From 23d2c1822920de1b4f904189c03b367ca1fe38b1 Mon Sep 17 00:00:00 2001
From: Luke Fishman <daiagi@gmail.com>
Date: Tue, 5 Nov 2024 13:28:25 +0700
Subject: [PATCH] prerequisite is a set (#132)

---
 text/accumulation.tex | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/text/accumulation.tex b/text/accumulation.tex
index 33a1437..06933e5 100644
--- a/text/accumulation.tex
+++ b/text/accumulation.tex
@@ -52,11 +52,11 @@ \subsection{History and Queuing}
 
 The newly available work-reports, $\mathbf{W}$, are partitioned into two sequences based on the condition of having zero prerequisite work-reports. Those meeting the condition, $\mathbf{W}^!$, are accumulated immediately. Those not, $\mathbf{W}^Q$, are for queued execution. Formally:
 \begin{align}
-  \mathbf{W}^! &\equiv [ w \mid w \orderedin \mathbf{W}, (w_x)_\mathbf{p} = \none \wedge w_\wr¬srlookup = \{\} ] \\
+  \mathbf{W}^! &\equiv [ w \mid w \orderedin \mathbf{W}, |(w_x)_\mathbf{p}| = 0 \wedge w_\wr¬srlookup = \{\} ] \\
   \mathbf{W}^Q &\equiv E(\sq{
     D(w) \mid
     w \orderedin \mathbf{W},
-    (w_x)_\mathbf{p} \ne \none \vee w_\wr¬srlookup \ne \{\}
+    |(w_x)_\mathbf{p}| > 0 \vee w_\wr¬srlookup \ne \{\}
   }, \accumulatedcup)\!\!\!\!\\
   D(w) &\equiv (w, \{(w_x)_\mathbf{p}\} \cup \keys{w_\wr¬srlookup})
 \end{align}