\documentclass [fleqn]{article}

\everymath{\rm}
\usepackage{latexsym}
\setlength {\overfullrule }{0mm}
\input{lgwinclude}

\usepackage{url}
\usepackage[dvipdfm=true]{hyperref}
\hypersetup{pdfpagemode=none}
\hypersetup{pdfstartpage=1}
\hypersetup{pdfstartview=FitBH}
\hypersetup{pdfpagescrop={120 130 490 730}}
\hypersetup{pdftitle=Logiweb sequent calculus - Chores}
\hypersetup{colorlinks=true}

\begin {document}



\title {Logiweb sequent calculus, Chores}
\author {Klaus Grue}
\date {\today}
\maketitle
\tableofcontents

\section{Test cases}



\section{Pyk definitions}

\begin{flushleft}
$(
[
[
\ast 
\stackrel {\circ}{=}
\ast 
]
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}general
\linebreak [0]\ \hskip0em plus2.0em{}macro
\linebreak [0]\ \hskip0em plus2.0em{}define
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}as
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}end
\linebreak [0]\ \hskip0em plus2.0em{}define
\mbox{''}
]
\linebreak[4] 
[
RootVisible(
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}make
\linebreak [0]\ \hskip0em plus2.0em{}root
\linebreak [0]\ \hskip0em plus2.0em{}visible
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}end
\linebreak [0]\ \hskip0em plus2.0em{}visible
\mbox{''}
]
\linebreak[4] 
[
A
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}sequent
\linebreak [0]\ \hskip0em plus2.0em{}example
\linebreak [0]\ \hskip0em plus2.0em{}axiom
\mbox{''}
]
\linebreak[4] 
[
R
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}sequent
\linebreak [0]\ \hskip0em plus2.0em{}example
\linebreak [0]\ \hskip0em plus2.0em{}rule
\mbox{''}
]
\linebreak[4] 
[
C
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}sequent
\linebreak [0]\ \hskip0em plus2.0em{}example
\linebreak [0]\ \hskip0em plus2.0em{}contradiction
\mbox{''}
]
\linebreak[4] 
[
T
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}sequent
\linebreak [0]\ \hskip0em plus2.0em{}example
\linebreak [0]\ \hskip0em plus2.0em{}theory
\mbox{''}
]
\linebreak[4] 
[
L
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}sequent
\linebreak [0]\ \hskip0em plus2.0em{}example
\linebreak [0]\ \hskip0em plus2.0em{}lemma
\mbox{''}
]
\linebreak[4] 
[
\{
\ast 
\}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}set
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}end
\linebreak [0]\ \hskip0em plus2.0em{}set
\mbox{''}
]
\linebreak[4] 
[\overline{
\ast }
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}object
\linebreak [0]\ \hskip0em plus2.0em{}var
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}end
\linebreak [0]\ \hskip0em plus2.0em{}var
\mbox{''}
]
\linebreak[4] 
[
\mathit{a}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}object
\linebreak [0]\ \hskip0em plus2.0em{}a
\mbox{''}
]
\linebreak[4] 
[
\mathit{b}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}object
\linebreak [0]\ \hskip0em plus2.0em{}b
\mbox{''}
]
\linebreak[4] 
[
\mathit{c}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}object
\linebreak [0]\ \hskip0em plus2.0em{}c
\mbox{''}
]
\linebreak[4] 
[
\mathit{d}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}object
\linebreak [0]\ \hskip0em plus2.0em{}d
\mbox{''}
]
\linebreak[4] 
[
\mathit{e}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}object
\linebreak [0]\ \hskip0em plus2.0em{}e
\mbox{''}
]
\linebreak[4] 
[
\mathit{f}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}object
\linebreak [0]\ \hskip0em plus2.0em{}f
\mbox{''}
]
\linebreak[4] 
[
\mathit{g}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}object
\linebreak [0]\ \hskip0em plus2.0em{}g
\mbox{''}
]
\linebreak[4] 
[
\mathit{h}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}object
\linebreak [0]\ \hskip0em plus2.0em{}h
\mbox{''}
]
\linebreak[4] 
[
\mathit{i}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}object
\linebreak [0]\ \hskip0em plus2.0em{}i
\mbox{''}
]
\linebreak[4] 
[
\mathit{j}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}object
\linebreak [0]\ \hskip0em plus2.0em{}j
\mbox{''}
]
\linebreak[4] 
[
\mathit{k}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}object
\linebreak [0]\ \hskip0em plus2.0em{}k
\mbox{''}
]
\linebreak[4] 
[
\mathit{l}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}object
\linebreak [0]\ \hskip0em plus2.0em{}l
\mbox{''}
]
\linebreak[4] 
[
\mathit{m}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}object
\linebreak [0]\ \hskip0em plus2.0em{}m
\mbox{''}
]
\linebreak[4] 
[
\mathit{n}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}object
\linebreak [0]\ \hskip0em plus2.0em{}n
\mbox{''}
]
\linebreak[4] 
[
\mathit{o}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}object
\linebreak [0]\ \hskip0em plus2.0em{}o
\mbox{''}
]
\linebreak[4] 
[
\mathit{p}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}object
\linebreak [0]\ \hskip0em plus2.0em{}p
\mbox{''}
]
\linebreak[4] 
[
\mathit{q}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}object
\linebreak [0]\ \hskip0em plus2.0em{}q
\mbox{''}
]
\linebreak[4] 
[
\mathit{r}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}object
\linebreak [0]\ \hskip0em plus2.0em{}r
\mbox{''}
]
\linebreak[4] 
[
\mathit{s}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}object
\linebreak [0]\ \hskip0em plus2.0em{}s
\mbox{''}
]
\linebreak[4] 
[
\mathit{t}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}object
\linebreak [0]\ \hskip0em plus2.0em{}t
\mbox{''}
]
\linebreak[4] 
[
\mathit{u}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}object
\linebreak [0]\ \hskip0em plus2.0em{}u
\mbox{''}
]
\linebreak[4] 
[
\mathit{v}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}object
\linebreak [0]\ \hskip0em plus2.0em{}v
\mbox{''}
]
\linebreak[4] 
[
\mathit{w}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}object
\linebreak [0]\ \hskip0em plus2.0em{}w
\mbox{''}
]
\linebreak[4] 
[
\mathit{x}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}object
\linebreak [0]\ \hskip0em plus2.0em{}x
\mbox{''}
]
\linebreak[4] 
[
\mathit{y}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}object
\linebreak [0]\ \hskip0em plus2.0em{}y
\mbox{''}
]
\linebreak[4] 
[
\mathit{z}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}object
\linebreak [0]\ \hskip0em plus2.0em{}z
\mbox{''}
]
\linebreak[4] 
[
\langle 
\ast 
{\equiv} 
\ast 
| 
\ast 
{:=} 
\ast 
\rangle 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}sub
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}is
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}where
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}is
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}end
\linebreak [0]\ \hskip0em plus2.0em{}sub
\mbox{''}
]
\linebreak[4] 
[
\langle 
\ast 
{\equiv}^0 
\ast 
| 
\ast 
{:=} 
\ast 
\rangle 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}sub
\linebreak [0]\ \hskip0em plus2.0em{}zero
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}is
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}where
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}is
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}end
\linebreak [0]\ \hskip0em plus2.0em{}sub
\mbox{''}
]
\linebreak[4] 
[
\langle 
\ast 
{\equiv}^1 
\ast 
| 
\ast 
{:=} 
\ast 
\rangle 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}sub
\linebreak [0]\ \hskip0em plus2.0em{}one
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}is
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}where
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}is
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}end
\linebreak [0]\ \hskip0em plus2.0em{}sub
\mbox{''}
]
\linebreak[4] 
[
\langle 
\ast 
{\equiv}^* 
\ast 
| 
\ast 
{:=} 
\ast 
\rangle 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}sub
\linebreak [0]\ \hskip0em plus2.0em{}star
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}is
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}where
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}is
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}end
\linebreak [0]\ \hskip0em plus2.0em{}sub
\mbox{''}
]
\linebreak[4] 
[
Ded(
\ast 
,
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}deduction
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}conclude
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}end
\linebreak [0]\ \hskip0em plus2.0em{}deduction
\mbox{''}
]
\linebreak[4] 
[
Ded_0(
\ast 
,
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}deduction
\linebreak [0]\ \hskip0em plus2.0em{}zero
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}conclude
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}end
\linebreak [0]\ \hskip0em plus2.0em{}deduction
\mbox{''}
]
\linebreak[4] 
[
Ded_1(
\ast 
,
\ast 
,
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}deduction
\linebreak [0]\ \hskip0em plus2.0em{}one
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}conclude
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}condition
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}end
\linebreak [0]\ \hskip0em plus2.0em{}deduction
\mbox{''}
]
\linebreak[4] 
[
Ded_2(
\ast 
,
\ast 
,
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}deduction
\linebreak [0]\ \hskip0em plus2.0em{}two
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}conclude
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}condition
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}end
\linebreak [0]\ \hskip0em plus2.0em{}deduction
\mbox{''}
]
\linebreak[4] 
[
Ded_3(
\ast 
,
\ast 
,
\ast 
,
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}deduction
\linebreak [0]\ \hskip0em plus2.0em{}three
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}conclude
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}condition
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}bound
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}end
\linebreak [0]\ \hskip0em plus2.0em{}deduction
\mbox{''}
]
\linebreak[4] 
[
Ded_4(
\ast 
,
\ast 
,
\ast 
,
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}deduction
\linebreak [0]\ \hskip0em plus2.0em{}four
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}conclude
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}condition
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}bound
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}end
\linebreak [0]\ \hskip0em plus2.0em{}deduction
\mbox{''}
]
\linebreak[4] 
[
Ded_4^*(
\ast 
,
\ast 
,
\ast 
,
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}deduction
\linebreak [0]\ \hskip0em plus2.0em{}four
\linebreak [0]\ \hskip0em plus2.0em{}star
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}conclude
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}condition
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}bound
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}end
\linebreak [0]\ \hskip0em plus2.0em{}deduction
\mbox{''}
]
\linebreak[4] 
[
Ded_5(
\ast 
,
\ast 
,
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}deduction
\linebreak [0]\ \hskip0em plus2.0em{}five
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}condition
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}bound
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}end
\linebreak [0]\ \hskip0em plus2.0em{}deduction
\mbox{''}
]
\linebreak[4] 
[
Ded_6(
\ast 
,
\ast 
,
\ast 
,
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}deduction
\linebreak [0]\ \hskip0em plus2.0em{}six
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}conclude
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}exception
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}bound
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}end
\linebreak [0]\ \hskip0em plus2.0em{}deduction
\mbox{''}
]
\linebreak[4] 
[
Ded_6^*(
\ast 
,
\ast 
,
\ast 
,
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}deduction
\linebreak [0]\ \hskip0em plus2.0em{}six
\linebreak [0]\ \hskip0em plus2.0em{}star
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}conclude
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}exception
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}bound
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}end
\linebreak [0]\ \hskip0em plus2.0em{}deduction
\mbox{''}
]
\linebreak[4] 
[
Ded_7(
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}deduction
\linebreak [0]\ \hskip0em plus2.0em{}seven
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}end
\linebreak [0]\ \hskip0em plus2.0em{}deduction
\mbox{''}
]
\linebreak[4] 
[
Ded_8(
\ast 
,
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}deduction
\linebreak [0]\ \hskip0em plus2.0em{}eight
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}bound
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}end
\linebreak [0]\ \hskip0em plus2.0em{}deduction
\mbox{''}
]
\linebreak[4] 
[
Ded_8^*(
\ast 
,
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}deduction
\linebreak [0]\ \hskip0em plus2.0em{}eight
\linebreak [0]\ \hskip0em plus2.0em{}star
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}bound
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}end
\linebreak [0]\ \hskip0em plus2.0em{}deduction
\mbox{''}
]
\linebreak[4] 
[
S
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}system
\linebreak [0]\ \hskip0em plus2.0em{}s
\mbox{''}
]
\linebreak[4] 
[
Neg
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}double
\linebreak [0]\ \hskip0em plus2.0em{}negation
\mbox{''}
]
\linebreak[4] 
[
MP
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}rule
\linebreak [0]\ \hskip0em plus2.0em{}mp
\mbox{''}
]
\linebreak[4] 
[
Gen
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}rule
\linebreak [0]\ \hskip0em plus2.0em{}gen
\mbox{''}
]
\linebreak[4] 
[
\mbox{rule div}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}rule
\linebreak [0]\ \hskip0em plus2.0em{}div
\mbox{''}
]
\linebreak[4] 
[
Ded
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}deduction
\mbox{''}
]
\linebreak[4] 
[
S1
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}axiom
\linebreak [0]\ \hskip0em plus2.0em{}s
\linebreak [0]\ \hskip0em plus2.0em{}one
\mbox{''}
]
\linebreak[4] 
[
S2
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}axiom
\linebreak [0]\ \hskip0em plus2.0em{}s
\linebreak [0]\ \hskip0em plus2.0em{}two
\mbox{''}
]
\linebreak[4] 
[
S3
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}axiom
\linebreak [0]\ \hskip0em plus2.0em{}s
\linebreak [0]\ \hskip0em plus2.0em{}three
\mbox{''}
]
\linebreak[4] 
[
S4
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}axiom
\linebreak [0]\ \hskip0em plus2.0em{}s
\linebreak [0]\ \hskip0em plus2.0em{}four
\mbox{''}
]
\linebreak[4] 
[
S5
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}axiom
\linebreak [0]\ \hskip0em plus2.0em{}s
\linebreak [0]\ \hskip0em plus2.0em{}five
\mbox{''}
]
\linebreak[4] 
[
S6
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}axiom
\linebreak [0]\ \hskip0em plus2.0em{}s
\linebreak [0]\ \hskip0em plus2.0em{}six
\mbox{''}
]
\linebreak[4] 
[
S7
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}axiom
\linebreak [0]\ \hskip0em plus2.0em{}s
\linebreak [0]\ \hskip0em plus2.0em{}seven
\mbox{''}
]
\linebreak[4] 
[
S8
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}axiom
\linebreak [0]\ \hskip0em plus2.0em{}s
\linebreak [0]\ \hskip0em plus2.0em{}eight
\mbox{''}
]
\linebreak[4] 
[
S9
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}axiom
\linebreak [0]\ \hskip0em plus2.0em{}s
\linebreak [0]\ \hskip0em plus2.0em{}nine
\mbox{''}
]
\linebreak[4] 
[
S10
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}axiom
\linebreak [0]\ \hskip0em plus2.0em{}s
\linebreak [0]\ \hskip0em plus2.0em{}ten
\mbox{''}
]
\linebreak[4] 
[
Repetition
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}repetition
