principia TeX package updates and PDFs

3 files changed, 470 insertions, 6 deletions

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diff --git a/List of Definitions.tex b/List of Definitions.tex
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+\documentclass[12pt,openany,leqno,twocolumn]{book}

+%Principia package requirements

+\usepackage{pifont} %This loads the eight-pointed asterisk.

+\usepackage{marvosym} %This loads the male and female symbol.

+\usepackage{graphicx} %This loads commands that flip iota for definite descriptions, Lambda for the universal class, and so on. The (superseded) graphics package should also work here, but is not recommended.

+\usepackage{amssymb} 

+\usepackage{amsmath}

+\usepackage{fullpage}

+\usepackage{perpage}

+\usepackage[T1]{fontenc}

+\usepackage[utf8]{inputenc}

+\usepackage{mathrsfs}

+\usepackage[hidelinks,pdfencoding=unicode]{hyperref}

+\usepackage{enumitem}

+\usepackage{moreenum}

+\usepackage[normalem]{ulem}

+\usepackage[perpage,symbol]{footmisc}

+\usepackage{setspace}

+

+%Meta-logical symbols

+\newcommand{\pmdem}{\textit{Dem}.} %This notation begins a proof.

+\newcommand{\pmsub}[2]{\bigg \lbrack \small \begin{array}{c} #1 \\ \hline #2 \end{array} \bigg \rbrack} %This is the substitution command.

+\newcommand{\pmSub}[3]{\bigg \lbrack \normalsize #1 \text{ } \small \begin{array}{c} #2 \\ \hline #3 \end{array}  \bigg \rbrack} %This is the substitution command.

+\newcommand{\pmsubb}[4]{\bigg \lbrack \small \begin{array}{c c} #1, & #3 \\ \hline #2, & #4 \end{array}  \bigg \rbrack} %This is the substitution command.

+\newcommand{\pmSubb}[5]{\bigg \lbrack \normalsize #1 \text{ } \small \begin{array}{c c} #2, & #4 \\ \hline #3, & #5 \end{array}  \bigg \rbrack} %This is the substitution command.

+\newcommand{\pmsubbb}[6]{\bigg \lbrack \small \begin{array}{c c c} #1, & #3, & #5 \\ \hline #2, & #4, & #6 \end{array}  \bigg \rbrack} %This is the substitution command.

+\newcommand{\pmSubbb}[7]{\bigg \lbrack \normalsize #1 \text{ } \small \begin{array}{c c c} #2, & #4, & #6 \\ \hline #3, & #5, & #7 \end{array}  \bigg \rbrack} %This is the substitution command.

+\newcommand{\pmsubbbb}[8]{\bigg \lbrack \small \begin{array}{c c c c} #1, & #3, & #5, & #7 \\ \hline #2, & #4, & #6, & #8 \end{array}  \bigg \rbrack} %This is the substitution command.

+\newcommand{\pmSubbbb}[9]{\bigg \lbrack \normalsize #1 \text{ } \small \begin{array}{c c c c} #1, & #3, & #5, & #7 \\ \hline #2, & #4, & #6, & #8 \end{array}  \bigg \rbrack} %This is the substitution command.

+\newcommand{\pmthm}{\text{\scalebox{.5}[1]{$\boldsymbol\vdash$}}} %This is the theorem sign.

+\newcommand{\pmast}{\text{\resizebox{!}{.75\height}{\ding{107}}}} %This is the sign introducing a theorem number.

+\newcommand{\pmcdot}{\text{\raisebox{.05cm}{$\boldsymbol\cdot$}}} %This is a sign introducing a theorem sub-number.

+\newcommand{\pmdf}{=_\text{Df}}

+\newcommand{\pmpp}{\text{Pp}}

+

+%Square dots for scope, defined for up to six dots

+\newcommand{\pmdot}{\mathop{\hbox{\rule{.3ex}{.3ex}}}}

+\newcommand{\pmdott}{\mathop{\overset{\pmdot}{\pmdot}}}

+\newcommand{\pmdottt}{\pmdott \pmdot}

+\newcommand{\pmdotttt}{\pmdott\pmdott}

+\newcommand{\pmdottttt}{\pmdott\pmdott\pmdot}

+\newcommand{\pmdotttttt}{\pmdott\pmdott\pmdott}

+

+%Logical connectives

+\newcommand{\pmnot}{\mathord{\sim}}

+\newcommand{\pmimp}{\boldsymbol{\supset}}

+\newcommand{\pmiff}{\equiv}

+\newcommand{\pmor}{\boldsymbol{\vee}}

+\newcommand{\pmall}[1]{(#1)}

+\newcommand{\pmsome}[1]{(\text{\raisebox{.5em}{\rotatebox{180}{E}}}#1)}

+\newcommand{\pmSome}{\text{\raisebox{.5em}{\rotatebox{180}{E}}}}

+\newcommand{\pmand}{\mathrel{\hbox{\rule{.3ex}{.3ex}}}}

+\newcommand{\pmandd}{\overset{\pmand}{\pmand}}

+\newcommand{\pmanddd}{\pmandd\hspace{.1em}\pmand}

+\newcommand{\pmandddd}{\pmandd\hspace{.1em}\pmandd}

+\newcommand{\pmanddddd}{\pmandd\hspace{.1em}\pmandd\hspace{.1em}\pmand}

+\newcommand{\pmandddddd}{\pmandd\hspace{.1em}\pmandd\hspace{.1em}\pmandd}

+

+%Additional defined logic signs

+\newcommand{\pmhat}[1]{\mathbf{\hat{\text{$#1$}}}}

+\newcommand{\pmpf}[2]{#1#2} %for propositional functions of one variable

+\newcommand{\pmpff}[3]{#1(#2, #3)} %for propositional functions of two variables

