From ce87116ec42d1dce03dd57484ab4a1f127dcfa06 Mon Sep 17 00:00:00 2001
From: Philip Kaludercic <philip.kaludercic@fau.de>
Date: Fri, 22 Mar 2024 15:05:28 +0100
Subject: [PATCH] Indicate that Kleene's theorem involves induction
---
sketches.tex | 2 +-
1 file changed, 1 insertion(+), 1 deletion(-)
diff --git a/sketches.tex b/sketches.tex
index c309f16..4db8d03 100644
--- a/sketches.tex
+++ b/sketches.tex
@@ -36,7 +36,7 @@
&& \bot &\sqsubseteq x\\
\implies && \phi(\bot) &\sqsubseteq \phi(x) = x \tag{\(\phi\) is \defn{monotone}{mono.}}\\
\implies && \phi^2(\bot) &\sqsubseteq \phi^2(x) = \phi(x) = x\\
- &&&\;\;\vdots\\
+ &&&\;\;\vdots \; \tag{i.e.\ induction}\\
% \implies && \phi^n(\bot) &\sqsubseteq \phi^n(x) = \dots = x\\
% &&&\;\;\vdots\\
\implies && \underline{\mu\phi} = \bigsqcup_{i = 0}^\infty \phi^i(\bot) &\sqsubseteq \bigsqcup_{i = 0}^\infty \phi^i(x) = \underline{x}
--
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