\mbox{''}
]
\linebreak[4] 
[
A1'
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}a
\linebreak [0]\ \hskip0em plus2.0em{}one
\mbox{''}
]
\linebreak[4] 
[
A2'
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}a
\linebreak [0]\ \hskip0em plus2.0em{}two
\mbox{''}
]
\linebreak[4] 
[
A4'
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}a
\linebreak [0]\ \hskip0em plus2.0em{}four
\mbox{''}
]
\linebreak[4] 
[
A5'
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}a
\linebreak [0]\ \hskip0em plus2.0em{}five
\mbox{''}
]
\linebreak[4] 
[
Prop\ 3.2a
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}three
\linebreak [0]\ \hskip0em plus2.0em{}two
\linebreak [0]\ \hskip0em plus2.0em{}a
\mbox{''}
]
\linebreak[4] 
[
Prop\ 3.2b
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}three
\linebreak [0]\ \hskip0em plus2.0em{}two
\linebreak [0]\ \hskip0em plus2.0em{}b
\mbox{''}
]
\linebreak[4] 
[
Prop\ 3.2c
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}three
\linebreak [0]\ \hskip0em plus2.0em{}two
\linebreak [0]\ \hskip0em plus2.0em{}c
\mbox{''}
]
\linebreak[4] 
[
Prop\ 3.2d
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}three
\linebreak [0]\ \hskip0em plus2.0em{}two
\linebreak [0]\ \hskip0em plus2.0em{}d
\mbox{''}
]
\linebreak[4] 
[
Prop\ 3.2e_1
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}three
\linebreak [0]\ \hskip0em plus2.0em{}two
\linebreak [0]\ \hskip0em plus2.0em{}e
\linebreak [0]\ \hskip0em plus2.0em{}one
\mbox{''}
]
\linebreak[4] 
[
Prop\ 3.2e_2
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}three
\linebreak [0]\ \hskip0em plus2.0em{}two
\linebreak [0]\ \hskip0em plus2.0em{}e
\linebreak [0]\ \hskip0em plus2.0em{}two
\mbox{''}
]
\linebreak[4] 
[
Prop\ 3.2e
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}three
\linebreak [0]\ \hskip0em plus2.0em{}two
\linebreak [0]\ \hskip0em plus2.0em{}e
\mbox{''}
]
\linebreak[4] 
[
Prop\ 3.2f_1
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}three
\linebreak [0]\ \hskip0em plus2.0em{}two
\linebreak [0]\ \hskip0em plus2.0em{}f
\linebreak [0]\ \hskip0em plus2.0em{}one
\mbox{''}
]
\linebreak[4] 
[
Prop\ 3.2f_2
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}three
\linebreak [0]\ \hskip0em plus2.0em{}two
\linebreak [0]\ \hskip0em plus2.0em{}f
\linebreak [0]\ \hskip0em plus2.0em{}two
\mbox{''}
]
\linebreak[4] 
[
Prop\ 3.2f
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}three
\linebreak [0]\ \hskip0em plus2.0em{}two
\linebreak [0]\ \hskip0em plus2.0em{}f
\mbox{''}
]
\linebreak[4] 
[
Prop\ 3.2g_1
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}three
\linebreak [0]\ \hskip0em plus2.0em{}two
\linebreak [0]\ \hskip0em plus2.0em{}g
\linebreak [0]\ \hskip0em plus2.0em{}one
\mbox{''}
]
\linebreak[4] 
[
Prop\ 3.2g_2
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}three
\linebreak [0]\ \hskip0em plus2.0em{}two
\linebreak [0]\ \hskip0em plus2.0em{}g
\linebreak [0]\ \hskip0em plus2.0em{}two
\mbox{''}
]
\linebreak[4] 
[
Prop\ 3.2g
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}three
\linebreak [0]\ \hskip0em plus2.0em{}two
\linebreak [0]\ \hskip0em plus2.0em{}g
\mbox{''}
]
\linebreak[4] 
[
Prop\ 3.2h_1
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}three
\linebreak [0]\ \hskip0em plus2.0em{}two
\linebreak [0]\ \hskip0em plus2.0em{}h
\linebreak [0]\ \hskip0em plus2.0em{}one
\mbox{''}
]
\linebreak[4] 
[
Prop\ 3.2h_2
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}three
\linebreak [0]\ \hskip0em plus2.0em{}two
\linebreak [0]\ \hskip0em plus2.0em{}h
\linebreak [0]\ \hskip0em plus2.0em{}two
\mbox{''}
]
\linebreak[4] 
[
Prop\ 3.2h
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}three
\linebreak [0]\ \hskip0em plus2.0em{}two
\linebreak [0]\ \hskip0em plus2.0em{}h
\mbox{''}
]
\linebreak[4] 
[
Prop\ 3.2i
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}three
\linebreak [0]\ \hskip0em plus2.0em{}two
\linebreak [0]\ \hskip0em plus2.0em{}i
\mbox{''}
]
\linebreak[4] 
[
Prop\ 3.2j_1
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}three
\linebreak [0]\ \hskip0em plus2.0em{}two
\linebreak [0]\ \hskip0em plus2.0em{}j
\linebreak [0]\ \hskip0em plus2.0em{}one
\mbox{''}
]
\linebreak[4] 
[
Prop\ 3.2j_2
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}three
\linebreak [0]\ \hskip0em plus2.0em{}two
\linebreak [0]\ \hskip0em plus2.0em{}j
\linebreak [0]\ \hskip0em plus2.0em{}two
\mbox{''}
]
\linebreak[4] 
[
Prop\ 3.2j
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}three
\linebreak [0]\ \hskip0em plus2.0em{}two
\linebreak [0]\ \hskip0em plus2.0em{}j
\mbox{''}
]
\linebreak[4] 
[
Prop\ 3.2k_1
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}three
\linebreak [0]\ \hskip0em plus2.0em{}two
\linebreak [0]\ \hskip0em plus2.0em{}k
\linebreak [0]\ \hskip0em plus2.0em{}one
\mbox{''}
]
\linebreak[4] 
[
Prop\ 3.2k_2
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}three
\linebreak [0]\ \hskip0em plus2.0em{}two
\linebreak [0]\ \hskip0em plus2.0em{}k
\linebreak [0]\ \hskip0em plus2.0em{}two
\mbox{''}
]
\linebreak[4] 
[
Prop\ 3.2k
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}three
\linebreak [0]\ \hskip0em plus2.0em{}two
\linebreak [0]\ \hskip0em plus2.0em{}k
\mbox{''}
]
\linebreak[4] 
[
Prop\ 3.2l_1
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}three
\linebreak [0]\ \hskip0em plus2.0em{}two
\linebreak [0]\ \hskip0em plus2.0em{}l
\linebreak [0]\ \hskip0em plus2.0em{}one
\mbox{''}
]
\linebreak[4] 
[
Prop\ 3.2l_2
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}three
\linebreak [0]\ \hskip0em plus2.0em{}two
\linebreak [0]\ \hskip0em plus2.0em{}l
\linebreak [0]\ \hskip0em plus2.0em{}two
\mbox{''}
]
\linebreak[4] 
[
Prop\ 3.2l
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}three
\linebreak [0]\ \hskip0em plus2.0em{}two
\linebreak [0]\ \hskip0em plus2.0em{}l
\mbox{''}
]
\linebreak[4] 
[
Prop\ 3.2m_1
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}three
\linebreak [0]\ \hskip0em plus2.0em{}two
\linebreak [0]\ \hskip0em plus2.0em{}m
\linebreak [0]\ \hskip0em plus2.0em{}one
\mbox{''}
]
\linebreak[4] 
[
Prop\ 3.2m_2
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}three
\linebreak [0]\ \hskip0em plus2.0em{}two
\linebreak [0]\ \hskip0em plus2.0em{}m
\linebreak [0]\ \hskip0em plus2.0em{}two
\mbox{''}
]
\linebreak[4] 
[
Prop\ 3.2m
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}three
\linebreak [0]\ \hskip0em plus2.0em{}two
\linebreak [0]\ \hskip0em plus2.0em{}m
\mbox{''}
]
\linebreak[4] 
[
Prop\ 3.2n_1
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}three
\linebreak [0]\ \hskip0em plus2.0em{}two
\linebreak [0]\ \hskip0em plus2.0em{}n
\linebreak [0]\ \hskip0em plus2.0em{}one
\mbox{''}
]
\linebreak[4] 
[
Prop\ 3.2n_2
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}three
\linebreak [0]\ \hskip0em plus2.0em{}two
\linebreak [0]\ \hskip0em plus2.0em{}n
\linebreak [0]\ \hskip0em plus2.0em{}two
\mbox{''}
]
\linebreak[4] 
[
Prop\ 3.2n
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}three
\linebreak [0]\ \hskip0em plus2.0em{}two
\linebreak [0]\ \hskip0em plus2.0em{}n
\mbox{''}
]
\linebreak[4] 
[
Prop\ 3.2o
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}three
\linebreak [0]\ \hskip0em plus2.0em{}two
\linebreak [0]\ \hskip0em plus2.0em{}o
\mbox{''}
]
\linebreak[4] 
[
Prop\ 3.4a_1
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}three
\linebreak [0]\ \hskip0em plus2.0em{}four
\linebreak [0]\ \hskip0em plus2.0em{}a
\linebreak [0]\ \hskip0em plus2.0em{}one
\mbox{''}
]
\linebreak[4] 
[
Prop\ 3.4a_2
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}three
\linebreak [0]\ \hskip0em plus2.0em{}four
\linebreak [0]\ \hskip0em plus2.0em{}a
\linebreak [0]\ \hskip0em plus2.0em{}two
\mbox{''}
]
\linebreak[4] 
[
Prop\ 3.4a
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}three
\linebreak [0]\ \hskip0em plus2.0em{}four
\linebreak [0]\ \hskip0em plus2.0em{}a
\mbox{''}
]
\linebreak[4] 
[
Prop\ 3.4b
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}three
\linebreak [0]\ \hskip0em plus2.0em{}four
\linebreak [0]\ \hskip0em plus2.0em{}b
\mbox{''}
]
\linebreak[4] 
[
Prop\ 3.4c_1
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}three
\linebreak [0]\ \hskip0em plus2.0em{}four
\linebreak [0]\ \hskip0em plus2.0em{}c
\linebreak [0]\ \hskip0em plus2.0em{}one
\mbox{''}
]
\linebreak[4] 
[
Prop\ 3.4c_2
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}three
\linebreak [0]\ \hskip0em plus2.0em{}four
\linebreak [0]\ \hskip0em plus2.0em{}c
\linebreak [0]\ \hskip0em plus2.0em{}two
\mbox{''}
]
\linebreak[4] 
[
Prop\ 3.4c
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}three
\linebreak [0]\ \hskip0em plus2.0em{}four
\linebreak [0]\ \hskip0em plus2.0em{}c
\mbox{''}
]
\linebreak[4] 
[
Prop\ 3.4d_1
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}three
\linebreak [0]\ \hskip0em plus2.0em{}four
\linebreak [0]\ \hskip0em plus2.0em{}d
\linebreak [0]\ \hskip0em plus2.0em{}one
\mbox{''}
]
\linebreak[4] 
[
Prop\ 3.4d_2
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}three
\linebreak [0]\ \hskip0em plus2.0em{}four
\linebreak [0]\ \hskip0em plus2.0em{}d
\linebreak [0]\ \hskip0em plus2.0em{}two
\mbox{''}
]
\linebreak[4] 
[
Prop\ 3.4d
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}three
\linebreak [0]\ \hskip0em plus2.0em{}four
\linebreak [0]\ \hskip0em plus2.0em{}d
\mbox{''}
]
\linebreak[4] 
[
Block_1(
\ast 
,
\ast 
,
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}block
\linebreak [0]\ \hskip0em plus2.0em{}one
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}state
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}cache
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}end
\linebreak [0]\ \hskip0em plus2.0em{}block
\mbox{''}
]
\linebreak[4] 
[
Block_2(
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}block
\linebreak [0]\ \hskip0em plus2.0em{}two
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}end
\linebreak [0]\ \hskip0em plus2.0em{}block
\mbox{''}
]
\linebreak[4] 
[
\ast 
{}^{hide}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}hide
\mbox{''}
]
\linebreak[4] 
[
MacroIndent(
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}macro
\linebreak [0]\ \hskip0em plus2.0em{}indent
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\mbox{''}
]
\linebreak[4] 
[
\ast 
{}'
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}suc
\mbox{''}
]
\linebreak[4] 
[
\ast 
= 
\ast 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}equal
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\mbox{''}
]
\linebreak[4] 
[
\ast 
\neq 
\ast 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}unequal
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\mbox{''}
]
\linebreak[4] 
[
\ast 
{}^{var}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}is
\linebreak [0]\ \hskip0em plus2.0em{}object
\linebreak [0]\ \hskip0em plus2.0em{}var
\mbox{''}
]
\linebreak[4] 
[
\ast 
\#^0
\ast 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}avoid
\linebreak [0]\ \hskip0em plus2.0em{}zero
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\mbox{''}
]
\linebreak[4] 
[
\ast 
\#^1
\ast 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}avoid
\linebreak [0]\ \hskip0em plus2.0em{}one
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\mbox{''}
]
\linebreak[4] 
[
\ast 
\#^*
\ast 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}avoid
\linebreak [0]\ \hskip0em plus2.0em{}star
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\mbox{''}
]
\linebreak[4] 
[
\exists 
\ast 
\colon 
\ast 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}exist
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}indeed
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\mbox{''}
]
\linebreak[4] 
[
\forall 
\ast 
\colon 
\ast 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}for
\linebreak [0]\ \hskip0em plus2.0em{}all
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}indeed
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\mbox{''}
]
\linebreak[4] 
[
\forall_{obj} 
\ast 
\colon 
\ast 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}for
\linebreak [0]\ \hskip0em plus2.0em{}all
\linebreak [0]\ \hskip0em plus2.0em{}objects
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}indeed
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\mbox{''}
]
\linebreak[4] 
[
\ast 
\Rightarrow 
\ast 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}imply
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\mbox{''}
]
\linebreak[4] 
[
\ast 
\Leftrightarrow 
\ast 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}if
\linebreak [0]\ \hskip0em plus2.0em{}and
\linebreak [0]\ \hskip0em plus2.0em{}only
\linebreak [0]\ \hskip0em plus2.0em{}if
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\mbox{''}
]
\linebreak[4] 
[
\ast 
\#
\ast 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}avoid
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\mbox{''}
]
\linebreak[4] 
[
\ast 
\unrhd 
\ast 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}object
\linebreak [0]\ \hskip0em plus2.0em{}modus
\linebreak [0]\ \hskip0em plus2.0em{}ponens
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\mbox{''}
]
\linebreak[4] 
[
\Pi 
\ast 
\colon 
\ast 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}for
\linebreak [0]\ \hskip0em plus2.0em{}all
\linebreak [0]\ \hskip0em plus2.0em{}terms
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}indeed
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\mbox{''}
]
\linebreak[4] 
[
Begin \, 
\ast 
 ; 
\ast 
 : End ; 
\ast 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}block
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}line
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}end
\linebreak [0]\ \hskip0em plus2.0em{}block
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\mbox{''}
]
\linebreak[4] 
[
Last\ block\ line \, 
\ast 
\gg 
\ast 
\,;
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}because
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}indeed
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}end
\linebreak [0]\ \hskip0em plus2.0em{}line
\mbox{''}
]
\linebreak[4] 
[
Arbitrary \gg 
\ast 
;
\ast 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}any
\linebreak [0]\ \hskip0em plus2.0em{}term
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}end
\linebreak [0]\ \hskip0em plus2.0em{}line
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\mbox{''}
]
\linebreak[4] 
[
\ast 
\mathrel{|} 
\ast 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}alternative
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\mbox{''}
]
\linebreak[4] 
[
 \rightarrow 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}evaluates
\linebreak [0]\ \hskip0em plus2.0em{}to
\mbox{''}
]
\linebreak[4] 
[
\ast 
\backslash \backslash 
\ast 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}safe
\linebreak [0]\ \hskip0em plus2.0em{}row
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\mbox{''}
]
\linebreak[4] 
[
\ast 
\| 
\ast 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}divides
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\mbox{''}
]
\linebreak[4] 
[
\mbox{opgave}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}opgave
\mbox{''}
]
\linebreak[4] 
)^{\mathbf {p}}$
\end{flushleft}



\section{\TeX\ definitions}

\begin{list}{}{
\setlength{\leftmargin}{5em}
\setlength{\itemindent}{-5em}}

\item $
[
[
\mathsf{x}
\stackrel {\circ}{=}
\mathsf{y}
]
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline [
\#1/tex
\linebreak [0]\ \hskip0em plus2.0em{}name/tex.
\newline 
\mbox {$\backslash $}stackrel
\linebreak [0]\ \hskip0em plus2.0em{}
\{
\mbox {$\backslash $}circ
\}
\{
{=}
\}
\#2.
\newline ]
\mbox{''}
]$