+\newcommand{\pmpfff}[4]{#1(#2, #3, #4)} %for propositional functions of three variables

+\newcommand{\pmshr}{\textbf{!}} %*12.1 and *12.11, used for predicative propositional functions

+\newcommand{\pmpred}[2]{#1\pmshr#2} %for predicates (``predicative functions'') of one variable

+\newcommand{\pmpredd}[3]{#1\pmshr(#2, #3)} %for predicates (``predicative functions'') of two variables

+\newcommand{\pmpreddd}[4]{#1\pmshr(#2, #3, #4)} %for predicates (``predicative functions'') of three variables

+\newcommand{\pmnid}{\mathrel{\ooalign{$=$\cr\hidewidth\footnotesize\rotatebox[origin=c]{210}{\textbf{/}}\hidewidth\cr}}} %*13.01

+\newcommand{\pmiota}{\rotatebox[origin=c]{180}{$\iota$}} %the rotated Greek iota used in definite descriptions

+\newcommand{\pmdsc}[1]{(\pmiota#1)} %*14.01

+\newcommand{\pmDsc}{\pmiota} %*14.01

+\newcommand{\pmexists}{\text{E}\pmshr} %*14.02

+

+%Class signs

+\newcommand{\pmcuni}{\text{\rotatebox[origin=c]{180}{$\Lambda$}}}

+\newcommand{\pmcnull}{\Lambda}

+\newcommand{\pmcls}[2]{\pmhat{#1}(#2)}

+\newcommand{\pmCls}{\text{Cls}}

+\newcommand{\pmClsn}[1]{\text{Cls}^{#1}}

+\newcommand{\pmcexists}{\text{\raisebox{.5em}{\rotatebox{180}{E}}}\mathop{\pmshr}}

+\newcommand{\pmccmp}[1]{\boldsymbol{-}#1}

+\newcommand{\pmcmin}[2]{#1\boldsymbol{-}#2}

+\newcommand{\pmcin}{\mathop{\epsilon}}

+\newcommand{\pmccup}{\mathop{\scalebox{1.3}[1.75]{$\put(3, 2.5){\oval(4,4)[b]}\phantom{\circ}$}}}

+\newcommand{\pmccap}{\mathop{\scalebox{1.3}[1.75]{$\put(3, 2){\oval(4,1)[t]}\phantom{\circ}$}}}

+\newcommand{\pmcinc}{\mathop{\boldsymbol{\subset}}}

+

+%Relation signs

+\newcommand{\pmruni}{\dot{\text{\rotatebox[origin=c]{180}{$\Lambda$}}}}

+\newcommand{\pmrnull}{\dot{\Lambda}}

+\newcommand{\pmdscf}[2]{#1\textbf{`}#2}

+\newcommand{\pmdscff}[2]{#1\textbf{`}\textbf{`}#2}

+\newcommand{\pmdscfff}[2]{#1\textbf{`}\textbf{`}\textbf{`}#2}

+\newcommand{\pmdscfr}[2]{#1_{\pmcin}\textbf{`}#2}

+\newcommand{\pmdscfR}[1]{#1_{\pmcin}}

+\newcommand{\pmdscfe}[2]{\mathop{\text{E}}\mathop{\pmshr\pmshr}\pmdscff{#1}{#2}}

+\newcommand{\pmdm}[1]{\text{D}\textbf{`}#1}

+\newcommand{\pmDm}{\text{D}}

+\newcommand{\pmcdm}[1]{\text{\rotatebox[origin=c]{180}{D}}\textbf{`}#1}

+\newcommand{\pmCdm}{\text{\rotatebox[origin=c]{180}{D}}}

+\newcommand{\pmcmp}[1]{C\textbf{`}#1}

+\newcommand{\pmCmp}{C}

+\newcommand{\pmfld}[1]{F\textbf{`}#1}

+\newcommand{\pmFld}{F}

+\newcommand{\pmrel}[3]{\pmhat{#1}\pmhat{#2}#3}

+\newcommand{\pmrele}[5]{#1\{\pmhat{#2}\pmhat{#3}#4(#2, #3)\}#5}

+\newcommand{\pmrelep}[3]{#1\{#2\}#3}

+\newcommand{\pmrcmp}[1]{\ooalign{$\hidewidth\raisebox{.25em}{$\cdot$}\hidewidth$\cr$\mathbf{\pmccmp}$}#1}

+\newcommand{\pmrmin}[2]{#1\mathrel{\ooalign{$\hidewidth\raisebox{.25em}{$\cdot$}\hidewidth$\cr$\mathbf{\pmccmp}$}}#2}

+\newcommand{\pmrexists}{\dot{\mathop{\text{\raisebox{.5em}{\rotatebox{180}{E}}}}}\mathop{\pmshr}}

