provide \bigexists

[topbloke-formulae.git] / notation.tex

diff --git a/notation.tex b/notation.tex
index e5212fa43804240793e060e44f381fb7e8f8ef9b..6eb2e80d947a8bd1cb7d960bd43738ebbd352d8c 100644 (file)
--- a/notation.tex
+++ b/notation.tex
@@ -1,5 +1,8 @@
 \section{Notation}
 
+Throughout, any free variables are implicitly universally quantified
+at the outermost level.
+
 \begin{basedescript}{
 \desclabelwidth{5em}
 \desclabelstyle{\nextlinelabel}
@@ -27,7 +30,12 @@ A patch $\p$ consists of two sets of commits $\pn$ and $\py$, which
 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 of these sets are disjoint.  Hence:
+All of these sets will be disjoint by construction
+(see Invariants, below).  Hence:
+
+\item[ $\set A$, $\set P$, $\ldots$ ]
+Arbitrary sets of commits.  Maybe $\set P = \p$ i.e.\ some $\py$ or $\pn$, but
+maybe not.
 
 \item[ $ \patchof{ C } $ ]
 Either $\p$ s.t. $ C \in \p $, or $\bot$.
@@ -58,11 +66,13 @@ $\displaystyle \bigforall_{D \in \py} D \isin C \equiv D \le C $.
 ~ Informally, $C$ has all the reachable contents of $\p$.
 
 \item[ $ C \haspatch \p $ ]
-$\displaystyle C \zhaspatch \p \land \exists_{D \in \py} D \le C $.
+$\displaystyle C \zhaspatch \p \land \exists_{F \in \py} F \le C $.
 ~ Informally, $C$ nontrivially has all the reachable contents of $\p$.
 
-Note that $\zhaspatch$ and $\nothaspatch$ are not mutually exclusive.
-$\haspatch$ and $\nothaspatch$ are.
+Note that $\zhaspatch$ and $\nothaspatch$ are neither
+mutually exclusive nor exhaustive.
+$\haspatch$ and $\nothaspatch$ are mutually exclusive but not
+necessarily exhaustive.
 
 Commits on Non-Topbloke branches are $\nothaspatch \p$ for all $\p$.  This
 includes commits on plain git branches made by applying a Topbloke