\item $
[
RootVisible(
\mathsf{x}
)
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\#1/tex
\linebreak [0]\ \hskip0em plus2.0em{}name/tex.
\mbox{''}
]$

\item $
[
RootVisible(
\mathsf{x}
)
\stackrel {\mathrm {name}}{=} 
\mbox{``}
\newline RootVisible(
\#1.
\newline )
\mbox{''}
]$

\item $
[
\mathsf{x}
{}^{hide}
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\#1.
\newline 
\{
\}
{\char94}
\{hide
\}
\mbox{''}
]$

\item $
[
\mathsf{x}
{}'
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\#1.
\newline 
\{
\}
\mbox {'}
\mbox{''}
]$

\item $
[
\mathsf{x}
= 
\mathsf{y}
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\#1.
\newline 
{=}
\linebreak [0]\ \hskip0em plus2.0em{}
\#2.
\mbox{''}
]$

\item $
[
\mathsf{x}
\neq 
\mathsf{y}
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\#1.
\newline 
\mbox {$\backslash $}neq
\linebreak [0]\ \hskip0em plus2.0em{}
\#2.
\mbox{''}
]$

\item $
[
\mathsf{x}
\Rightarrow 
\mathsf{y}
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\#1.
\newline 
\mbox {$\backslash $}Rightarrow
\linebreak [0]\ \hskip0em plus2.0em{}
\#2.
\mbox{''}
]$

\item $
[
\mathsf{x}
\Leftrightarrow 
\mathsf{y}
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\#1.
\newline 
\mbox {$\backslash $}Leftrightarrow
\linebreak [0]\ \hskip0em plus2.0em{}
\#2.
\mbox{''}
]$

\item $
[
\mathsf{x}
\mathrel{|} 
\mathsf{y}
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\#1.
\newline 
\mbox {$\backslash $}mathrel
\{|
\}
\linebreak [0]\ \hskip0em plus2.0em{}
\#2.
\mbox{''}
]$

\item $
[
\exists 
\mathsf{x}
\colon 
\mathsf{y}
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline 
\mbox {$\backslash $}exists
\linebreak [0]\ \hskip0em plus2.0em{}
\#1.
\newline 
\mbox {$\backslash $}colon
\linebreak [0]\ \hskip0em plus2.0em{}
\#2.
\mbox{''}
]$

\item $
[
\forall 
\mathsf{x}
\colon 
\mathsf{y}
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline 
\mbox {$\backslash $}forall
\linebreak [0]\ \hskip0em plus2.0em{}
\#1.
\newline 
\mbox {$\backslash $}colon
\linebreak [0]\ \hskip0em plus2.0em{}
\#2.
\mbox{''}
]$

\item $
[
\forall_{obj} 
\mathsf{x}
\colon 
\mathsf{y}
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline 
\mbox {$\backslash $}forall
\_
\{obj
\}
\linebreak [0]\ \hskip0em plus2.0em{}
\#1.
\newline 
\mbox {$\backslash $}colon
\linebreak [0]\ \hskip0em plus2.0em{}
\#2.
\mbox{''}
]$

\item $
[
\Pi 
\mathsf{x}
\colon 
\mathsf{y}
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline 
\mbox {$\backslash $}Pi
\linebreak [0]\ \hskip0em plus2.0em{}
\#1.
\newline 
\mbox {$\backslash $}colon
\linebreak [0]\ \hskip0em plus2.0em{}
\#2.
\mbox{''}
]$

\item $
[
Arbitrary \gg 
\mathsf {i}
;
\mathsf {p}
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline 
\mbox {$\backslash $}newline
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {$\backslash $}makebox
\linebreak [0]\ \hskip0em plus2.0em{}[0.1
\mbox {$\backslash $}textwidth
\linebreak [0]\ \hskip0em plus2.0em{}][l]
\{
\$
\newline 
\mbox {$\backslash $}if
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {$\backslash $}relax
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {$\backslash $}csname
\linebreak [0]\ \hskip0em plus2.0em{}lgwprooflinep
\mbox {$\backslash $}endcsname
\linebreak [0]\ \hskip0em plus2.0em{}L
\_?
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {$\backslash $}else
\newline 
\mbox {$\backslash $}global
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {$\backslash $}advance
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {$\backslash $}lgwproofline
\linebreak [0]\ \hskip0em plus2.0em{}by
\linebreak [0]\ \hskip0em plus2.0em{}1
\newline L
\mbox {$\backslash $}ifnum
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {$\backslash $}lgwproofline
\linebreak [0]\ \hskip0em plus2.0em{}
{<}10
\linebreak [0]\ \hskip0em plus2.0em{}0
\mbox {$\backslash $}fi
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {$\backslash $}number
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {$\backslash $}lgwproofline
\newline 
\mbox {$\backslash $}fi
\linebreak [0]\ \hskip0em plus2.0em{}
\newline 
\$
{:}
\}
\mbox {$\backslash $}makebox
\linebreak [0]\ \hskip0em plus2.0em{}[0.4
\mbox {$\backslash $}textwidth
\linebreak [0]\ \hskip0em plus2.0em{}][l]
\{
\$Arbitrary
\{
\}
\mbox {$\backslash $}gg
\{
\}
\$
\}
\mbox {$\backslash $}quad
\newline 
\mbox {$\backslash $}parbox
\linebreak [0]\ \hskip0em plus2.0em{}[t]
\{0.4
\mbox {$\backslash $}textwidth
\linebreak [0]\ \hskip0em plus2.0em{}
\}
\{
\$
\#1.
\newline 
\$
\mbox {$\backslash $}hfill
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {$\backslash $}makebox
\linebreak [0]\ \hskip0em plus2.0em{}[0mm][l]
\{
\mbox {$\backslash $}quad
\linebreak [0]\ \hskip0em plus2.0em{};
\}
\}
\#2.
\mbox{''}
]$

\item $
[
Arbitrary \gg 
\mathsf {i}
;
\mathsf {p}
\stackrel {\mathrm {name}}{=} 
\mbox{``}
\newline Arbitrary
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {$\backslash $}gg
\linebreak [0]\ \hskip0em plus2.0em{}
\#1.
\newline ;
\#2.
\mbox{''}
]$

\item $
[
\mathsf{x}
\backslash \backslash 
\mathsf{y}
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\#1.
\newline 
\mbox {$\backslash $}
\mbox {$\backslash $}
\{
\}
\#2.
\mbox{''}
]$

\item $
[
\mathsf{x}
\backslash \backslash 
\mathsf{y}
\stackrel {\mathrm {name}}{=} 
\mbox{``}
\#1.
\newline 
\mbox {$\backslash $}backslash
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {$\backslash $}backslash
\linebreak [0]\ \hskip0em plus2.0em{}
\#2.
\mbox{''}
]$

\item $
[
A
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline A
\mbox{''}
]$

\item $
[
R
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline R
\mbox{''}
]$

\item $
[
C
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline C
\mbox{''}
]$

\item $
[
T
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline T
\mbox{''}
]$

\item $
[
L
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline L
\mbox{''}
]$

\item $
[
\{
\mathsf{x}
\}
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline 
\mbox {$\backslash $}
\{
\#1.
\newline 
\mbox {$\backslash $}
\}
\mbox{''}
]$

\item $
[
S
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline S
\mbox{''}
]$

\item $
[
Neg
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline Neg
\mbox{''}
]$

\item $
[
S1
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline S1
\mbox{''}
]$

\item $
[
S2
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline S2
\mbox{''}
]$

\item $
[
S3
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline S3
\mbox{''}
]$

\item $
[
S4
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline S4
\mbox{''}
]$

\item $
[
S5
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline S5
\mbox{''}
]$

\item $
[
S6
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline S6
\mbox{''}
]$

\item $
[
S7
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline S7
\mbox{''}
]$

\item $
[
S8
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline S8
\mbox{''}
]$

\item $
[
S9
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline S9
\mbox{''}
]$

\item $
[
S10
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline S10
\mbox{''}
]$

\item $
[
MP
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline MP
\mbox{''}
]$

\item $
[
Gen
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline Gen
\mbox{''}
]$

\item $
[
Ded
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline Ded
\mbox{''}
]$

\item $
[
Repetition
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline Repetition
\mbox{''}
]$

\item $
[
A1'
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline A1
\mbox {'}
\mbox{''}
]$

\item $
[
A2'
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline A2
\mbox {'}
\mbox{''}
]$

\item $
[
A4'
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline A4
\mbox {'}
\mbox{''}
]$

\item $
[
A5'
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline A5
\mbox {'}
\mbox{''}
]$

\item $
[
\mathsf{x}
{}^{var}
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\#1.
\newline 
\{
\}
{\char94}
\{var
\}
\mbox{''}
]$

\item $
[
\mathsf{x}
\#
\mathsf{y}
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\#1.
\newline 
\mbox {$\backslash $}
\#.
\#2.
\mbox{''}
]$

\item $
[
\mathsf{x}
\#^0
\mathsf{y}
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\#1.
\newline 
\mbox {$\backslash $}
\#.
{\char94}0
\#2.
\mbox{''}
]$

\item $
[
\mathsf{x}
\#^1
\mathsf{y}
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\#1.
\newline 
\mbox {$\backslash $}
\#.
{\char94}1
\#2.
\mbox{''}
]$

\item $
[
\mathsf{x}
\#^*
\mathsf{y}
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\#1.
\newline 
\mbox {$\backslash $}
\#.
{\char94}
{*}
\#2.
\mbox{''}
]$

\item $
[
\langle 
\mathsf{x}
{\equiv} 
\mathsf{y}
| 
\mathsf{z}
{:=} 
\mathsf {u}
\rangle 
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline 
\mbox {$\backslash $}langle
\linebreak [0]\ \hskip0em plus2.0em{}
\#1.
\newline 
\{
\mbox {$\backslash $}equiv
\}
\linebreak [0]\ \hskip0em plus2.0em{}
\#2.
\newline |
\linebreak [0]\ \hskip0em plus2.0em{}
\#3.
\newline 
\{
{:}
{=}
\}
\linebreak [0]\ \hskip0em plus2.0em{}
\#4.
\newline 
\mbox {$\backslash $}rangle
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox{''}
]$

\item $
[
\langle 
\mathsf{x}
{\equiv}^0 
\mathsf{y}
| 
\mathsf{z}
{:=} 
\mathsf {u}
\rangle 
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline 
\mbox {$\backslash $}langle
\linebreak [0]\ \hskip0em plus2.0em{}
\#1.
\newline 
\{
\mbox {$\backslash $}equiv
\}
{\char94}0
\linebreak [0]\ \hskip0em plus2.0em{}
\#2.
\newline |
\linebreak [0]\ \hskip0em plus2.0em{}
\#3.
\newline 
\{
{:}
{=}
\}
\linebreak [0]\ \hskip0em plus2.0em{}
\#4.
\newline 
\mbox {$\backslash $}rangle
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox{''}
]$

\item $
[
\langle 
\mathsf{x}
{\equiv}^1 
\mathsf{y}
| 
\mathsf{z}
{:=} 
\mathsf {u}
\rangle 
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline 
\mbox {$\backslash $}langle
\linebreak [0]\ \hskip0em plus2.0em{}
\#1.
\newline 
\{
\mbox {$\backslash $}equiv
\}
{\char94}1
\linebreak [0]\ \hskip0em plus2.0em{}
\#2.
\newline |
\linebreak [0]\ \hskip0em plus2.0em{}
\#3.
\newline 
\{
{:}
{=}
\}
\linebreak [0]\ \hskip0em plus2.0em{}
\#4.
\newline 
\mbox {$\backslash $}rangle
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox{''}
]$

\item $
[
\langle 
\mathsf{x}
{\equiv}^* 
\mathsf{y}
| 
\mathsf{z}
{:=} 
\mathsf {u}
\rangle 
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline 
\mbox {$\backslash $}langle
\linebreak [0]\ \hskip0em plus2.0em{}
\#1.
\newline 
\{
\mbox {$\backslash $}equiv
\}
{\char94}
{*}
\linebreak [0]\ \hskip0em plus2.0em{}
\#2.
\newline |
\linebreak [0]\ \hskip0em plus2.0em{}
\#3.
\newline 
\{
{:}
{=}
\}
\linebreak [0]\ \hskip0em plus2.0em{}
\#4.
\newline 
\mbox {$\backslash $}rangle
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox{''}
]$

\item $
[
Ded(
\mathsf{x}
,
\mathsf{y}
)
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline Ded(
\#1.
\newline ,
\#2.
\newline )
\mbox{''}
]$

\item $
[
Ded_0(
\mathsf{x}
,
\mathsf{y}
)
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline Ded
\_0(
\#1.
\newline ,
\#2.
\newline )
\mbox{''}
]$

\item $
[
Ded_1(
\mathsf{x}
,
\mathsf{y}
,
\mathsf{z}
)
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline Ded
\_1(
\#1.
\newline ,
\#2.
\newline ,
\#3.
\newline )
\mbox{''}
]$

\item $
[
Ded_2(
\mathsf{x}
,
\mathsf{y}
,
\mathsf{z}
)
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline Ded
\_2(
\#1.
\newline ,
\#2.
\newline ,
\#3.
\newline )
\mbox{''}
]$

\item $
[
Ded_3(
\mathsf{x}
,
\mathsf{y}
,
\mathsf{z}
,
\mathsf {u}
)
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline Ded
\_3(
\#1.
\newline ,
\#2.
\newline ,
\#3.
\newline ,
\#4.
\newline )
\mbox{''}
]$

\item $
[
Ded_4(
\mathsf{x}
,
\mathsf{y}
,
\mathsf{z}
,
\mathsf {u}
)
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline Ded
\_4(
\#1.
\newline ,
\#2.
\newline ,
\#3.
\newline ,
\#4.
\newline )
\mbox{''}
]$

\item $
[
Ded_4^*(
\mathsf{x}
,
\mathsf{y}
,
\mathsf{z}
,
\mathsf {u}
)
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline Ded
\_4
{\char94}
{*}(
\#1.
\newline ,
\#2.
\newline ,
\#3.
\newline ,
\#4.
\newline )
\mbox{''}
]$

\item $
[
Ded_5(
\mathsf{x}
,
\mathsf{y}
,
\mathsf{z}
)
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline Ded
\_5(
\#1.
\newline ,
\#2.
\newline ,
\#3.
\newline )
\mbox{''}
]$

\item $
[
Ded_6(
\mathsf {p}
,
\mathsf {c}
,
\mathsf {e}
,
\mathsf {b}
)
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline Ded
\_6(
\#1.
\newline ,
\#2.
\newline ,
\#3.
\newline ,
\#4.
\newline )
\mbox{''}
]$

\item $
[
Ded_6^*(
\mathsf {p}
,
\mathsf {c}
,
\mathsf {e}
,
\mathsf {b}
)
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline Ded
\_6
{\char94}
{*}(
\#1.
\newline ,
\#2.
\newline ,
\#3.
\newline ,
\#4.
\newline )
\mbox{''}
]$

\item $
[
Ded_7(
\mathsf {p}
)
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline Ded
\_7(
\#1.
\newline )
\mbox{''}
]$

\item $
[
Ded_8(
\mathsf {p}
,
\mathsf {b}
)
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline Ded
\_8(
\#1.
\newline ,
\#2.
\newline )
\mbox{''}
]$

\item $
[
Ded_8^*(
\mathsf {p}
,
\mathsf {b}
)
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline Ded
\_8
{\char94}
{*}(
\#1.
\newline ,
\#2.
\newline )
\mbox{''}
]$