+\newcommand{\pmcrel}[1]{\breve{#1}}

+\newcommand{\pmCnv}{\text{Cnv}}

+\newcommand{\pmcnv}[1]{\breve{#1}}

+\newcommand{\pmcnvr}[1]{\text{Cnv}\textbf{`}#1}

+\newcommand{\pmrcup}{\mathrel{\ooalign{$\hidewidth\cdot\hidewidth$\cr$\mathbf{\pmccup}$}}}

+\newcommand{\pmrcap}{\mathrel{\ooalign{$\hidewidth\raisebox{.3em}{$\cdot$}\hidewidth$\cr$\mathbf{\pmccap}$}}}

+\newcommand{\pmrinc}{\mathrel{\ooalign{$\hidewidth\cdot\hidewidth$\cr$\mathbf{\pmcinc}$}}}

+\newcommand{\pmrrf}[2]{\overset{\boldsymbol{\rightarrow}}{#1\textbf{`}}#2}

+\newcommand{\pmRrf}[1]{\overset{\boldsymbol{\rightarrow}}{#1}}

+\newcommand{\pmrrl}[2]{\overset{\boldsymbol{\leftarrow}}{#1\textbf{`}}#2}

+\newcommand{\pmRrl}[1]{\overset{\boldsymbol{\leftarrow}}{#1}}

+\newcommand{\pmsg}[1]{\text{sg}\textbf{`}#1}

+\newcommand{\pmgs}[1]{\text{gs}\textbf{`}#1}

+\newcommand{\pmSg}{\text{sg}}

+\newcommand{\pmGs}{\text{gs}}

+\newcommand{\pmRprd}{\mathop{|}}

+\newcommand{\pmrprd}[2]{{#1}\mathop{|}{#2}}

+\newcommand{\pmrprdn}[2]{#1^{#2}}

+\newcommand{\pmrld}[2]{#1 \boldsymbol{\upharpoonleft} #2}

+\newcommand{\pmrlcd}[2]{#1 \boldsymbol{\upharpoonright} #2}

+\newcommand{\pmrlf}[3]{#1 \boldsymbol{\upharpoonleft} #2 \boldsymbol{\upharpoonright} #3}

+\newcommand{\pmrl}[2]{#1 \boldsymbol{\uparrow} #2}

+\newcommand{\pmrlF}[2]{#1 \mathbin{\ooalign{$\upharpoonright$\cr\hidewidth\rotatebox[origin=c]{180}{\text{$\upharpoonleft$}}\hidewidth\cr}} #2}

