $D \in \py$.  
 
-We will use $X,Y$ s.t. $\{X,Y\} = \{L,R\}$.
-
 \subsubsection{For $L \nothaspatch P, R \nothaspatch P$:}
 $D \not\isin L \land D \not\isin R$.  $C \not\in \py$ (otherwise $L
 \in \py$ ie $L \haspatch P$ by Tip Self Inpatch).  So $D \neq C$.