\item $
[
Begin \, 
\mathsf {b}
 ; 
\mathsf {l}
 : End ; 
\mathsf {p}
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline 
\mbox {$\backslash $}newline
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {$\backslash $}makebox
\linebreak [0]\ \hskip0em plus2.0em{}[0.1
\mbox {$\backslash $}textwidth]
\{
\}
\%
\newline 
\mbox {$\backslash $}parbox
\linebreak [0]\ \hskip0em plus2.0em{}[b]
\{0.4
\mbox {$\backslash $}textwidth
\linebreak [0]\ \hskip0em plus2.0em{}
\}
\{
\mbox {$\backslash $}raggedright
\newline 
\mbox {$\backslash $}setlength
\linebreak [0]\ \hskip0em plus2.0em{}
\{
\mbox {$\backslash $}parindent
\linebreak [0]\ \hskip0em plus2.0em{}
\}
\{
\mbox{-}0.1
\mbox {$\backslash $}textwidth
\linebreak [0]\ \hskip0em plus2.0em{}
\}
\%
\newline 
\mbox {$\backslash $}makebox
\linebreak [0]\ \hskip0em plus2.0em{}[0.1
\mbox {$\backslash $}textwidth
\linebreak [0]\ \hskip0em plus2.0em{}][l]
\{
\$
\newline 
\mbox {$\backslash $}if
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {$\backslash $}relax
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {$\backslash $}csname
\linebreak [0]\ \hskip0em plus2.0em{}lgwprooflinep
\mbox {$\backslash $}endcsname
\linebreak [0]\ \hskip0em plus2.0em{}L
\_?
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {$\backslash $}else
\newline 
\mbox {$\backslash $}global
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {$\backslash $}advance
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {$\backslash $}lgwproofline
\linebreak [0]\ \hskip0em plus2.0em{}by
\linebreak [0]\ \hskip0em plus2.0em{}1
\newline L
\mbox {$\backslash $}ifnum
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {$\backslash $}lgwproofline
\linebreak [0]\ \hskip0em plus2.0em{}
{<}10
\linebreak [0]\ \hskip0em plus2.0em{}0
\mbox {$\backslash $}fi
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {$\backslash $}number
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {$\backslash $}lgwproofline
\newline 
\mbox {$\backslash $}fi
\linebreak [0]\ \hskip0em plus2.0em{}
\newline 
\$
{:}
\}
\$Block
\linebreak [0]\ \hskip0em plus2.0em{}
\{
\}
\mbox {$\backslash $}gg
\linebreak [0]\ \hskip0em plus2.0em{}
\{
\}
\$
\}
\mbox {$\backslash $}quad
\newline 
\mbox {$\backslash $}parbox
\linebreak [0]\ \hskip0em plus2.0em{}[t]
\{0.4
\mbox {$\backslash $}textwidth
\linebreak [0]\ \hskip0em plus2.0em{}
\}
\{
\$Begin
\newline 
\$
\mbox {$\backslash $}hfill
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {$\backslash $}makebox
\linebreak [0]\ \hskip0em plus2.0em{}[0mm][l]
\{
\mbox {$\backslash $}quad
\linebreak [0]\ \hskip0em plus2.0em{};
\}
\}
\#1.
\newline 
\mbox {$\backslash $}newline
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {$\backslash $}makebox
\linebreak [0]\ \hskip0em plus2.0em{}[0.1
\mbox {$\backslash $}textwidth]
\{
\}
\%
\newline 
\mbox {$\backslash $}parbox
\linebreak [0]\ \hskip0em plus2.0em{}[b]
\{0.4
\mbox {$\backslash $}textwidth
\linebreak [0]\ \hskip0em plus2.0em{}
\}
\{
\mbox {$\backslash $}raggedright
\newline 
\mbox {$\backslash $}setlength
\linebreak [0]\ \hskip0em plus2.0em{}
\{
\mbox {$\backslash $}parindent
\linebreak [0]\ \hskip0em plus2.0em{}
\}
\{
\mbox{-}0.1
\mbox {$\backslash $}textwidth
\linebreak [0]\ \hskip0em plus2.0em{}
\}
\%
\newline 
\mbox {$\backslash $}makebox
\linebreak [0]\ \hskip0em plus2.0em{}[0.1
\mbox {$\backslash $}textwidth
\linebreak [0]\ \hskip0em plus2.0em{}][l]
\{
\$
\#2.
\newline 
\$
{:}
\}
\$Block
\linebreak [0]\ \hskip0em plus2.0em{}
\{
\}
\mbox {$\backslash $}gg
\linebreak [0]\ \hskip0em plus2.0em{}
\{
\}
\$
\}
\mbox {$\backslash $}quad
\newline 
\mbox {$\backslash $}parbox
\linebreak [0]\ \hskip0em plus2.0em{}[t]
\{0.4
\mbox {$\backslash $}textwidth
\linebreak [0]\ \hskip0em plus2.0em{}
\}
\{
\$End
\newline 
\$
\mbox {$\backslash $}hfill
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {$\backslash $}makebox
\linebreak [0]\ \hskip0em plus2.0em{}[0mm][l]
\{
\mbox {$\backslash $}quad
\linebreak [0]\ \hskip0em plus2.0em{};
\}
\}
\#3.
\mbox{''}
]$

\item $
[
Begin \, 
\mathsf {b}
 ; 
\mathsf {l}
 : End ; 
\mathsf {p}
\stackrel {\mathrm {name}}{=} 
\mbox{``}
\newline Begin
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {$\backslash $},
\linebreak [0]\ \hskip0em plus2.0em{}
\#1.
\newline 
\linebreak [0]\ \hskip0em plus2.0em{};
\linebreak [0]\ \hskip0em plus2.0em{}
\#2.
\newline 
\linebreak [0]\ \hskip0em plus2.0em{}
{:}
\linebreak [0]\ \hskip0em plus2.0em{}End
\linebreak [0]\ \hskip0em plus2.0em{};
\linebreak [0]\ \hskip0em plus2.0em{}
\#3.
\mbox{''}
]$

\item $
[
Last\ block\ line \, 
\mathsf {a}
\gg 
\mathsf {i}
\,;
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline 
\mbox {$\backslash $}newline
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {$\backslash $}makebox
\linebreak [0]\ \hskip0em plus2.0em{}[0.1
\mbox {$\backslash $}textwidth]
\{
\}
\%
\newline 
\mbox {$\backslash $}parbox
\linebreak [0]\ \hskip0em plus2.0em{}[b]
\{0.4
\mbox {$\backslash $}textwidth
\linebreak [0]\ \hskip0em plus2.0em{}
\}
\{
\mbox {$\backslash $}raggedright
\newline 
\mbox {$\backslash $}setlength
\linebreak [0]\ \hskip0em plus2.0em{}
\{
\mbox {$\backslash $}parindent
\linebreak [0]\ \hskip0em plus2.0em{}
\}
\{
\mbox{-}0.1
\mbox {$\backslash $}textwidth
\linebreak [0]\ \hskip0em plus2.0em{}
\}
\%
\newline 
\mbox {$\backslash $}makebox
\linebreak [0]\ \hskip0em plus2.0em{}[0.1
\mbox {$\backslash $}textwidth
\linebreak [0]\ \hskip0em plus2.0em{}][l]
\{
\$
\newline 
\mbox {$\backslash $}if
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {$\backslash $}relax
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {$\backslash $}csname
\linebreak [0]\ \hskip0em plus2.0em{}lgwprooflinep
\mbox {$\backslash $}endcsname
\linebreak [0]\ \hskip0em plus2.0em{}L
\_?
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {$\backslash $}else
\newline 
\mbox {$\backslash $}global
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {$\backslash $}advance
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {$\backslash $}lgwproofline
\linebreak [0]\ \hskip0em plus2.0em{}by
\linebreak [0]\ \hskip0em plus2.0em{}1
\newline L
\mbox {$\backslash $}ifnum
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {$\backslash $}lgwproofline
\linebreak [0]\ \hskip0em plus2.0em{}
{<}10
\linebreak [0]\ \hskip0em plus2.0em{}0
\mbox {$\backslash $}fi
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {$\backslash $}number
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {$\backslash $}lgwproofline
\newline 
\mbox {$\backslash $}fi
\linebreak [0]\ \hskip0em plus2.0em{}
\newline 
\$
{:}
\}
\$
\#1.
\newline 
\{
\}
\mbox {$\backslash $}gg
\linebreak [0]\ \hskip0em plus2.0em{}
\{
\}
\$
\}
\mbox {$\backslash $}quad
\newline 
\mbox {$\backslash $}parbox
\linebreak [0]\ \hskip0em plus2.0em{}[t]
\{0.4
\mbox {$\backslash $}textwidth
\linebreak [0]\ \hskip0em plus2.0em{}
\}
\{
\$
\#2.
\newline 
\$
\mbox {$\backslash $}hfill
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {$\backslash $}makebox
\linebreak [0]\ \hskip0em plus2.0em{}[0mm][l]
\{
\mbox {$\backslash $}quad
\linebreak [0]\ \hskip0em plus2.0em{};
\}
\}
\mbox{''}
]$

\item $
[
Last\ block\ line \, 
\mathsf {a}
\gg 
\mathsf {i}
\,;
\stackrel {\mathrm {name}}{=} 
\mbox{``}
\newline Last
\mbox {$\backslash $}
\linebreak [0]\ \hskip0em plus2.0em{}block
\mbox {$\backslash $}
\linebreak [0]\ \hskip0em plus2.0em{}line
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {$\backslash $},
\linebreak [0]\ \hskip0em plus2.0em{}
\#1.
\newline 
\mbox {$\backslash $}gg
\linebreak [0]\ \hskip0em plus2.0em{}
\#2.
\newline 
\mbox {$\backslash $},;
\mbox{''}
]$

\item $
[
\mathsf{x}
\unrhd 
\mathsf{y}
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\#1.
\newline 
\mbox {$\backslash $}unrhd
\linebreak [0]\ \hskip0em plus2.0em{}
\#2.
\mbox{''}
]$

\item $
[
\mathsf{x}
\| 
\mathsf{y}
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\#1.
\newline 
\mbox {$\backslash $}|
\linebreak [0]\ \hskip0em plus2.0em{}
\#2.
\mbox{''}
]$

\item $
[
Prop\ 3.2a
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline Prop
\mbox {$\backslash $}
\linebreak [0]\ \hskip0em plus2.0em{}3.2a
\mbox{''}
]$

\item $
[
Prop\ 3.2b
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline Prop
\mbox {$\backslash $}
\linebreak [0]\ \hskip0em plus2.0em{}3.2b
\mbox{''}
]$

\item $
[
Prop\ 3.2c
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline Prop
\mbox {$\backslash $}
\linebreak [0]\ \hskip0em plus2.0em{}3.2c
\mbox{''}
]$

\item $
[
Prop\ 3.2d
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline Prop
\mbox {$\backslash $}
\linebreak [0]\ \hskip0em plus2.0em{}3.2d
\mbox{''}
]$

\item $
[
Prop\ 3.2e_1
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline Prop
\mbox {$\backslash $}
\linebreak [0]\ \hskip0em plus2.0em{}3.2e
\_1
\mbox{''}
]$

\item $
[
Prop\ 3.2e_2
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline Prop
\mbox {$\backslash $}
\linebreak [0]\ \hskip0em plus2.0em{}3.2e
\_2
\mbox{''}
]$

\item $
[
Prop\ 3.2e
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline Prop
\mbox {$\backslash $}
\linebreak [0]\ \hskip0em plus2.0em{}3.2e
\mbox{''}
]$

\item $
[
Prop\ 3.2f_1
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline Prop
\mbox {$\backslash $}
\linebreak [0]\ \hskip0em plus2.0em{}3.2f
\_1
\mbox{''}
]$

\item $
[
Prop\ 3.2f_2
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline Prop
\mbox {$\backslash $}
\linebreak [0]\ \hskip0em plus2.0em{}3.2f
\_2
\mbox{''}
]$

\item $
[
Prop\ 3.2f
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline Prop
\mbox {$\backslash $}
\linebreak [0]\ \hskip0em plus2.0em{}3.2f
\mbox{''}
]$

\item $
[
Prop\ 3.2g_1
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline Prop
\mbox {$\backslash $}
\linebreak [0]\ \hskip0em plus2.0em{}3.2g
\_1
\mbox{''}
]$

\item $
[
Prop\ 3.2g_2
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline Prop
\mbox {$\backslash $}
\linebreak [0]\ \hskip0em plus2.0em{}3.2g
\_2
\mbox{''}
]$

\item $
[
Prop\ 3.2g
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline Prop
\mbox {$\backslash $}
\linebreak [0]\ \hskip0em plus2.0em{}3.2g
\mbox{''}
]$

\item $
[
Prop\ 3.2h_1
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline Prop
\mbox {$\backslash $}
\linebreak [0]\ \hskip0em plus2.0em{}3.2h
\_1
\mbox{''}
]$

\item $
[
Prop\ 3.2h_2
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline Prop
\mbox {$\backslash $}
\linebreak [0]\ \hskip0em plus2.0em{}3.2h
\_2
\mbox{''}
]$

\item $
[
Prop\ 3.2h
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline Prop
\mbox {$\backslash $}
\linebreak [0]\ \hskip0em plus2.0em{}3.2h
\mbox{''}
]$

\item $
[
Prop\ 3.2i
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline Prop
\mbox {$\backslash $}
\linebreak [0]\ \hskip0em plus2.0em{}3.2i
\mbox{''}
]$

\item $
[
Prop\ 3.2j
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline Prop
\mbox {$\backslash $}
\linebreak [0]\ \hskip0em plus2.0em{}3.2j
\mbox{''}
]$
\item $
[
Prop\ 3.2j_1
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline Prop
\mbox {$\backslash $}
\linebreak [0]\ \hskip0em plus2.0em{}3.2j
\_1
\mbox{''}
]$
\item $
[
Prop\ 3.2j_2
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline Prop
\mbox {$\backslash $}
\linebreak [0]\ \hskip0em plus2.0em{}3.2j
\_2
\mbox{''}
]$

\item $
[
Prop\ 3.2k
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline Prop
\mbox {$\backslash $}
\linebreak [0]\ \hskip0em plus2.0em{}3.2k
\mbox{''}
]$
\item $
[
Prop\ 3.2k_1
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline Prop
\mbox {$\backslash $}
\linebreak [0]\ \hskip0em plus2.0em{}3.2k
\_1
\mbox{''}
]$
\item $
[
Prop\ 3.2k_2
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline Prop
\mbox {$\backslash $}
\linebreak [0]\ \hskip0em plus2.0em{}3.2k
\_2
\mbox{''}
]$

\item $
[
Prop\ 3.2l
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline Prop
\mbox {$\backslash $}
\linebreak [0]\ \hskip0em plus2.0em{}3.2l
\mbox{''}
]$
\item $
[
Prop\ 3.2l_1
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline Prop
\mbox {$\backslash $}
\linebreak [0]\ \hskip0em plus2.0em{}3.2l
\_1
\mbox{''}
]$
\item $
[
Prop\ 3.2l_2
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline Prop
\mbox {$\backslash $}
\linebreak [0]\ \hskip0em plus2.0em{}3.2l
\_2
\mbox{''}
]$

\item $
[
Prop\ 3.2m
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline Prop
\mbox {$\backslash $}
\linebreak [0]\ \hskip0em plus2.0em{}3.2m
\mbox{''}
]$
\item $
[
Prop\ 3.2m_1
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline Prop
\mbox {$\backslash $}
\linebreak [0]\ \hskip0em plus2.0em{}3.2m
\_1
\mbox{''}
]$
\item $
[
Prop\ 3.2m_2
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline Prop
\mbox {$\backslash $}
\linebreak [0]\ \hskip0em plus2.0em{}3.2m
\_2
\mbox{''}
]$