+\newcommand{\pmop}{\mathop{\text{\Female}}}

+\newcommand{\pmopc}[2]{#1 \mathop{\underset{\textbf{''}}{\text{\Female}}} #2}

+

+%Products and sums of classes of classes or relations

+\newcommand{\pmccsum}[1]{p\textbf{`}#1}

+\newcommand{\pmccprd}[1]{s\textbf{`}#1}

+\newcommand{\pmcrsum}[1]{\dot{p}\textbf{`}#1}

+\newcommand{\pmcrprd}[1]{\dot{s}\textbf{`}#1}

+\newcommand{\pmRprdd}{\mathop{||}}

+\newcommand{\pmrprdd}[2]{{#1}\mathop{||}{#2}}

+

+%Identity and Diversity

+\newcommand{\pmrid}{I}

+\newcommand{\pmrdiv}{J}

+\newcommand{\pmcunit}[1]{\iota\textbf{`}#1}

+\newcommand{\pmcUnit}{\iota}

+\newcommand{\pmcunits}[1]{\breve{\iota}\textbf{`}#1}

+

+%Cardinal numbers

+\newcommand{\pmcn}[1]{#1}

+

+%Ordinal numbers

+\newcommand{\pmrn}[1]{#1_r}

+\newcommand{\pmdn}[1]{\dot{#1}}

+\newcommand{\pmoc}[2]{#1 \boldsymbol{\downarrow} #2}

+

+%Subclasses and subrelations

+\newcommand{\pmscl}[1]{\text{Cl}\textbf{`}#1}

+\newcommand{\pmsCl}{\text{Cl}}

+\newcommand{\pmscle}[1]{\text{Cl ex}\textbf{`}#1}

+\newcommand{\pmsCle}{\text{Cl ex}}

+\newcommand{\pmscls}[1]{\text{Cls}\textbf{`}#1}

+\newcommand{\pmsrl}[1]{\text{Rl}\textbf{`}#1}

+\newcommand{\pmsRl}{\text{Rl}}

+\newcommand{\pmsrle}[1]{\text{Rl ex}\textbf{`}#1}

+\newcommand{\pmsRle}{\text{Rl ex}}

+\newcommand{\pmsrel}[1]{\text{Rel}\textbf{`}#1}

+\newcommand{\pmRel}{\text{Rel}}

+\newcommand{\pmReln}[1]{\text{Rel}^{#1}}

+\newcommand{\pmrin}{\mathop{\epsilon}}

+

+%Relative type symbols

+\newcommand{\pmrt}[1]{t\textbf{`}#1}

+\newcommand{\pmrti}[2]{t^{#1}\textbf{`}#2}

+\newcommand{\pmrtc}[2]{t_{#1}\textbf{`}#2}

+\newcommand{\pmrtri}[2]{t^{#1}\textbf{`}#2}

+\newcommand{\pmrtrc}[2]{t_{#1}\textbf{`}#2}

+\newcommand{\pmrtrci}[3]{t_{#1}^{\text{ }#2}\textbf{`}#3}

+\newcommand{\pmrtric}[3]{^{#1}t_{#2}\textbf{`}#3}

+\newcommand{\pmrtdi}[2]{#1_{#2}}

+\newcommand{\pmrtdc}[2]{#1(#2)}

+\newcommand{\pmrtdri}[2]{#1_{#2}}

+\newcommand{\pmrtdrc}[2]{#1(#2)}

+

+%Similarity relation signs

+\newcommand{\pmrdc}[2]{#1\boldsymbol{\to}#2}

+\newcommand{\pmsm}{\mathrel{\text{sm}}}

+\newcommand{\pmsmbar}{\mathrel{\overline{\text{sm}}}}

+\newcommand{\pmsmarr}{\overrightarrow{{\pmsm}}}

+\newcommand{\pmonemany}{1\boldsymbol{\to}\pmCls}

+\newcommand{\pmmanyone}{\pmCls\boldsymbol{\to}1}

+\newcommand{\pmoneone}{1\boldsymbol{\to}1}

+

+%Selections

+\newcommand{\pmselp}[1]{P_{\small\Delta}\mathbf{`}#1}

+\newcommand{\pmSelp}{P_{\Delta}}

+\newcommand{\pmsele}[1]{\pmcin_{\small\Delta}\mathbf{`}#1}

+\newcommand{\pmSele}{\pmcin_{\Delta}}

+\newcommand{\pmself}[1]{F_{\small\Delta}\mathbf{`}#1}

+\newcommand{\pmSelf}{F_{\Delta}}

+\newcommand{\pmexc}{\text{Cls}^2 \mathop{\text{excl}}}

+\newcommand{\pmexcc}[1]{\text{Cl} \mathop{\text{excl}}\textbf{`}#1}

+\newcommand{\pmexcn}{\text{Cls} \mathop{\text{ex}}^2 \mathop{\text{excl}}}

+\newcommand{\pmselc}[2]{#1 \mathrel{\rotatebox[origin=c]{270}{$\boldsymbol{\mapsto}$}} #2}

+\newcommand{\pmmultr}{\mathop{\text{Rel}} \mathop{\text{Mult}}}

+\newcommand{\pmmultc}{\mathop{\text{Cls}^2} \mathop{\text{Mult}}}

+\newcommand{\pmmultax}{\mathop{\text{Mult}} \mathop{\text{ax}}}

+

+%Inductive relations

+\newcommand{\pmanc}[1]{#1_\pmast}

+\newcommand{\pmancc}[1]{\pmcnv{#1}_\pmast}

+\newcommand{\pmrst}[1]{#1_\text{st}}

+\newcommand{\pmrts}[1]{#1_\text{ts}}

+\newcommand{\pmpot}[1]{\text{Pot}\mathbf{`}#1}

+\newcommand{\pmpotid}[1]{\text{Potid}\mathbf{`}#1}

+\newcommand{\pmpo}[1]{#1_\text{po}}

+\newcommand{\pmB}{B}

+\newcommand{\pmmin}[1]{\text{min}_{#1}}

+\newcommand{\pmmax}[1]{\text{max}_{#1}}

+\newcommand{\pmMin}{\text{min}}

+\newcommand{\pmMax}{\text{max}}

+\newcommand{\pmgen}[1]{\text{gen}\mathbf{`}#1}

+\newcommand{\pmGen}{\text{gen}}

+\newcommand{\pmefr}[2]{#1\pmast#2}

+\newcommand{\pmipr}[2]{I_{#1}\textbf{`}#2}

+\newcommand{\pmjpr}[2]{J_{#1}\textbf{`}#2}

+\newcommand{\pmfr}[2]{\overset{\boldsymbol{\leftrightarrow}}{#1}\textbf{`}#2}

+

+%Cardinality 

+\newcommand{\pmnc}[1]{\text{Nc}\textbf{`}#1}

+\newcommand{\pmNc}{\text{Nc}}

+\newcommand{\pmNC}{\text{NC}}

+\newcommand{\pmnoc}[1]{\text{N}_0\text{c}\textbf{`}#1}

+\newcommand{\pmNoc}{\text{N}_0\text{c}}

+

+\begin{document}

+	

+\chapter*{\centering LIST OF DEFINITIONS}

+\onehalfspacing

+\begin{tabular}{l l}

+	\text{ }$\pmast1\pmcdot01$. & $p \pmimp q$ \\

+	\text{ }$\pmast2\pmcdot33$. & $p \pmor q \pmor r$ \\

+	\text{ }$\pmast3\pmcdot01$. & $p \pmand q$ \\

+	\text{ }$\pmast3\pmcdot02$. & $p \pmimp q \pmimp r$ \\

+	\text{ }$\pmast4\pmcdot01$. & $p \pmiff q$ \\

+	\text{ }$\pmast4\pmcdot02$. & $p \pmiff q \pmiff r$ \\

+	\text{ }$\pmast4\pmcdot34$. & $p \pmand q \pmand r$ \\

+	\text{ }$\pmast9\pmcdot01$. & $\pmnot\{(\pmall{x})\pmdot \phi x\}$ \\

+	\text{ }$\pmast9\pmcdot011$. & $\pmnot(\pmall{x})\pmdot \phi x$ \\

+	\text{ }$\pmast9\pmcdot02$. & $\pmnot\{(\pmsome{x})\pmdot \phi x\}$ \\

+	\text{ }$\pmast9\pmcdot021$. & $\pmnot(\pmsome{x})\pmdot \phi x$ \\

+	\text{ }$\pmast9\pmcdot03$. & $(\pmall{x})\pmdot \phi x \pmdot \pmor \pmdot p$ \\

