diff --git a/Isabelle_DOF-Example-II/document/preamble.tex b/Isabelle_DOF-Example-II/document/preamble.tex
index 38c30447..0e10611a 100644
--- a/Isabelle_DOF-Example-II/document/preamble.tex
+++ b/Isabelle_DOF-Example-II/document/preamble.tex
@@ -1,6 +1,8 @@
%% This is a placeholder for user-specific configuration and packages.
\usepackage{stmaryrd}
+\usepackage{pifont}% http://ctan.org/pkg/pifont
+
\title{
}
\author{}
diff --git a/Isabelle_DOF-Example-II/paper.thy b/Isabelle_DOF-Example-II/paper.thy
index 61d6387b..4902da42 100644
--- a/Isabelle_DOF-Example-II/paper.thy
+++ b/Isabelle_DOF-Example-II/paper.thy
@@ -146,7 +146,7 @@ Note that the trace sets, representing all \<^emph>\partial\ histor
text*[ex1::math_example, status=semiformal, level="Some 1"] \
Let two processes be defined as follows:
- \<^enum> \P\<^sub>d\<^sub>e\<^sub>t = (a \ Stop) \ (b \ Stop)\
+ \<^enum> \P\<^sub>d\<^sub>e\<^sub>t = (a \ Stop) \ (b \ Stop)\
\<^enum> \P\<^sub>n\<^sub>d\<^sub>e\<^sub>t = (a \ Stop) \ (b \ Stop)\
\
@@ -212,7 +212,7 @@ distribution comes with rich libraries comprising Sets, Numbers, Lists, etc. whi
For this work, a particular library called \<^theory_text>\HOLCF\ is intensively used. It provides classical
domain theory for a particular type-class \\::pcpo\, \<^ie> the class of types \\\ for which
- \<^enum> a least element \\\ is defined, and
+ \<^enum> a least element \\\ is defined, and
\<^enum> a complete partial order \_\_\ is defined.
For these types, \<^theory_text>\HOLCF\ provides a fixed-point operator \\X. f X\ as well as the
@@ -222,15 +222,13 @@ automatically infer, for example, that if \\::pcpo\, then \<
section*["csphol"::tc,main_author="Some(@{docitem ''bu''}::author)", level="Some 2"]
\Formalising Denotational \<^csp> Semantics in HOL \
-text\\
-
subsection*["processinv"::tc, main_author="Some(@{docitem ''bu''})"]
\Process Invariant and Process Type\
text\ First, we need a slight revision of the concept
of \<^emph>\trace\: if \\\ is the type of the atomic events (represented by a type variable), then
-we need to extend this type by a special event \\\ (called "tick") signaling termination.
-Thus, traces have the type \(\+\)\<^sup>*\, written \\\<^sup>\\<^sup>*\; since \\\ may only occur at the end of a trace,
-we need to define a predicate \front\<^sub>-tickFree t\ that requires from traces that \\\ can only occur
+we need to extend this type by a special event \\\ (called "tick") signaling termination.
+Thus, traces have the type \(\\\)\<^sup>*\, written \\\<^sup>\\<^sup>*\; since \\\ may only occur at the end of a trace,
+we need to define a predicate \front\<^sub>-tickFree t\ that requires from traces that \\\ can only occur
at the end.
Second, in the traditional literature, the semantic domain is implicitly described by 9 "axioms"
@@ -245,24 +243,24 @@ Informally, these are:
\<^item> the tick accepted after a trace \s\ implies that all other events are refused;
\<^item> a divergence trace with any suffix is itself a divergence one
\<^item> once a process has diverged, it can engage in or refuse any sequence of events.
- \<^item> a trace ending with \\\ belonging to divergence set implies that its
- maximum prefix without \\\ is also a divergent trace.
+ \<^item> a trace ending with \\\ belonging to divergence set implies that its
+ maximum prefix without \\\ is also a divergent trace.
More formally, a process \P\ of the type \\ process\ should have the following properties:
-@{cartouche [display] \([],{}) \ \ P \
+@{cartouche [display, indent=10] \([],{}) \ \ P \
(\ s X. (s,X) \ \ P \ front_tickFree s) \
(\ s t . (s@t,{}) \ \ P \ (s,{}) \ \ P) \
(\ s X Y. (s,Y) \ \ P \ X\Y \ (s,X) \ \ P) \
(\ s X Y. (s,X) \ \ P \ (\c \ Y. ((s@[c],{}) \ \ P)) \ (s,X \ Y) \ \ P) \
-(\ s X. (s@[\],{}) \ \ P \ (s,X-{\}) \ \ P) \
+(\ s X. (s@[\],{}) \ \ P \ (s,X-{\}) \ \ P) \
(\ s t. s \ \ P \ tickFree s \ front_tickFree t \ s@t \ \ P) \
(\ s X. s \ \ P \ (s,X) \ \ P) \
-(\ s. s@[\] \ \ P \ s \ \ P)\}
+(\ s. s@[\] \ \ P \ s \ \ P)\}
Our objective is to encapsulate this wishlist into a type constructed as a conservative
theory extension in our theory \<^holcsp>.
-Therefore third, we define a pre-type for processes \\ process\<^sub>0\ by \ \(\\<^sup>\\<^sup>* \ \(\\<^sup>\)) \ \(\\<^sup>\)\.
+Therefore third, we define a pre-type for processes \\ process\<^sub>0\ by \ \(\\<^sup>\\<^sup>* \ \(\\<^sup>\)) \ \(\\<^sup>\)\.
Forth, we turn our wishlist of "axioms" above into the definition of a predicate \is_process P\
of type \\ process\<^sub>0 \ bool\ deciding if its conditions are fulfilled. Since \P\ is a pre-process,
we replace \\\ by \fst\ and \