\item $
[
Prop\ 3.2n
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline Prop
\mbox {$\backslash $}
\linebreak [0]\ \hskip0em plus2.0em{}3.2n
\mbox{''}
]$
\item $
[
Prop\ 3.2n_1
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline Prop
\mbox {$\backslash $}
\linebreak [0]\ \hskip0em plus2.0em{}3.2n
\_1
\mbox{''}
]$
\item $
[
Prop\ 3.2n_2
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline Prop
\mbox {$\backslash $}
\linebreak [0]\ \hskip0em plus2.0em{}3.2n
\_2
\mbox{''}
]$

\item $
[
Prop\ 3.2o
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline Prop
\mbox {$\backslash $}
\linebreak [0]\ \hskip0em plus2.0em{}3.2o
\mbox{''}
]$

\item $
[
Prop\ 3.4a_1
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline Prop
\mbox {$\backslash $}
\linebreak [0]\ \hskip0em plus2.0em{}3.4a
\_1
\mbox{''}
]$
\item $
[
Prop\ 3.4a_2
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline Prop
\mbox {$\backslash $}
\linebreak [0]\ \hskip0em plus2.0em{}3.4a
\_2
\mbox{''}
]$
\item $
[
Prop\ 3.4a
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline Prop
\mbox {$\backslash $}
\linebreak [0]\ \hskip0em plus2.0em{}3.4a
\mbox{''}
]$
\item $
[
Prop\ 3.4b
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline Prop
\mbox {$\backslash $}
\linebreak [0]\ \hskip0em plus2.0em{}3.4b
\mbox{''}
]$
\item $
[
Prop\ 3.4c_1
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline Prop
\mbox {$\backslash $}
\linebreak [0]\ \hskip0em plus2.0em{}3.4c
\_1
\mbox{''}
]$
\item $
[
Prop\ 3.4c_2
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline Prop
\mbox {$\backslash $}
\linebreak [0]\ \hskip0em plus2.0em{}3.4c
\_2
\mbox{''}
]$
\item $
[
Prop\ 3.4c
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline Prop
\mbox {$\backslash $}
\linebreak [0]\ \hskip0em plus2.0em{}3.4c
\mbox{''}
]$
\item $
[
Prop\ 3.4d_1
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline Prop
\mbox {$\backslash $}
\linebreak [0]\ \hskip0em plus2.0em{}3.4d
\_1
\mbox{''}
]$
\item $
[
Prop\ 3.4d_2
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline Prop
\mbox {$\backslash $}
\linebreak [0]\ \hskip0em plus2.0em{}3.4d
\_2
\mbox{''}
]$
\item $
[
Prop\ 3.4d
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline Prop
\mbox {$\backslash $}
\linebreak [0]\ \hskip0em plus2.0em{}3.4d
\mbox{''}
]$

\item $
[
MacroIndent(
\mathsf{x}
)
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline 
\$
\%
\newline 
\mbox {$\backslash $}leftskip
{=}1em
\%
\newline 
\$
\#1.
\mbox{''}
]$

\item $
[
MacroIndent(
\mathsf{x}
)
\stackrel {\mathrm {name}}{=} 
\mbox{``}
\newline MacroIndent(
\#1.
\newline )
\mbox{''}
]$

\item $
[
Block_1(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
)
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline Block
\_1(
\#1.
\newline ,
\#2.
\newline ,
\#3.
\newline )
\mbox{''}
]$

\item $
[
Block_2(
\mathsf {b}
)
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline Block
\_2(
\#1.
\newline )
\mbox{''}
]$

\item $
[
 \rightarrow 
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline 
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {$\backslash $}rightarrow
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox{''}
]$

\end{list}



\subsection{Variables}

$
[\overline{
\mathsf{x}}
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\mbox {$\backslash $}overline
\{
\#1.
\}
\mbox{''}
]$



$
[
\mathit{a}
\mathrel {\ddot {=}}\overline{
\mathsf {a}}
]$

$
[
\mathit{b}
\mathrel {\ddot {=}}\overline{
\mathsf {b}}
]$

$
[
\mathit{c}
\mathrel {\ddot {=}}\overline{
\mathsf {c}}
]$

$
[
\mathit{d}
\mathrel {\ddot {=}}\overline{
\mathsf {d}}
]$

$
[
\mathit{e}
\mathrel {\ddot {=}}\overline{
\mathsf {e}}
]$

$
[
\mathit{f}
\mathrel {\ddot {=}}\overline{
\mathsf {f}}
]$

$
[
\mathit{g}
\mathrel {\ddot {=}}\overline{
\mathsf {g}}
]$

$
[
\mathit{h}
\mathrel {\ddot {=}}\overline{
\mathsf {h}}
]$

$
[
\mathit{i}
\mathrel {\ddot {=}}\overline{
\mathsf {i}}
]$

$
[
\mathit{j}
\mathrel {\ddot {=}}\overline{
\mathsf {j}}
]$

$
[
\mathit{k}
\mathrel {\ddot {=}}\overline{
\mathsf {k}}
]$

$
[
\mathit{l}
\mathrel {\ddot {=}}\overline{
\mathsf {l}}
]$

$
[
\mathit{m}
\mathrel {\ddot {=}}\overline{
\mathsf {m}}
]$

$
[
\mathit{n}
\mathrel {\ddot {=}}\overline{
\mathsf {n}}
]$

$
[
\mathit{o}
\mathrel {\ddot {=}}\overline{
\mathsf {o}}
]$

$
[
\mathit{p}
\mathrel {\ddot {=}}\overline{
\mathsf {p}}
]$

$
[
\mathit{q}
\mathrel {\ddot {=}}\overline{
\mathsf {q}}
]$

$
[
\mathit{r}
\mathrel {\ddot {=}}\overline{
\mathsf {r}}
]$

$
[
\mathit{s}
\mathrel {\ddot {=}}\overline{
\mathsf {s}}
]$

$
[
\mathit{t}
\mathrel {\ddot {=}}\overline{
\mathsf {t}}
]$

$
[
\mathit{u}
\mathrel {\ddot {=}}\overline{
\mathsf {u}}
]$

$
[
\mathit{v}
\mathrel {\ddot {=}}\overline{
\mathsf {v}}
]$

$
[
\mathit{w}
\mathrel {\ddot {=}}\overline{
\mathsf {w}}
]$

$
[
\mathit{x}
\mathrel {\ddot {=}}\overline{
\mathsf{x}}
]$

$
[
\mathit{y}
\mathrel {\ddot {=}}\overline{
\mathsf{y}}
]$

$
[
\mathit{z}
\mathrel {\ddot {=}}\overline{
\mathsf{z}}
]$



$
[
\mathit{a}
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline 
\mbox {$\backslash $}mathit
\{a
\}
\mbox{''}
]$

$
[
\mathit{b}
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline 
\mbox {$\backslash $}mathit
\{b
\}
\mbox{''}
]$

$
[
\mathit{c}
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline 
\mbox {$\backslash $}mathit
\{c
\}
\mbox{''}
]$

$
[
\mathit{d}
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline 
\mbox {$\backslash $}mathit
\{d
\}
\mbox{''}
]$

$
[
\mathit{e}
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline 
\mbox {$\backslash $}mathit
\{e
\}
\mbox{''}
]$

$
[
\mathit{f}
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline 
\mbox {$\backslash $}mathit
\{f
\}
\mbox{''}
]$

$
[
\mathit{g}
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline 
\mbox {$\backslash $}mathit
\{g
\}
\mbox{''}
]$

$
[
\mathit{h}
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline 
\mbox {$\backslash $}mathit
\{h
\}
\mbox{''}
]$

$
[
\mathit{i}
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline 
\mbox {$\backslash $}mathit
\{i
\}
\mbox{''}
]$

$
[
\mathit{j}
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline 
\mbox {$\backslash $}mathit
\{j
\}
\mbox{''}
]$

$
[
\mathit{k}
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline 
\mbox {$\backslash $}mathit
\{k
\}
\mbox{''}
]$

$
[
\mathit{l}
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline 
\mbox {$\backslash $}mathit
\{l
\}
\mbox{''}
]$

$
[
\mathit{m}
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline 
\mbox {$\backslash $}mathit
\{m
\}
\mbox{''}
]$

$
[
\mathit{n}
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline 
\mbox {$\backslash $}mathit
\{n
\}
\mbox{''}
]$

$
[
\mathit{o}
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline 
\mbox {$\backslash $}mathit
\{o
\}
\mbox{''}
]$

$
[
\mathit{p}
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline 
\mbox {$\backslash $}mathit
\{p
\}
\mbox{''}
]$

$
[
\mathit{q}
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline 
\mbox {$\backslash $}mathit
\{q
\}
\mbox{''}
]$

$
[
\mathit{r}
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline 
\mbox {$\backslash $}mathit
\{r
\}
\mbox{''}
]$

$
[
\mathit{s}
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline 
\mbox {$\backslash $}mathit
\{s
\}
\mbox{''}
]$

$
[
\mathit{t}
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline 
\mbox {$\backslash $}mathit
\{t
\}
\mbox{''}
]$

$
[
\mathit{u}
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline 
\mbox {$\backslash $}mathit
\{u
\}
\mbox{''}
]$

$
[
\mathit{v}
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline 
\mbox {$\backslash $}mathit
\{v
\}
\mbox{''}
]$

$
[
\mathit{w}
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline 
\mbox {$\backslash $}mathit
\{w
\}
\mbox{''}
]$

$
[
\mathit{x}
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline 
\mbox {$\backslash $}mathit
\{x
\}
\mbox{''}
]$

$
[
\mathit{y}
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline 
\mbox {$\backslash $}mathit
\{y
\}
\mbox{''}
]$

$
[
\mathit{z}
\stackrel {\mathrm {tex}}{=} 
\mbox{``}
\newline 
\mbox {$\backslash $}mathit
\{z
\}
\mbox{''}
]$