+	\text{ }$\pmast9\pmcdot04$. & $p \pmdot \pmor \pmdot (\pmall{x})\pmdot \phi x$ \\

+	\text{ }$\pmast9\pmcdot05$. & $(\pmsome{x})\pmdot \phi x \pmdot \pmor \pmdot p$ \\

+	\text{ }$\pmast9\pmcdot06$. & $p \pmdot \pmor \pmdot (\pmsome{x})\pmdot \phi x$ \\

+	\text{ }$\pmast9\pmcdot07$. & $(\pmall{x})\pmdot \phi x \pmdot \pmor \pmdot (\pmsome{x})\pmdot \phi x$ \\

+	\text{ }$\pmast9\pmcdot08$. & $(\pmsome{x})\pmdot \phi x \pmdot \pmor \pmdot (\pmall{x})\pmdot \phi x$ \\

+	$\pmast10\pmcdot01$. & $(\pmsome{x})\pmdot \phi x$ \\

+	$\pmast10\pmcdot02$. & $\phi x \pmimp_x \psi x$ \\

+	$\pmast10\pmcdot03$. & $\phi x \pmiff_x \psi x$ \\

+	$\pmast11\pmcdot01$. & $(\pmall{x,y})\pmdot \phi(x, y)$ \\

+	$\pmast11\pmcdot02$. & $(\pmall{x,y,z})\pmdot \phi(x, y, z)$ \\

+	$\pmast11\pmcdot03$. & $(\pmsome{x,y})\pmdot \phi(x, y)$ \\

+	$\pmast11\pmcdot04$. & $(\pmsome{x,y,z})\pmdot \phi(x, y, z)$ \\

+	$\pmast11\pmcdot05$. & $\phi(x, y) \pmimp_{x, y} \psi(x, y)$ \\

+	$\pmast11\pmcdot06$. & $\phi(x, y) \pmiff_{x, y} \psi(x, y)$ \\

+	$\pmast13\pmcdot01$. & $x = y$ \\

+	$\pmast13\pmcdot02$. & $x \pmnid y$ 

+\end{tabular}

+

+\begin{tabular}{l l}

+	$\pmast13\pmcdot03$. & $x = y = z$ \\

+	$\pmast14\pmcdot01$. & $[(\pmdsc{x})(\phi x)]\pmdot \psi(\pmdsc{x})(\phi x)$ \\

+	$\pmast14\pmcdot02$. & $\pmexists(\pmdsc{x})(\phi x)$ \\

+	$\pmast14\pmcdot03$. & $[(\pmdsc{x})(\phi x), (\pmdsc{x})(\psi x)]\pmdot f\{(\pmdsc{x})(\phi x),$\\

+		& \indent $(\pmdsc{x})(\psi x)\}$ \\

+	$\pmast14\pmcdot04$. & $[(\pmdsc{x})(\psi x)]\pmdot f\{(\pmdsc{x})(\phi x), (\pmdsc{x})(\psi x)\}$ \\

+	$\pmast20\pmcdot01$. & $f\{\pmcls{z}{\psi z}\}$ \\

+	$\pmast20\pmcdot02$. & $x \pmcin \pmpred{\phi}{\pmhat{z}}$ \\

+	$\pmast20\pmcdot03$. & $\pmsCl$ \\

+	$\pmast20\pmcdot04$. & $x, y \pmcin \alpha$ \\

+	$\pmast20\pmcdot05$. & $x, y, z \pmcin \alpha$ \\

+	$\pmast20\pmcdot06$. & $x \pmnot \pmcin \alpha$ \\

+	$\pmast20\pmcdot07$. & $(\pmall{\alpha})\pmdot f\alpha$ \\

+	$\pmast20\pmcdot071$. & $(\pmsome{\alpha})\pmdot f\alpha$ \\

+	$\pmast20\pmcdot072$. & $[(\pmdsc{\alpha})(\phi \alpha)]\pmdot f(\pmdsc{\alpha})(\phi \alpha)$ \\

+	$\pmast20\pmcdot08$. & $f\{\pmcls{\alpha}{\psi \alpha}\}$ \\

+	$\pmast20\pmcdot081$. & $\alpha \pmcin \pmpred{\psi}{\pmhat{z}}$ \\

+	$\pmast21\pmcdot01$. & $f\{\pmrel{x}{y}{\phi(x,y)}\}$ \\

+	$\pmast21\pmcdot02$. & $\pmrelep{a}{\pmpredd{\phi}{\pmhat{x}}{\pmhat{y}}}{b}$ \\

