\let\numberwithin=\notdef
\usepackage{amsmath}
\usepackage{mathabx}
-\usepackage{stmaryrd}
-\usepackage{slashed}
\usepackage{txfonts}
\usepackage{amsfonts}
\usepackage{mdwlist}
\newcommand{\has}{\sqsupseteq}
\newcommand{\isin}{\sqsubseteq}
-\newcommand{\nothaspatch}{{%
- \declareslashed{}{\sslash}{-0.04}{0}{\sqSupset}\slashed{\sqSupset}}}
-\newcommand{\notpatchisin}{{%
- \declareslashed{}{\sslash}{-0.04}{0}{\sqSubset}\slashed{\sqSubset}}}
+\newcommand{\nothaspatch}{\mathrel{\,\not\!\not\relax\haspatch}}
+\newcommand{\notpatchisin}{\mathrel{\,\not\!\not\relax\patchisin}}
\newcommand{\haspatch}{\sqSupset}
\newcommand{\patchisin}{\sqSubset}
\newcommand{\areparents}{<_{\mkern-14.0mu _1\mkern+5.0mu}}
\renewcommand{\implies}{\Rightarrow}
+\renewcommand{\equiv}{\Leftrightarrow}
+\renewcommand{\land}{\wedge}
+\renewcommand{\lor}{\vee}
\newcommand{\pancs}[2]{{\mathcal A} ( #1 , #2 ) }
\newcommand{\pends}[2]{{\mathcal E} ( #1 , #2 ) }
-\renewcommand{\land}{\wedge}
+\newcommand{\patchof}[1]{{\mathcal P} ( #1 ) }
+\newcommand{\baseof}[1]{{\mathcal B} ( #1 ) }
+
+\newcommand{\eqn}[2]{ #2 \tag*{\mbox{#1}} }
+
+%\newcommand{\bigforall}{\mathop{\hbox{\huge$\forall$}}}
+\newcommand{\bigforall}{%
+ \mathop{\mathchoice%
+ {\hbox{\huge$\forall$}}%
+ {\hbox{\Large$\forall$}}%
+ {\hbox{\normalsize$\forall$}}%
+ {\hbox{\scriptsize$\forall$}}}%
+}
\begin{document}
are respectively the base and tip git branches. $\p$ may be used
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.
+All these sets are distinct. Hence:
+
+\item[ $ \patchof{ C } $ ]
+Either $\p$ s.t. $ C \in \p $, or $\bot$.
+A function from commits to sets $\p$.
\item[ $ \pancs{C}{\set P} $ ]
$ \{ A \; | \; A \le C \land A \in \set P \} $
A \neq E \land E \le A \} $
i.e. all $\le$-maximal commits in $\pancs{C}{\set P}$.
+\item[ $ \baseof{C} $ ]
+$ \pends{C}{\pn} = \{ \baseof{C} \} $ where $ C \in \py $.
+A partial function from commits to commits.
+See ``unique base'', below.
+
+\item[ $ C \haspatch \p $ ]
+$ \bigforall_{D \in \py} D \isin C \equiv D \le C $.
+Informally, $C$ has the contents of $\p$.
+
+\item[ $\displaystyle C \nothaspatch \p $ ]
+$\displaystyle \bigforall_{D \in \py} D \not\isin C $.
+~ Informally, $C$ has none of the contents of $\p$.
+
\end{basedescript}
\section{Invariants}
-\[ C \has D \implies C \ge D \tag*{\mbox{No replay:}} \]
-
-Unique base: \[ \mathop{\forall}_{C \in \py} \pends{C}{\pn} = \{ B \} \]
+\[ \eqn{No replay:}{
+ C \has D \implies C \ge D
+}\]
+\[\eqn{Unique base:}{
+ \bigforall_{C \in \py} \pends{C}{\pn} = \{ B \}
+}\]
+\[\eqn{Tip contents:}{
+ \bigforall_{C \in \py} D \isin C \equiv
+ { D \isin \baseof{C} \lor \atop
+ (D \in \py \land D \le C) }
+}\]
+\[\eqn{Base non-circ:}{
+ \bigforall_{B \in \pn} D \isin B \implies D \notin \py
+}\]
\section{Test more symbols}
$ C \nothaspatch \p $
+$ \p \patchisin C $
+
+$ \p \notpatchisin C $
+
$ \{ B \} \areparents C $
\end{document}