\section{Priority table}


\begin {flushleft}$
\mathbf{Priority\ table} 
\newline \mathbf {Preassociative} \newline 
[
\mbox{opgave}
] , \linebreak [0] 
[
\mbox{base}
] , \linebreak [0] 
[
\mbox{bracket $
\ast $ end bracket}
] , \linebreak [0] 
[
\mbox{big bracket $
\ast $ end bracket}
] , \linebreak [0] 
[
\ \$
\ast \$\linebreak[0]\ 
] , \linebreak [0] 
[
\mathbf{flush\ left\ }[ 
\ast 
]
] , \linebreak [0] 
[
\mathsf{x}
] , \linebreak [0] 
[
\mathsf{y}
] , \linebreak [0] 
[
\mathsf{z}
] , \linebreak [0] 
[
[
\ast 
\bowtie
\ast 
]
] , \linebreak [0] 
[
[
\ast 
\stackrel{
\ast 
}{\rightarrow}
\ast 
]
] , \linebreak [0] 
[
\mathrm{pyk}
] , \linebreak [0] 
[
\mathrm{tex}
] , \linebreak [0] 
[
\mathrm{name}
] , \linebreak [0] 
[
\mathrm{prio}
] , \linebreak [0] 
[
\ast 
] , \linebreak [0] 
[
\mathsf {T}
] , \linebreak [0] 
[
\mathrm {if}(
\ast 
,\linebreak [0]
\ast 
,\linebreak [0]
\ast 
)
] , \linebreak [0] 
[
[
\ast 
\stackrel {
\ast 
}{\Rightarrow }
\ast 
]
] , \linebreak [0] 
[
\mathrm {val}
] , \linebreak [0] 
[
\mathrm {claim}
] , \linebreak [0] 
[
\bot 
] , \linebreak [0] 
[
f(
\ast 
)
] , \linebreak [0] 
[
(
\ast 
){}^{I} 
] , \linebreak [0] 
[
\mathsf {F}
] , \linebreak [0] 
[
\underline {0}
] , \linebreak [0] 
[
\underline {1}
] , \linebreak [0] 
[
\underline {2}
] , \linebreak [0] 
[
\underline {3}
] , \linebreak [0] 
[
\underline {4}
] , \linebreak [0] 
[
\underline {5}
] , \linebreak [0] 
[
\underline {6}
] , \linebreak [0] 
[
\underline {7}
] , \linebreak [0] 
[
\underline {8}
] , \linebreak [0] 
[
\underline {9}
] , \linebreak [0] 
[
0
] , \linebreak [0] 
[
1
] , \linebreak [0] 
[
2
] , \linebreak [0] 
[
3
] , \linebreak [0] 
[
4
] , \linebreak [0] 
[
5
] , \linebreak [0] 
[
6
] , \linebreak [0] 
[
7
] , \linebreak [0] 
[
8
] , \linebreak [0] 
[
9
] , \linebreak [0] 
[
\mathsf {a}
] , \linebreak [0] 
[
\mathsf {b}
] , \linebreak [0] 
[
\mathsf {c}
] , \linebreak [0] 
[
\mathsf {d}
] , \linebreak [0] 
[
\mathsf {e}
] , \linebreak [0] 
[
\mathsf {f}
] , \linebreak [0] 
[
\mathsf {g}
] , \linebreak [0] 
[
\mathsf {h}
] , \linebreak [0] 
[
\mathsf {i}
] , \linebreak [0] 
[
\mathsf {j}
] , \linebreak [0] 
[
\mathsf {k}
] , \linebreak [0] 
[
\mathsf {l}
] , \linebreak [0] 
[
\mathsf {m}
] , \linebreak [0] 
[
\mathsf {n}
] , \linebreak [0] 
[
\mathsf {o}
] , \linebreak [0] 
[
\mathsf {p}
] , \linebreak [0] 
[
\mathsf {q}
] , \linebreak [0] 
[
\mathsf {r}
] , \linebreak [0] 
[
\mathsf {s}
] , \linebreak [0] 
[
\mathsf {t}
] , \linebreak [0] 
[
\mathsf {u}
] , \linebreak [0] 
[
\mathsf {v}
] , \linebreak [0] 
[
\mathsf {w}
] , \linebreak [0] 
[
(
\ast 
)^M
] , \linebreak [0] 
[
\mathrm {If}(
\ast 
,\linebreak [0]
\ast 
,\linebreak [0]
\ast 
)
] , \linebreak [0] 
[\mathrm {array}\{
\ast 
\}
\ast 
\mathrm {end\ array}
] , \linebreak [0] 
[
l
] , \linebreak [0] 
[
c
] , \linebreak [0] 
[
r
] , \linebreak [0] 
[
\mathrm {empty}
] , \linebreak [0] 
[
\langle 
\ast 
\,{|}
\ast 
{:=}\,
\ast 
\rangle 
] , \linebreak [0] 
[
{\cal M}(
\ast 
)
] , \linebreak [0] 
[
\tilde {{\cal U}}(
\ast 
)
] , \linebreak [0] 
[
{\cal U}(
\ast 
)
] , \linebreak [0] 
[
{\cal U}^M(
\ast 
)
] , \linebreak [0] 
[
\mathbf {apply}(
\ast 
,
\ast 
)
] , \linebreak [0] 
[
\mathbf {apply}_1(
\ast 
,
\ast 
)
] , \linebreak [0] 
[
identifier( 
\ast 
)
] , \linebreak [0] 
[
identifier_{1}( 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
array\mbox{-}\linebreak[0]plus( 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
array\mbox{-}\linebreak[0]remove( 
\ast 
, 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
array\mbox{-}\linebreak[0]put( 
\ast 
, 
\ast 
, 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
array\mbox{-}\linebreak[0]add( 
\ast 
, 
\ast 
, 
\ast 
, 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
bit( 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
bit_1( 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
rack
] , \linebreak [0] 
[
\mbox {\tt \char34}\mathrm {vector}\mbox {\tt \char34}
] , \linebreak [0] 
[
\mbox {\tt \char34}\mathrm {bibliography}\mbox {\tt \char34}
] , \linebreak [0] 
[
\mbox {\tt \char34}\mathrm {dictionary}\mbox {\tt \char34}
] , \linebreak [0] 
[
\mbox {\tt \char34}\mathrm {body}\mbox {\tt \char34}
] , \linebreak [0] 
[
\mbox {\tt \char34}\mathrm {codex}\mbox {\tt \char34}
] , \linebreak [0] 
[
\mbox {\tt \char34}\mathrm {expansion}\mbox {\tt \char34}
] , \linebreak [0] 
[
\mbox {\tt \char34}\mathrm {code}\mbox {\tt \char34}
] , \linebreak [0] 
[
\mbox {\tt \char34}\mathrm {cache}\mbox {\tt \char34}
] , \linebreak [0] 
[
\mbox {\tt \char34}\mathrm {diagnose}\mbox {\tt \char34}
] , \linebreak [0] 
[
\mbox {\tt \char34}\mathrm {pyk}\mbox {\tt \char34}
] , \linebreak [0] 
[
\mbox {\tt \char34}\mathrm {tex}\mbox {\tt \char34}
] , \linebreak [0] 
[
\mbox {\tt \char34}\mathrm {texname}\mbox {\tt \char34}
] , \linebreak [0] 
[
\mbox {\tt \char34}\mathrm {value}\mbox {\tt \char34}
] , \linebreak [0] 
[
\mbox {\tt \char34}\mathrm {message}\mbox {\tt \char34}
] , \linebreak [0] 
[
\mbox {\tt \char34}\mathrm {macro}\mbox {\tt \char34}
] , \linebreak [0] 
[
\mbox {\tt \char34}\mathrm {definition}\mbox {\tt \char34}
] , \linebreak [0] 
[
\mbox {\tt \char34}\mathrm {unpack}\mbox {\tt \char34}
] , \linebreak [0] 
[
\mbox {\tt \char34}\mathrm {claim}\mbox {\tt \char34}
] , \linebreak [0] 
[
\mbox {\tt \char34}\mathrm {priority}\mbox {\tt \char34}
] , \linebreak [0] 
[
\mbox {\tt \char34}\mathrm {lambda}\mbox {\tt \char34}
] , \linebreak [0] 
[
\mbox {\tt \char34}\mathrm {apply}\mbox {\tt \char34}
] , \linebreak [0] 
[
\mbox {\tt \char34}\mathrm {true}\mbox {\tt \char34}
] , \linebreak [0] 
[
\mbox {\tt \char34}\mathrm {if}\mbox {\tt \char34}
] , \linebreak [0] 
[
\mbox {\tt \char34}\mathrm {quote}\mbox {\tt \char34}
] , \linebreak [0] 
[
\mbox {\tt \char34}\mathrm {proclaim}\mbox {\tt \char34}
] , \linebreak [0] 
[
\mbox {\tt \char34}\mathrm {define}\mbox {\tt \char34}
] , \linebreak [0] 
[
\mbox {\tt \char34}\mathrm {introduce}\mbox {\tt \char34}
] , \linebreak [0] 
[
\mbox {\tt \char34}\mathrm {hide}\mbox {\tt \char34}
] , \linebreak [0] 
[
\mbox {\tt \char34}\mathrm {pre}\mbox {\tt \char34}
] , \linebreak [0] 
[
\mbox {\tt \char34}\mathrm {post}\mbox {\tt \char34}
] , \linebreak [0] 
[
{\cal E}(
\ast 
,
\ast 
,
\ast 
)
] , \linebreak [0] 
[
{\cal E}_2(
\ast 
,
\ast 
,
\ast 
,
\ast 
,
\ast 
)
] , \linebreak [0] 
[
{\cal E}_3(
\ast 
,
\ast 
,
\ast 
,
\ast 
)
] , \linebreak [0] 
[
{\cal E}_4(
\ast 
,
\ast 
,
\ast 
,
\ast 
)
] , \linebreak [0] 
[
\mathbf {lookup}(
\ast 
,
\ast 
,
\ast 
)
] , \linebreak [0] 
[
\mathbf {abstract}(
\ast 
,
\ast 
,
\ast 
,
\ast 
)
] , \linebreak [0] 
[
\lceil 
\ast 
\rceil 
] , \linebreak [0] 
[
{\cal M}(
\ast 
,
\ast 
,
\ast 
)
] , \linebreak [0] 
[
{\cal M}_2(
\ast 
,
\ast 
,
\ast 
,
\ast 
)
] , \linebreak [0] 
[
{\cal M}^*(
\ast 
,
\ast 
,
\ast 
)
] , \linebreak [0] 
[
\mathrm {macro}
] , \linebreak [0] 
[
s_0
] , \linebreak [0] 
[
\mathbf {zip}(
\ast 
,
\ast 
)
] , \linebreak [0] 
[
\mathbf {assoc}_1(
\ast 
,
\ast 
,
\ast 
)
] , \linebreak [0] 
[(
\ast 
)^{\mathbf {p}}
] , \linebreak [0] 
[
\mbox{self}
] , \linebreak [0] 
[
[
\ast 
\mathrel {\ddot {=}}
\ast 
]
] , \linebreak [0] 
[
[
\ast 
\mathrel {\dot {=}}
\ast 
]
] , \linebreak [0] 
[
[
\ast 
\mathrel {\acute {=}}
\ast 
]
] , \linebreak [0] 
[
[
\ast 
\stackrel {\mathrm {pyk}}{=} 
\ast 
]
] , \linebreak [0] 
[
[
\ast 
\stackrel {\mathrm {tex}}{=} 
\ast 
]
] , \linebreak [0] 
[
[
\ast 
\stackrel {\mathrm {name}}{=} 
\ast 
]
] , \linebreak [0] 
[
\mathbf{Priority\ table} [ 
\ast 
]
] , \linebreak [0] 
[
\tilde {{\cal M}}_1
] , \linebreak [0] 
[
\tilde {{\cal M}}_2(
\ast 
)
] , \linebreak [0] 
[
\tilde {{\cal M}}_3(
\ast 
)
] , \linebreak [0] 
[
\tilde {{\cal M}}_4(
\ast 
,
\ast 
,
\ast 
,
\ast 
)
] , \linebreak [0] 
[
\tilde {{\cal M}}(
\ast 
,
\ast 
,
\ast 
)
] , \linebreak [0] 
[
\tilde {{\cal Q}}(
\ast 
,
\ast 
,
\ast 
)
] , \linebreak [0] 
[
\tilde {{\cal Q}}_2(
\ast 
,
\ast 
,
\ast 
)
] , \linebreak [0] 
[
\tilde {{\cal Q}}_3(
\ast 
,
\ast 
,
\ast 
,
\ast 
)
] , \linebreak [0] 
[
\tilde {{\cal Q}}^*(
\ast 
,
\ast 
,
\ast 
)
] , \linebreak [0] 
[
(
\ast 
)
] , \linebreak [0] 
[
\left( 
\ast 
\right) 
] , \linebreak [0] 
[
display(
\ast 
)
] , \linebreak [0] 
[
statement(
\ast 
)
] , \linebreak [0] 
[
[
\ast 
]^{\cdot}
] , \linebreak [0] 
[
[
\ast 
]^-
] , \linebreak [0] 
[
\mathbf{aspect}( 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
\mathbf{aspect}( 
\ast 
, 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
\langle 
\ast 
\rangle 
] , \linebreak [0] 
[
\mathbf {tuple}_1( 
\ast 
) 
] , \linebreak [0] 
[
\mathbf {tuple}_2( 
\ast 
) 
] , \linebreak [0] 
[
let_2( 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
let_1( 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
[
\ast 
\stackrel {claim}{=}
\ast 
]
] , \linebreak [0] 
[
\mbox{checker}
] , \linebreak [0] 
[
\mathbf{check}( 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
\mathbf{check}_2( 
\ast 
, 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
\mathbf{check}_3( 
\ast 
, 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
\mathbf{check}^*( 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
\mathbf{check}^*_2( 
\ast 
, 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
\relax [ 
\ast 
\relax ]^{\cdot} 
] , \linebreak [0] 
[
\relax [ 
\ast 
\relax ]^{-} 
] , \linebreak [0] 
[
\relax [ 
\ast 
\relax ]^{\circ} 
] , \linebreak [0] 
[
msg
] , \linebreak [0] 
[
[
\ast 
\stackrel {msg}{=} 
\ast 
]
] , \linebreak [0] 
[
{<}stmt{>}
] , \linebreak [0] 
[
stmt
] , \linebreak [0] 
[
[
\ast 
\stackrel {stmt}{=}
\ast 
]
] , \linebreak [0] 
[
HeadNil'
] , \linebreak [0] 
[
HeadPair'
] , \linebreak [0] 
[
Transitivity'
] , \linebreak [0] 
[
{\makebox [0mm][l]{$\bot $}\,{\bot }}
] , \linebreak [0] 
[
Contra'
] , \linebreak [0] 
[
T'_{E}
] , \linebreak [0] 
[
L_{1}
] , \linebreak [0] 
[\underline{
\ast }
] , \linebreak [0] 
[{\cal A}
] , \linebreak [0] 
[{\cal B}
] , \linebreak [0] 
[{\cal C}
] , \linebreak [0] 
[{\cal D}
] , \linebreak [0] 
[{\cal E}
] , \linebreak [0] 
[{\cal F}
] , \linebreak [0] 
[{\cal G}
] , \linebreak [0] 
[{\cal H}
] , \linebreak [0] 
[{\cal I}
] , \linebreak [0] 
[{\cal J}
] , \linebreak [0] 
[{\cal K}
] , \linebreak [0] 
[{\cal L}
] , \linebreak [0] 
[{\cal M}
] , \linebreak [0] 
[{\cal N}
] , \linebreak [0] 
[{\cal O}
] , \linebreak [0] 
[{\cal P}
] , \linebreak [0] 
[{\cal Q}
] , \linebreak [0] 
[{\cal R}
] , \linebreak [0] 
[{\cal S}
] , \linebreak [0] 
[{\cal T}
] , \linebreak [0] 
[{\cal U}
] , \linebreak [0] 
[{\cal V}
] , \linebreak [0] 
[{\cal W}
] , \linebreak [0] 
[{\cal X}
] , \linebreak [0] 
[{\cal Y}
] , \linebreak [0] 
[{\cal Z}
] , \linebreak [0] 
[
\langle 
\ast 
\,{\protect\vert}
\ast 
{:=}\,
\ast 
\rangle 
] , \linebreak [0] 
[
\langle ^ { \ast } 
\ast 
\,{\protect\vert}
\ast 
{:=}\,
\ast 
\rangle 
] , \linebreak [0] 
[
\emptyset 
] , \linebreak [0] 
[
Remainder
] , \linebreak [0] 
[
( 
\ast 
)^{\bf v}
] , \linebreak [0] 
[
intro(
\ast 
,
\ast 
,
\ast 
,
\ast 
)
] , \linebreak [0] 
[
intro(
\ast 
,
\ast 
,
\ast 
)
] , \linebreak [0] 
[
error(
\ast 
,
\ast 
)
] , \linebreak [0] 
[
error_{2}(
\ast 
,
\ast 
)
] , \linebreak [0] 
[
proof( 
\ast 
, 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
proof_{2}( 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
{\cal S}(
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
{\cal S}^{I}(
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
{\cal S}^{\rhd}(
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
{\cal S}_{1}^{\rhd}(
\ast 