+	$\pmast21\pmcdot03$. & $\pmRel$ \\

+	$\pmast21\pmcdot07$. & $(\pmall{R})\pmdot fR$ \\

+	$\pmast21\pmcdot071$. & $(\pmsome{R})\pmdot fR$ \\

+	$\pmast21\pmcdot072$. & $[(\pmdsc{R})(\phi R)]\pmdot f(\pmdsc{R})(\phi R)$ \\

+	$\pmast21\pmcdot08$. & $f\{\pmrel{R}{S}{\psi(R, S}\}$ \\

+	$\pmast21\pmcdot081$. & $\pmrelep{P}{\pmpredd{\phi}{\pmhat{R}}{\pmhat{S}}}{Q}$ \\

+	$\pmast21\pmcdot082$. & $f\{\pmcls{R}{\psi R}\}$ \\

+	$\pmast21\pmcdot083$. & $R \pmcin \pmpred{\psi}{\pmhat{R}}$ \\

+	$\pmast22\pmcdot01$. & $\alpha \pmcin \beta$ \\

+	$\pmast22\pmcdot02$. & $\alpha \pmccap \beta$ 

+\end{tabular}

+

+\begin{tabular}{l l}

+$\pmast22\pmcdot03$. & $\alpha \pmccup \beta$ \\

+$\pmast22\pmcdot04$. & $\pmccmp{\alpha}$ \\

+$\pmast22\pmcdot05$. & $\pmcmin{\alpha}{\beta}$ \\

+$\pmast22\pmcdot53$. & $\alpha \pmccap \beta \pmccap \gamma$ \\

+$\pmast22\pmcdot71$. & $\alpha \pmccup \beta \pmccup \gamma$ \\

+$\pmast23\pmcdot01$. & $R \pmrinc S$ \\

+$\pmast23\pmcdot02$. & $R \pmrcap S$ \\

+$\pmast23\pmcdot03$. & $R \pmrcup S$ \\

+$\pmast23\pmcdot04$. & $\pmrcmp{R}$ \\

+$\pmast23\pmcdot05$. & $\pmrmin{R}{S}$ \\

+$\pmast23\pmcdot53$. & $R \pmrcap S \pmrcap T$ \\

+$\pmast23\pmcdot71$. & $R \pmrcup S \pmrcup T$ \\

+$\pmast24\pmcdot01$. & $\pmcuni$ \\

+$\pmast24\pmcdot02$. & $\pmcnull$ \\

+$\pmast24\pmcdot03$. & $\pmcexists \alpha$ \\

+$\pmast25\pmcdot01$. & $\pmruni$ \\

+$\pmast25\pmcdot02$. & $\pmrnull$ \\

+$\pmast25\pmcdot03$. & $\pmrexists R$ \\

+$\pmast30\pmcdot01$. & $\pmdscf{R}{y}$ \\

+$\pmast30\pmcdot02$. & $\pmdscf{R}{\pmdscf{S}{y}}$ \\

+$\pmast31\pmcdot01$. & $\pmCnv$ \\

+$\pmast31\pmcdot02$. & $\pmcnv{P}$ \\

+$\pmast32\pmcdot01$. & $\pmRrf{R}$ \\

+$\pmast32\pmcdot02$. & $\pmRrl{R}$ \\

+$\pmast32\pmcdot03$. & $\pmsg$ \\

+$\pmast32\pmcdot04$. & $\pmgs$ \\

+$\pmast33\pmcdot01$. & $\pmDm$ \\

+$\pmast33\pmcdot02$. & $\pmCdm$ \\

+$\pmast33\pmcdot03$. & $\pmCmp$ \\

+$\pmast33\pmcdot04$. & $\pmFld$ \\

+$\pmast34\pmcdot01$. & $\pmrprd{R}{S}$ \\

+$\pmast34\pmcdot02$. & $\pmrprdn{R}{2}$ 

+\end{tabular}

+

+\begin{tabular}{l l}

+$\pmast34\pmcdot03$. & $\pmrprdn{R}{3}$ \\

+$\pmast35\pmcdot01$. & $\pmrld{\alpha}{R}$ \\

+$\pmast35\pmcdot02$. & $\pmrlcd{R}{\beta}$ \\

+$\pmast35\pmcdot03$. & $\pmrlf{\alpha}{R}{\beta}$ \\

+$\pmast35\pmcdot04$. & $\pmrl{\alpha}{\beta}$ \\

+$\pmast35\pmcdot05$. & $\pmrl{\pmdscf{R}{x}}{\beta}$ \\

+$\pmast35\pmcdot24$. & $\pmrld{\alpha}{\pmrprd{R}{S}}$ \\

+$\pmast35\pmcdot25$. & $\pmrlF{P}{\alpha}$ \\

+$\pmast36\pmcdot01$. & $\pmrlf{R}{\beta}$ \\

+$\pmast37\pmcdot01$. & $\pmdscf{R}{\beta}$ \\

+$\pmast37\pmcdot02$. & $\pmdscfR{R}$ \\

+$\pmast37\pmcdot03$. & $\pmcnv{\pmdscfR{R}}$\\

+$\pmast37\pmcdot04$. & $\pmdscfff{R}{\kappa}$ \\

+$\pmast37\pmcdot05$. & $\pmdscfe{R}{\beta}$ \\

+$\pmast38\pmcdot01$. & $x \pmop$ \\

+$\pmast38\pmcdot02$. & $\pmop x$ \\

+$\pmast38\pmcdot03$. & $\pmopc{\alpha}{y}$\\

+$\pmast40\pmcdot01$. & $\pmccsum{\kappa}$ \\

+$\pmast40\pmcdot02$. & $\pmccprd{\kappa}$ \\

