pancs, pends

[topbloke-formulae.git] / article.tex

diff --git a/article.tex b/article.tex
index d9689c228d88ea26770ab65d88d85f4b192a9c9d..e16ac24a2f616fa3b6fda8e52353b5da1d585e3f 100644 (file)
--- a/article.tex
+++ b/article.tex
@@ -1,5 +1,6 @@
 \documentclass[a4paper,leqno]{strayman}
 \let\numberwithin=\notdef
+\usepackage{amsmath}
 \usepackage{mathabx}
 \usepackage{stmaryrd}
 \usepackage{slashed}
@@ -36,11 +37,13 @@
 \newcommand{\hasparents}{>_{\mkern-7.0mu _1}}
 \newcommand{\areparents}{<_{\mkern-14.0mu _1\mkern+5.0mu}}
 
-\newcommand{\implies}{\Rightarrow}
+\renewcommand{\implies}{\Rightarrow}
 
 \newcommand{\pancs}[2]{{\mathcal A} ( #1 , #2 ) }
 \newcommand{\pends}[2]{{\mathcal E} ( #1 , #2 ) }
 
+\renewcommand{\land}{\wedge}
+
 \begin{document}
 
 \section{Notation}
@@ -74,11 +77,22 @@ where the context requires a set, in which case the statement
 is to be taken as applying to both $\py$ and $\pn$.
 All these sets are distinct.
 
+\item[ $ \pancs{C}{\set P} $ ]
+$ \{ A \; | \; A \le C \land A \in \set P \} $ 
+i.e. all the ancestors of $C$
+which are in $\set P$.
+
+\item[ $ \pends{C}{\set P} $ ]
+$ \{ E \; | \; E \in \pancs{C}{\set P}
+  \land \mathop{\not\exists}_{A \in \pancs{C}{\set P}}
+  A \neq E \land E \le A \} $ 
+i.e. all $\le$-maximal commits in $\pancs{C}{\set P}$.
+
 \end{basedescript}
 
 \section{Invariants}
 
-$$ C \has D \implies C \ge D \eqno{No replay} $$
+\[ C \has D \implies C \ge D \tag*{\mbox{No replay:}} \]
 
 Unique base: \[ \mathop{\forall}_{C \in \py} \pends{C}{\pn} = \{ B \} \]