, 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
{\cal S}^{E}(
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
{\cal S}_{1}^{E}(
\ast 
, 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
{\cal S}^{+}(
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
{\cal S}_{1}^{+}(
\ast 
, 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
{\cal S}^{-}(
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
{\cal S}_{1}^{-}(
\ast 
, 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
{\cal S}^{\ast}(
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
{\cal S}_{1}^{\ast}(
\ast 
, 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
{\cal S}_{2}^{\ast}(
\ast 
, 
\ast 
, 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
{\cal S}^{\char64}(
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
{\cal S}_{1}^{\char64}(
\ast 
, 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
{\cal S}^{\vdash}(
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
{\cal S}_{1}^{\vdash}(
\ast 
, 
\ast 
, 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
{\cal S}^{\makebox [0mm][l]{\scriptsize $\vdash $}\,{\vdash }}(
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
{\cal S}_{1}^{\makebox [0mm][l]{\scriptsize $\vdash $}\,{\vdash }}(
\ast 
, 
\ast 
, 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
{\cal S}^{i.e.}(
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
{\cal S}_{1}^{i.e.}(
\ast 
, 
\ast 
, 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
{\cal S}_{2}^{i.e.}(
\ast 
, 
\ast 
, 
\ast 
, 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
{\cal S}^{\forall}(
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
{\cal S}_{1}^{\forall}(
\ast 
, 
\ast 
, 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
{\cal S}^{;}(
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
{\cal S}_{1}^{;}(
\ast 
, 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
{\cal S}_{2}^{;}(
\ast 
, 
\ast 
, 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
{\cal T}( 
\ast 
)
] , \linebreak [0] 
[
claims( 
\ast 
, 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
claims_2( 
\ast 
, 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
{<}proof{>}
] , \linebreak [0] 
[
proof
] , \linebreak [0] 
[
[ \mathbf{Lemma\ } 
\ast 
\colon 
\ast 
]
] , \linebreak [0] 
[
[ \mathbf{Proof\ of\ }
\ast 
\colon 
\ast 
]
] , \linebreak [0] 
[
[ 
\ast 
\mathbf{\ lemma\ } 
\ast 
\colon 
\ast 
]
] , \linebreak [0] 
[
[ 
\ast 
\mathbf{\ antilemma\ } 
\ast 
\colon 
\ast 
]
] , \linebreak [0] 
[
[ 
\ast 
\mathbf{\ rule\ } 
\ast 
\colon 
\ast 
]
] , \linebreak [0] 
[
[ 
\ast 
\mathbf{\ antirule\ } 
\ast 
\colon 
\ast 
]
] , \linebreak [0] 
[
\mbox{verifier}
] , \linebreak [0] 
[
{\cal V}_1( 
\ast 
)
] , \linebreak [0] 
[
{\cal V}_2( 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
{\cal V}_3( 
\ast 
, 
\ast 
, 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
{\cal V}_4( 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
{\cal V}_5( 
\ast 
, 
\ast 
, 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
{\cal V}_6( 
\ast 
, 
\ast 
, 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
{\cal V}_7( 
\ast 
, 
\ast 
, 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
Cut( 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
Head_{\oplus} ( 
\ast 
)
] , \linebreak [0] 
[
Tail_{\oplus} ( 
\ast 
)
] , \linebreak [0] 
[
rule_1( 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
rule( 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
Rule\ tactic
] , \linebreak [0] 
[
Plus( 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
[ \mathbf{Theory\ } 
\ast 
]
] , \linebreak [0] 
[
theory_2( 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
theory_3( 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
theory_4( 
\ast 
, 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
HeadNil''
] , \linebreak [0] 
[
HeadPair''
] , \linebreak [0] 
[
Transitivity''
] , \linebreak [0] 
[
Contra''
] , \linebreak [0] 
[
HeadNil
] , \linebreak [0] 
[
HeadPair
] , \linebreak [0] 
[
Transitivity
] , \linebreak [0] 
[
Contra
] , \linebreak [0] 
[
T_E
] , \linebreak [0] 
[
ragged\ right
] , \linebreak [0] 
[
ragged\ right\ expansion\ 
] , \linebreak [0] 
[
parm(
\ast 
,
\ast 
,
\ast 
)
] , \linebreak [0] 
[
parm^*(
\ast 
,
\ast 
,
\ast 
)
] , \linebreak [0] 
[
inst(
\ast 
,
\ast 
)
] , \linebreak [0] 
[
inst^*(
\ast 
,
\ast 
)
] , \linebreak [0] 
[
occur(
\ast 
,
\ast 
,
\ast 
)
] , \linebreak [0] 
[
occur^*(
\ast 
,
\ast 
,
\ast 
)
] , \linebreak [0] 
[
unify(
\ast 
=
\ast 
,
\ast 
)
] , \linebreak [0] 
[
unify^*(
\ast 
=
\ast 
,
\ast 
)
] , \linebreak [0] 
[
unify_2(
\ast 
=
\ast 
,
\ast 
)
] , \linebreak [0] 
[L_a
] , \linebreak [0] 
[L_b
] , \linebreak [0] 
[L_c
] , \linebreak [0] 
[L_d
] , \linebreak [0] 
[L_e
] , \linebreak [0] 
[L_f
] , \linebreak [0] 
[L_g
] , \linebreak [0] 
[L_h
] , \linebreak [0] 
[L_i
] , \linebreak [0] 
[L_j
] , \linebreak [0] 
[L_k
] , \linebreak [0] 
[L_l
] , \linebreak [0] 
[L_m
] , \linebreak [0] 
[L_n
] , \linebreak [0] 
[L_o
] , \linebreak [0] 
[L_p
] , \linebreak [0] 
[L_q
] , \linebreak [0] 
[L_r
] , \linebreak [0] 
[L_s
] , \linebreak [0] 
[L_t
] , \linebreak [0] 
[L_u
] , \linebreak [0] 
[L_v
] , \linebreak [0] 
[L_w
] , \linebreak [0] 
[L_x
] , \linebreak [0] 
[L_y
] , \linebreak [0] 
[L_z
] , \linebreak [0] 
[L_A
] , \linebreak [0] 
[L_B
] , \linebreak [0] 
[L_C
] , \linebreak [0] 
[L_D
] , \linebreak [0] 
[L_E
] , \linebreak [0] 
[L_F
] , \linebreak [0] 
[L_G
] , \linebreak [0] 
[L_H
] , \linebreak [0] 
[L_I
] , \linebreak [0] 
[L_J
] , \linebreak [0] 
[L_K
] , \linebreak [0] 
[L_L
] , \linebreak [0] 
[L_M
] , \linebreak [0] 
[L_N
] , \linebreak [0] 
[L_O
] , \linebreak [0] 
[L_P
] , \linebreak [0] 
[L_Q
] , \linebreak [0] 
[L_R
] , \linebreak [0] 
[L_S
] , \linebreak [0] 
[L_T
] , \linebreak [0] 
[L_U
] , \linebreak [0] 
[L_V
] , \linebreak [0] 
[L_W
] , \linebreak [0] 
[L_X
] , \linebreak [0] 
[L_Y
] , \linebreak [0] 
[L_Z
] , \linebreak [0] 
[L_?
] , \linebreak [0] 
[
Reflexivity
] , \linebreak [0] 
[
Reflexivity_1
] , \linebreak [0] 
[
Commutativity
] , \linebreak [0] 
[
Commutativity_1
] , \linebreak [0] 
[
{<}tactic{>}
] , \linebreak [0] 
[
tactic
] , \linebreak [0] 
[
[
\ast 
\stackrel {tactic}{=}
\ast 
]
] , \linebreak [0] 
[
{\cal P}( 
\ast 
, 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
{\cal P}^*( 
\ast 
, 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
p_0
] , \linebreak [0] 
[
conclude_1 ( 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
conclude_2 ( 
\ast 
, 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
conclude_3 ( 
\ast 
, 
\ast 
, 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
conclude_4 ( 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
[
\ast 
\stackrel {\circ}{=}
\ast 
]
] , \linebreak [0] 
[
RootVisible(
\ast 
)
] , \linebreak [0] 
[
A
] , \linebreak [0] 
[
R
] , \linebreak [0] 
[
C
] , \linebreak [0] 
[
T
] , \linebreak [0] 
[
L
] , \linebreak [0] 
[
\{
\ast 
\}
] , \linebreak [0] 
[\overline{
\ast }
] , \linebreak [0] 
[
\mathit{a}
] , \linebreak [0] 
[
\mathit{b}
] , \linebreak [0] 
[
\mathit{c}
] , \linebreak [0] 
[
\mathit{d}
] , \linebreak [0] 
[
\mathit{e}
] , \linebreak [0] 
[
\mathit{f}
] , \linebreak [0] 
[
\mathit{g}
] , \linebreak [0] 
[
\mathit{h}
] , \linebreak [0] 
[
\mathit{i}
] , \linebreak [0] 
[
\mathit{j}
] , \linebreak [0] 
[
\mathit{k}
] , \linebreak [0] 
[
\mathit{l}
] , \linebreak [0] 
[
\mathit{m}
] , \linebreak [0] 
[
\mathit{n}
] , \linebreak [0] 
[
\mathit{o}
] , \linebreak [0] 
[
\mathit{p}
] , \linebreak [0] 
[
\mathit{q}
] , \linebreak [0] 
[
\mathit{r}
] , \linebreak [0] 
[
\mathit{s}
] , \linebreak [0] 
[
\mathit{t}
] , \linebreak [0] 
[
\mathit{u}
] , \linebreak [0] 
[
\mathit{v}
] , \linebreak [0] 
[
\mathit{w}
] , \linebreak [0] 
[
\mathit{x}
] , \linebreak [0] 
[
\mathit{y}
] , \linebreak [0] 
[
\mathit{z}
] , \linebreak [0] 
[
\langle 
\ast 
{\equiv} 
\ast 
| 
\ast 
{:=} 
\ast 
\rangle 
] , \linebreak [0] 
[
\langle 
\ast 
{\equiv}^0 
\ast 
| 
\ast 
{:=} 
\ast 
\rangle 
] , \linebreak [0] 
[
\langle 
\ast 
{\equiv}^1 
\ast 
| 
\ast 
{:=} 
\ast 
\rangle 
] , \linebreak [0] 
[
\langle 
\ast 
{\equiv}^* 
\ast 
| 
\ast 
{:=} 
\ast 
\rangle 
] , \linebreak [0] 
[
Ded(
\ast 
,
\ast 
)
] , \linebreak [0] 
[
Ded_0(
\ast 
,
\ast 
)
] , \linebreak [0] 
[
Ded_1(
\ast 
,
\ast 
,
\ast 
)
] , \linebreak [0] 
[
Ded_2(
\ast 
,
\ast 
,
\ast 
)
] , \linebreak [0] 
[
Ded_3(
\ast 
,
\ast 
,
\ast 
,
\ast 
)
] , \linebreak [0] 
[
Ded_4(
\ast 
,
\ast 
,
\ast 
,
\ast 
)
] , \linebreak [0] 
[
Ded_4^*(
\ast 
,
\ast 
,
\ast 
,
\ast 
)
] , \linebreak [0] 
[
Ded_5(
\ast 
,
\ast 
,
\ast 
)
] , \linebreak [0] 
[
Ded_6(
\ast 
,
\ast 
,
\ast 
,
\ast 
)
] , \linebreak [0] 
[
Ded_6^*(
\ast 
,
\ast 
,
\ast 
,
\ast 
)
] , \linebreak [0] 
[
Ded_7(
\ast 
)
] , \linebreak [0] 
[
Ded_8(
\ast 
,
\ast 
)
] , \linebreak [0] 
[
Ded_8^*(
\ast 
,
\ast 
)
] , \linebreak [0] 
[
S
] , \linebreak [0] 
[
Neg
] , \linebreak [0] 
[
MP
] , \linebreak [0] 
[
Gen
] , \linebreak [0] 
[
\mbox{rule div}
] , \linebreak [0] 
[
Ded
] , \linebreak [0] 
[
S1
] , \linebreak [0] 
[
S2
] , \linebreak [0] 
[
S3
] , \linebreak [0] 
[
S4
] , \linebreak [0] 
[
S5
] , \linebreak [0] 
[
S6
] , \linebreak [0] 
[
S7
] , \linebreak [0] 
[
S8
] , \linebreak [0] 
[
S9
] , \linebreak [0] 
[
S10
] , \linebreak [0] 
[
Repetition
] , \linebreak [0] 
[
A1'
] , \linebreak [0] 
[
A2'
] , \linebreak [0] 
[
A4'
] , \linebreak [0] 
[
A5'
] , \linebreak [0] 
[
Prop\ 3.2a
] , \linebreak [0] 
[
Prop\ 3.2b
] , \linebreak [0] 
[
Prop\ 3.2c
] , \linebreak [0] 
[
Prop\ 3.2d
] , \linebreak [0] 
[
Prop\ 3.2e_1
] , \linebreak [0] 
[
Prop\ 3.2e_2
] , \linebreak [0] 
[
Prop\ 3.2e
] , \linebreak [0] 
[
Prop\ 3.2f_1
] , \linebreak [0] 
[
Prop\ 3.2f_2
] , \linebreak [0] 
[
Prop\ 3.2f
] , \linebreak [0] 
[
Prop\ 3.2g_1
] , \linebreak [0] 
[
Prop\ 3.2g_2
] , \linebreak [0] 
[
Prop\ 3.2g
] , \linebreak [0] 
[
Prop\ 3.2h_1
] , \linebreak [0] 
[
Prop\ 3.2h_2
] , \linebreak [0] 
[
Prop\ 3.2h
] , \linebreak [0] 
[
Prop\ 3.2i
] , \linebreak [0] 
[
Prop\ 3.2j_1
] , \linebreak [0] 
[
Prop\ 3.2j_2
] , \linebreak [0] 
[
Prop\ 3.2j
] , \linebreak [0] 
[
Prop\ 3.2k_1
] , \linebreak [0] 
[
Prop\ 3.2k_2
] , \linebreak [0] 
[
Prop\ 3.2k
] , \linebreak [0] 
[
Prop\ 3.2l_1
] , \linebreak [0] 
[
Prop\ 3.2l_2
] , \linebreak [0] 
[
Prop\ 3.2l
] , \linebreak [0] 
[
Prop\ 3.2m_1
] , \linebreak [0] 
[
Prop\ 3.2m_2
] , \linebreak [0] 
[
Prop\ 3.2m
] , \linebreak [0] 
[
Prop\ 3.2n_1
] , \linebreak [0] 
[
Prop\ 3.2n_2
] , \linebreak [0] 
[
Prop\ 3.2n
] , \linebreak [0] 
[
Prop\ 3.2o
] , \linebreak [0] 
[
Prop\ 3.4a_1
] , \linebreak [0] 
[
Prop\ 3.4a_2
] , \linebreak [0] 
[
Prop\ 3.4a
] , \linebreak [0] 
[
Prop\ 3.4b
] , \linebreak [0] 
[
Prop\ 3.4c_1
] , \linebreak [0] 
[
Prop\ 3.4c_2
] , \linebreak [0] 
[
Prop\ 3.4c
] , \linebreak [0] 
[
Prop\ 3.4d_1
] , \linebreak [0] 
[
Prop\ 3.4d_2
] , \linebreak [0] 
[
Prop\ 3.4d
] , \linebreak [0] 
[
Block_1(
\ast 
,
\ast 
,
\ast 
)
] , \linebreak [0] 
[
Block_2(
\ast 
)
]
; 
\newline \mathbf {Preassociative} \newline 
[
\ast 
\_\{
\ast 
\}
] , \linebreak [0] 
[
\ast 
/indexintro(
\ast 
,
\ast 
,
\ast 
,
\ast 
)
] , \linebreak [0] 
[
\ast 
/intro(
\ast 
,
\ast 
,
\ast 
)
] , \linebreak [0] 
[
\ast 
/bothintro(
\ast 
,
\ast 
,
\ast 
,
\ast 
,
\ast 
)
] , \linebreak [0] 
[
\ast 
/nameintro(
\ast 
,
\ast 
,
\ast 
,
\ast 
)
] , \linebreak [0] 
[
\ast '
] , \linebreak [0] 
[
\ast 
{[}
\ast 
{]}
] , \linebreak [0] 
[
\ast 
[ 
\ast 
{\rightarrow} 
\ast 
]
] , \linebreak [0] 
[
\ast 
[ 
\ast 
{\Rightarrow} 
\ast 
]