+$\pmast41\pmcdot01$. & $\pmcrsum{\lambda}$ \\

+$\pmast41\pmcdot02$. & $\pmcrprd{\lambda}$ \\

+$\pmast43\pmcdot01$. & $\pmrprdd{R}{S}$ \\

+$\pmast50\pmcdot01$. & $\pmrid$ \\

+$\pmast50\pmcdot02$. & $\pmrdiv$ \\

+$\pmast51\pmcdot01$. & $\pmcUnit$ \\

+$\pmast52\pmcdot01$. & $\pmcn{1}$ \\

+$\pmast54\pmcdot01$. & $\pmcn{0}$ \\

+$\pmast54\pmcdot02$. & $\pmcn{2}$ \\

+$\pmast55\pmcdot01$. & $\pmoc{x}{y}$ \\

+$\pmast55\pmcdot02$. & $\pmoc{\pmdscf{R}{x}}{y}$ \\

+$\pmast56\pmcdot01$. & $\pmdn{2}$ \\

+$\pmast56\pmcdot02$. & $\pmrn{2}$ 

+\end{tabular}

+

+\begin{tabular}{l l}

+$\pmast56\pmcdot03$. & $\pmrn{0}$ \\

+$\pmast60\pmcdot01$. & $\pmsCl$ \\

+$\pmast60\pmcdot02$. & $\pmsCle$ \\

+$\pmast60\pmcdot03$. & $\pmClsn{2}$ \\

+$\pmast60\pmcdot04$. & $\pmClsn{3}$ \\

+$\pmast61\pmcdot01$. & $\pmsRl$ \\

+$\pmast61\pmcdot02$. & $\pmsRle$ \\

+$\pmast61\pmcdot03$. & $\pmReln{2}$ \\

+$\pmast61\pmcdot04$. & $\pmReln{3}$ \\

+$\pmast62\pmcdot01$. & $\pmrin$ \\

+$\pmast63\pmcdot01$. & $\pmrt{x}$ \\

+$\pmast63\pmcdot011$. & $\pmrtc{1}{x}$ \\

+$\pmast63\pmcdot02$. & $\pmrti{0}{\alpha}$ \\

+$\pmast63\pmcdot03$. & $\pmrti{1}{\kappa}$ \\

+$\pmast63\pmcdot04$. & $\pmrtc{2}{\kappa}$ \\

+$\pmast63\pmcdot041$. & $\pmrtc{3}{\kappa}$ \\

+$\pmast63\pmcdot05$. & $\pmrti{2}{\kappa}$ \\

+$\pmast63\pmcdot051$. & $\pmrti{3}{\kappa}$ \\

+$\pmast64\pmcdot01$. & $\pmrtri{00}{\alpha}$ \\

+$\pmast64\pmcdot011$. & $\pmrtrc{11}{x}$ \\

+$\pmast64\pmcdot012$. & $\pmrtc{12}{x}$ \\

+$\pmast64\pmcdot013$. & $\pmrtc{21}{x}$ \\

+$\pmast64\pmcdot014$. & $\pmrtc{22}{x}$ \\

+$\pmast64\pmcdot02$. & $\pmrti{01}{\alpha}$ \\

+$\pmast64\pmcdot021$. & $\pmrti{10}{\alpha}$ \\

+$\pmast64\pmcdot022$. & $\pmrti{11}{\alpha}$ \\

+$\pmast64\pmcdot03$. & $\pmrtric{0}{1}{\alpha}$ \\

+$\pmast64\pmcdot031$. & $\pmrtric{1}{1}{\alpha}$ \\

+$\pmast64\pmcdot04$. & $\pmrtrci{1}{0}{\alpha}$ \\

+$\pmast64\pmcdot041$. & $\pmrtrci{1}{1}{\alpha}$ \\

+$\pmast65\pmcdot01$. & $\pmrtdi{\alpha}{x}$ \\

+$\pmast65\pmcdot02$. & $\pmrtdc{\alpha}{x}$ 

+\end{tabular}

+

+\begin{tabular}{l l}

+$\pmast65\pmcdot03$. & $\pmrtdri{R}{x}$ \\

+$\pmast65\pmcdot04$. & $\pmrtdrc{R}{x}$ \\

+$\pmast65\pmcdot1$. & $\pmrtdri{R}{(x,y)}$ \\

+$\pmast65\pmcdot11$. & $\pmrtdrc{R}{x_y}$\\

+$\pmast65\pmcdot12$. & $\pmrtdrc{R}{x, y}$ \\

+$\pmast70\pmcdot01$. & $\pmrdc{\alpha}{\beta}$ \\

+$\pmast73\pmcdot01$. & $\alpha \pmsmbar \beta$ \\

+$\pmast73\pmcdot02$. & $\pmsm$\\

+$\pmast80\pmcdot01$. & $\pmSelp$ \\

+$\pmast84\pmcdot01$. & $\pmexc$ \\

+$\pmast84\pmcdot02$. & $\pmexcc{\gamma}$ \\

+$\pmast84\pmcdot03$. & $\pmexcn$\\

+$\pmast85\pmcdot5$. & $\pmselc{P}{y}$ \\

+$\pmast88\pmcdot01$. & $\pmmultr$ \\

+$\pmast88\pmcdot02$. & $\pmmultc$ \\

+$\pmast88\pmcdot03$. & $\pmmultax$ \\

+$\pmast90\pmcdot01$. & $\pmanc{R}$ \\

+$\pmast90\pmcdot02$. & $\pmancc{R}$ \\

+$\pmast91\pmcdot01$. & $\pmrst{R}$ \\

+$\pmast91\pmcdot02$. & $\pmrts{R}$ \\

+$\pmast91\pmcdot03$. & $\pmpot{R}$ \\