] , \linebreak [0] 
[
\ast 
0
] , \linebreak [0] 
[
\ast 
1
] , \linebreak [0] 
[
0 \mathrm {b}
] , \linebreak [0] 
[
\ast 
\mbox {-color}( 
\ast 
)
] , \linebreak [0] 
[
\ast 
\mbox {-color}^{\ast}( 
\ast 
)
] , \linebreak [0] 
[
\ast 
{}^H
] , \linebreak [0] 
[
\ast 
{}^T
] , \linebreak [0] 
[
\ast 
{}^U
] , \linebreak [0] 
[
\ast 
{}^h
] , \linebreak [0] 
[
\ast 
{}^t
] , \linebreak [0] 
[
\ast 
{}^s
] , \linebreak [0] 
[
\ast 
{}^c
] , \linebreak [0] 
[
\ast 
{}^d
] , \linebreak [0] 
[
\ast 
{}^a
] , \linebreak [0] 
[
\ast 
{}^C
] , \linebreak [0] 
[
\ast 
{}^M
] , \linebreak [0] 
[
\ast 
{}^B
] , \linebreak [0] 
[
\ast 
{}^{r}
] , \linebreak [0] 
[
\ast 
{}^{i}
] , \linebreak [0] 
[
\ast 
{}^{d}
] , \linebreak [0] 
[
\ast 
{}^{R}
] , \linebreak [0] 
[
\ast 
{}^{0}
] , \linebreak [0] 
[
\ast 
{}^{1}
] , \linebreak [0] 
[
\ast 
{}^{2}
] , \linebreak [0] 
[
\ast 
{}^{3}
] , \linebreak [0] 
[
\ast 
{}^{4}
] , \linebreak [0] 
[
\ast 
{}^{5}
] , \linebreak [0] 
[
\ast 
{}^{6}
] , \linebreak [0] 
[
\ast 
{}^{7}
] , \linebreak [0] 
[
\ast 
{}^{8}
] , \linebreak [0] 
[
\ast 
{}^{9}
] , \linebreak [0] 
[
\ast 
{} ^ { E }
] , \linebreak [0] 
[
\ast 
{} ^ {\cal V}
] , \linebreak [0] 
[
\ast 
{} ^ {\cal C}
] , \linebreak [0] 
[
\ast 
{} ^ {{\cal C} ^ { \ast }}
] , \linebreak [0] 
[
\ast 
{}^{hide}
]
; 
\newline \mathbf {Preassociative} \newline 
[
\mbox{``}
\ast 
\mbox{''}
] , \linebreak [0] 
[
] , \linebreak [0] 
[
(
\ast 
)^{\bf t}
] , \linebreak [0] 
[
\mbox{string}(
\ast 
)+
\ast 
] , \linebreak [0] 
[\mbox{string}(
\ast 
)\mathrel{++}
\ast 
] , \linebreak [0] 
[
\newline 
\ast 
] , \linebreak [0] 
[
\linebreak [0]\ \hskip0em plus2.0em{}
\ast 
] , \linebreak [0] 
[!
\ast 
] , \linebreak [0] 
[
\mbox {\tt \char34}
\ast 
] , \linebreak [0] 
[
\#
\ast 
] , \linebreak [0] 
[
\$
\ast 
] , \linebreak [0] 
[
\%
\ast 
] , \linebreak [0] 
[
\&
\ast 
] , \linebreak [0] 
[
\mbox {'}
\ast 
] , \linebreak [0] 
[(
\ast 
] , \linebreak [0] 
[)
\ast 
] , \linebreak [0] 
[
{*}
\ast 
] , \linebreak [0] 
[
{+}
\ast 
] , \linebreak [0] 
[,
\ast 
] , \linebreak [0] 
[
\mbox{-}
\ast 
] , \linebreak [0] 
[.
\ast 
] , \linebreak [0] 
[/
\ast 
] , \linebreak [0] 
[0
\ast 
] , \linebreak [0] 
[1
\ast 
] , \linebreak [0] 
[2
\ast 
] , \linebreak [0] 
[3
\ast 
] , \linebreak [0] 
[4
\ast 
] , \linebreak [0] 
[5
\ast 
] , \linebreak [0] 
[6
\ast 
] , \linebreak [0] 
[7
\ast 
] , \linebreak [0] 
[8
\ast 
] , \linebreak [0] 
[9
\ast 
] , \linebreak [0] 
[
{:}
\ast 
] , \linebreak [0] 
[;
\ast 
] , \linebreak [0] 
[
{<}
\ast 
] , \linebreak [0] 
[
{=}
\ast 
] , \linebreak [0] 
[
{>}
\ast 
] , \linebreak [0] 
[?
\ast 
] , \linebreak [0] 
[@
\ast 
] , \linebreak [0] 
[A
\ast 
] , \linebreak [0] 
[B
\ast 
] , \linebreak [0] 
[C
\ast 
] , \linebreak [0] 
[D
\ast 
] , \linebreak [0] 
[E
\ast 
] , \linebreak [0] 
[F
\ast 
] , \linebreak [0] 
[G
\ast 
] , \linebreak [0] 
[H
\ast 
] , \linebreak [0] 
[I
\ast 
] , \linebreak [0] 
[J
\ast 
] , \linebreak [0] 
[K
\ast 
] , \linebreak [0] 
[L
\ast 
] , \linebreak [0] 
[M
\ast 
] , \linebreak [0] 
[N
\ast 
] , \linebreak [0] 
[O
\ast 
] , \linebreak [0] 
[P
\ast 
] , \linebreak [0] 
[Q
\ast 
] , \linebreak [0] 
[R
\ast 
] , \linebreak [0] 
[S
\ast 
] , \linebreak [0] 
[T
\ast 
] , \linebreak [0] 
[U
\ast 
] , \linebreak [0] 
[V
\ast 
] , \linebreak [0] 
[W
\ast 
] , \linebreak [0] 
[X
\ast 
] , \linebreak [0] 
[Y
\ast 
] , \linebreak [0] 
[Z
\ast 
] , \linebreak [0] 
[[
\ast 
] , \linebreak [0] 
[
\mbox {$\backslash $}
\ast 
] , \linebreak [0] 
[]
\ast 
] , \linebreak [0] 
[
{\char94}
\ast 
] , \linebreak [0] 
[
\_
\ast 
] , \linebreak [0] 
[
\mbox {`}
\ast 
] , \linebreak [0] 
[a
\ast 
] , \linebreak [0] 
[b
\ast 
] , \linebreak [0] 
[c
\ast 
] , \linebreak [0] 
[d
\ast 
] , \linebreak [0] 
[e
\ast 
] , \linebreak [0] 
[f
\ast 
] , \linebreak [0] 
[g
\ast 
] , \linebreak [0] 
[h
\ast 
] , \linebreak [0] 
[i
\ast 
] , \linebreak [0] 
[j
\ast 
] , \linebreak [0] 
[k
\ast 
] , \linebreak [0] 
[l
\ast 
] , \linebreak [0] 
[m
\ast 
] , \linebreak [0] 
[n
\ast 
] , \linebreak [0] 
[o
\ast 
] , \linebreak [0] 
[p
\ast 
] , \linebreak [0] 
[q
\ast 
] , \linebreak [0] 
[r
\ast 
] , \linebreak [0] 
[s
\ast 
] , \linebreak [0] 
[t
\ast 
] , \linebreak [0] 
[u
\ast 
] , \linebreak [0] 
[v
\ast 
] , \linebreak [0] 
[w
\ast 
] , \linebreak [0] 
[x
\ast 
] , \linebreak [0] 
[y
\ast 
] , \linebreak [0] 
[z
\ast 
] , \linebreak [0] 
[
\{
\ast 
] , \linebreak [0] 
[|
\ast 
] , \linebreak [0] 
[
\}
\ast 
] , \linebreak [0] 
[
\char126 
\ast 
] , \linebreak [0] 
[
\mathbf{Preassociative}\,
\ast 
; 
\ast 
] , \linebreak [0] 
[
\mathbf{Postassociative}\,
\ast 
; 
\ast 
] , \linebreak [0] 
[
[
\ast 
] , \linebreak [0] 
\ast 
] , \linebreak [0] 
[
\mathrm{priority} \,
\ast 
\, \mathrm{end}
] , \linebreak [0] 
[
newline\ 
\ast 
] , \linebreak [0] 
[
macro\ newline\ 
\ast 
] , \linebreak [0] 
[
MacroIndent(
\ast 
)
]
; 
\newline \mathbf {Preassociative} \newline 
[
\ast 
\mathbin {\mbox {'}}
\ast 
] , \linebreak [0] 
[
\ast 
\mathbin {\mbox {`}}
\ast 
]
; 
\newline \mathbf {Preassociative} \newline 
[
\ast 
{}'
]
; 
\newline \mathbf {Preassociative} \newline 
[
\ast 
\cdot 
\ast 
] , \linebreak [0] 
[
\ast 
\cdot_0 
\ast 
]
; 
\newline \mathbf {Preassociative} \newline 
[
\ast 
+ 
\ast 
] , \linebreak [0] 
[
\ast 
\mathop{+_0} 
\ast 
] , \linebreak [0] 
[
\ast 
\mathop{+_1} 
\ast 
] , \linebreak [0] 
[
\ast 
- 
\ast 
] , \linebreak [0] 
[
\ast 
\mathop{-_0} 
\ast 
] , \linebreak [0] 
[
\ast 
\mathop{-_1} 
\ast 
]
; 
\newline \mathbf {Preassociative} \newline 
[
\ast 
\cup \{ 
\ast 
\}
] , \linebreak [0] 
[
\ast 
\cup 
\ast 
] , \linebreak [0] 
[
\ast 
\backslash \{ 
\ast 
\}
]
; 
\newline\mathbf{Postassociative} \newline 
[
\ast 
\mathrel { \dot { . \, . } }
\ast 
] , \linebreak [0] 
[
\ast 
\mathrel { \underline { \dot { . \, . } } }
\ast 
] , \linebreak [0] 
[
\ast 
\mathrel { \underline { : \, : } }
\ast 
] , \linebreak [0] 
[
\ast 
\mathrel { \underline { {+} 2 \ast } }
\ast 
] , \linebreak [0] 
[
\ast 
\mathrel { : \, : }
\ast 
] , \linebreak [0] 
[
\ast 
\mathrel { {+} 2 \ast }
\ast 
]
; 
\newline\mathbf{Postassociative} \newline 
[
\ast 
,\linebreak [0] 
\ast 
]
; 
\newline \mathbf {Preassociative} \newline 
[
\ast 
\stackrel {B}{\approx }
\ast 
] , \linebreak [0] 
[
\ast 
\stackrel {D}{\approx }
\ast 
] , \linebreak [0] 
[
\ast 
\stackrel {C}{\approx }
\ast 
] , \linebreak [0] 
[
\ast 
\stackrel {P}{\approx }
\ast 
] , \linebreak [0] 
[
\ast 
\approx 
\ast 
] , \linebreak [0] 
[
\ast 
=
\ast 
] , \linebreak [0] 
[
\ast 
\stackrel {+}{\rightarrow }
\ast 
] , \linebreak [0] 
[
\ast 
\stackrel {t}{=}
\ast 
] , \linebreak [0] 
[
\ast 
\stackrel {t^*}{=}
\ast 
] , \linebreak [0] 
[
\ast 
\stackrel{r}{=} 
\ast 
] , \linebreak [0] 
[
\ast 
\in_t 
\ast 
] , \linebreak [0] 
[
\ast 
\subseteq_T 
\ast 
] , \linebreak [0] 
[
\ast 
\stackrel{T}{=} 
\ast 
] , \linebreak [0] 
[
\ast 
\stackrel{s}{=} 
\ast 
] , \linebreak [0] 
[
\ast 
\mathrel {free\ in} 
\ast 
] , \linebreak [0] 
[
\ast 
\mathrel {free\ in}^{\ast} 
\ast 
] , \linebreak [0] 
[
\ast 
\mathrel {free\ for} 
\ast 
\mathrel {in} 
\ast 
] , \linebreak [0] 
[
\ast 
\mathrel {free\ for}^{\ast} 
\ast 
\mathrel {in} 
\ast 
] , \linebreak [0] 
[
\ast 
\in_c 
\ast 
] , \linebreak [0] 
[
\ast 
< 
\ast 
] , \linebreak [0] 
[
\ast 
<' 
\ast 
] , \linebreak [0] 
[
\ast 
\le' 
\ast 
] , \linebreak [0] 
[
\ast 
= 
\ast 
] , \linebreak [0] 
[
\ast 
\neq 
\ast 
] , \linebreak [0] 
[
\ast 
{}^{var}
] , \linebreak [0] 
[
\ast 
\#^0
\ast 
] , \linebreak [0] 
[
\ast 
\#^1
\ast 
] , \linebreak [0] 
[
\ast 
\#^*
\ast 
]
; 
\newline \mathbf {Preassociative} \newline 
[
{\neg }
\ast 
]
; 
\newline \mathbf {Preassociative} \newline 
[
\ast 
\wedge 
\ast 
] , \linebreak [0] 
[
\ast 
\mathrel{\ddot{\wedge}} 
\ast 
] , \linebreak [0] 
[
\ast 
\mathrel{\tilde{\wedge}} 
\ast 
] , \linebreak [0] 
[
\ast 
\wedge_c 
\ast 
]
; 
\newline \mathbf {Preassociative} \newline 
[
\ast 
\vee 
\ast 
] , \linebreak [0] 
[
\ast 
\parallel 
\ast 
] , \linebreak [0] 
[
\ast 
\mathrel{\ddot{\vee}} 
\ast 
]
; 
\newline \mathbf {Preassociative} \newline 
[
\exists 
\ast 
\colon 
\ast 
] , \linebreak [0] 
[
\forall 
\ast 
\colon 
\ast 
] , \linebreak [0] 
[
\forall_{obj} 
\ast 
\colon 
\ast 
]
; 
\newline\mathbf{Postassociative} \newline 
[
\ast 
\mathrel{\ddot{\Rightarrow}} 
\ast 
] , \linebreak [0] 
[
\ast 
\Rightarrow 
\ast 
] , \linebreak [0] 
[
\ast 
\Leftrightarrow 
\ast 
]
; 
\newline\mathbf{Postassociative} \newline 
[
\ast 
:
\ast 
] , \linebreak [0] 
[
\ast 
\mathrel{spy}
\ast 
] , \linebreak [0] 
[
\ast 
!
\ast 
]
; 
\newline \mathbf {Preassociative} \newline 
[
\ast 
\left\{\protect \begin {array}{l}
\ast 
\\
\ast 
\protect \end {array}\right.
]
; 
\newline \mathbf {Preassociative} \newline 
[
\lambda 
\ast 
.
\ast 
] , \linebreak [0] 
[
\Lambda 
\ast 
. 
\ast 
] , \linebreak [0] 
[
\Lambda 
\ast 
] , \linebreak [0] 
[
{\bf if} \ 
\ast 
\ {\bf then} \ 
\ast 
\ {\bf else} \ 
\ast 
] , \linebreak [0] 
[
\mathbf{let\ } 
\ast 
= 
\ast 
\mathbf{\ in\ } 
\ast 
] , \linebreak [0] 
[
\mathbf{let\ } 
\ast 
\mathrel{\ddot{=}} 
\ast 
\mathrel{\ in\ } 
\ast 
]
; 
\newline \mathbf {Preassociative} \newline 
[
\ast 
\#
\ast 
]
; 
\newline \mathbf {Preassociative} \newline 
[
\ast 
{} ^ { I }
] , \linebreak [0] 
[
\ast 
{} ^ { \rhd }
] , \linebreak [0] 
[
\ast 
{} ^ { V } 
] , \linebreak [0] 
[
\ast 
{} ^ { + } 
] , \linebreak [0] 
[
\ast 
{} ^ { - } 
] , \linebreak [0] 
[
\ast 
{} ^ { \ast } 
]
; 
\newline \mathbf {Preassociative} \newline 
[
\ast 
\mathop {\char64} 
\ast 
] , \linebreak [0] 
[
\ast 
\rhd 
\ast 
] , \linebreak [0] 
[
\ast 
\mathrel {\makebox [0mm][l]{$\rhd $}\,{\rhd }} 
\ast 
] , \linebreak [0] 
[
\ast 
\gg 
\ast 
] , \linebreak [0] 
[
\ast 
\unrhd 
\ast 
]
; 
\newline\mathbf{Postassociative} \newline 
[
\ast 
\vdash 
\ast 
] , \linebreak [0] 
[
\ast 
\mathrel {\makebox [0mm][l]{$\vdash $}\,{\vdash }} 
\ast 
] , \linebreak [0] 
[
\ast 
\mathrel {i.e.} 
\ast 
]
; 
\newline \mathbf {Preassociative} \newline 
[
\forall 
\ast 
\colon 
\ast 
] , \linebreak [0] 
[
\Pi 
\ast 
\colon 
\ast 
]
; 
\newline\mathbf{Postassociative} \newline 
[
\ast 
\mathrel {\oplus} 
\ast 
]
; 
\newline\mathbf{Postassociative} \newline 
[
\ast 
; 
\ast 
]
; 
\newline \mathbf {Preassociative} \newline 
[
\ast 
\ proves\ 
\ast 
]
; 
\newline \mathbf {Preassociative} \newline 
[
\ast 
\mathbf{\ proof\ of\ } 
\ast 
: 
\ast 
] , \linebreak [0] 
[
Line \, 
\ast 
: 
\ast 
\gg 
\ast 
; 
\ast 
] , \linebreak [0] 
[
Last\ line \, 
\ast 
\gg 
\ast 
\,\Box
] , \linebreak [0] 
[
Line \, 
\ast 
: Premise \gg 
\ast 
;
\ast 
] , \linebreak [0] 
[
Line \, 
\ast 
: \mbox{Side-condition} \gg 
\ast 
; 
\ast 
] , \linebreak [0] 
[
Arbitrary \gg 
\ast 
;
\ast 
] , \linebreak [0] 
[
Local \gg 
\ast 
= 
\ast 
; 
\ast 
] , \linebreak [0] 
[
Begin \, 
\ast 
 ; 
\ast 
 : End ; 
\ast 
] , \linebreak [0] 
[
Last\ block\ line \, 
\ast 
\gg 
\ast 
\,;
] , \linebreak [0] 
[
Arbitrary \gg 
\ast 
;
\ast 
]
; 
\newline\mathbf{Postassociative} \newline 
[
\ast 
\mathrel{|} 
\ast 
]
; 
\newline\mathbf{Postassociative} \newline 
[
\ast 
\mathrel{\mathrm{,}}
\ast 
] , \linebreak [0] 
[
\ast 
{[}
\ast 
{]}
\ast 
]
; 
\newline \mathbf {Preassociative} \newline 
[
\ast 
\& 
\ast 
] , \linebreak [0] 
[
 \rightarrow 
]
; 
\newline \mathbf {Preassociative} \newline 
[
\ast 
\backslash \backslash 
\ast 
] , \linebreak [0] 
[
\ast 
\mathrel{linebreak[4]} 
\ast 
] , \linebreak [0] 
[
\ast 
\backslash \backslash 
\ast 
] , \linebreak [0] 
[
\ast 
\| 
\ast 
]
; 
\mathbf{End\ table}$
\end {flushleft}

\end{document}