+$\pmast91\pmcdot04$. & $\pmpotid{R}$ \\

+$\pmast91\pmcdot05$. & $\pmpo{R}$ \\

+$\pmast93\pmcdot01$. & $\pmB$ \\

+$\pmast93\pmcdot02$. & $\pmmin{P}$ \\

+$\pmast93\pmcdot021$. & $\pmmax{P}$ \\

+$\pmast93\pmcdot03$. & $\pmgen{P}$ \\

+$\pmast95\pmcdot01$. & $\pmefr{P}{Q}$ \\

+$\pmast96\pmcdot01$. & $\pmipr{R}{x}$ \\

+$\pmast96\pmcdot02$. & $\pmjpr{R}{x}$ \\

+$\pmast97\pmcdot01$. & $\pmfr{R}{x}$ \\

+$\pmast100\pmcdot01$. & $\pmNc$ 

+\end{tabular}

+

+\end{document}
\ No newline at end of file
diff --git a/principia.sty b/principia.sty
index 33010b4..0ceafab 100644
--- a/principia.sty
+++ b/principia.sty
@@ -15,14 +15,26 @@
 

 %Meta-logical symbols

 \newcommand{\pmdem}{\textit{Dem}.} %This notation begins a proof.

+\newcommand{\pmdemi}{\indent \pmdem} %This idents the notation that begins a proof.

+\newcommand{\pmprop}{\text{Prop}} %This occurs at the end of a proof.

+\newcommand{\pmithm}{\pmimp\;\pmthm} %This occurs when a meta-theoretic implication is asserted.

+\newcommand{\pmbr}[1]{\bigg \lbrack \normalsize #1 \bigg \rbrack} %These are larger brackets for substitution.

 \newcommand{\pmsub}[2]{\bigg \lbrack \small \begin{array}{c} #1 \\ \hline #2 \end{array} \bigg \rbrack} %This is the substitution command.

-\newcommand{\pmSub}[3]{\bigg \lbrack \normalsize #1 \text{ } \small \begin{array}{c} #2 \\ \hline #3 \end{array}  \bigg \rbrack} %This is the substitution command.

 \newcommand{\pmsubb}[4]{\bigg \lbrack \small \begin{array}{c c} #1, & #3 \\ \hline #2, & #4 \end{array}  \bigg \rbrack} %This is the substitution command.

-\newcommand{\pmSubb}[5]{\bigg \lbrack \normalsize #1 \text{ } \small \begin{array}{c c} #2, & #4 \\ \hline #3, & #5 \end{array}  \bigg \rbrack} %This is the substitution command.

 \newcommand{\pmsubbb}[6]{\bigg \lbrack \small \begin{array}{c c c} #1, & #3, & #5 \\ \hline #2, & #4, & #6 \end{array}  \bigg \rbrack} %This is the substitution command.

-\newcommand{\pmSubbb}[7]{\bigg \lbrack \normalsize #1 \text{ } \small \begin{array}{c c c} #2, & #4, & #6 \\ \hline #3, & #5, & #7 \end{array}  \bigg \rbrack} %This is the substitution command.

 \newcommand{\pmsubbbb}[8]{\bigg \lbrack \small \begin{array}{c c c c} #1, & #3, & #5, & #7 \\ \hline #2, & #4, & #6, & #8 \end{array}  \bigg \rbrack} %This is the substitution command.

-\newcommand{\pmSubbbb}[9]{\bigg \lbrack \normalsize #1 \text{ } \small \begin{array}{c c c c} #1, & #3, & #5, & #7 \\ \hline #2, & #4, & #6, & #8 \end{array}  \bigg \rbrack} %This is the substitution command.

+\newcommand{\pmSub}[3]{\bigg \lbrack \normalsize #1 \text{ } \small \begin{array}{c} #2 \\ \hline #3 \end{array}  \bigg \rbrack} %This is the substitution command.

+\newcommand{\pmSubb}[5]{\bigg \lbrack \normalsize #1 \text{ } \small \begin{array}{c c} #2, & #4 \\ \hline #3, & #5 \end{array}  \bigg \rbrack} %This is the substitution command.

+\newcommand{\pmSubbb}[7]{\bigg \lbrack \normalsize #1 \text{ } \small \begin{array}{c c c} #2, & #4, & #6 \\ \hline #3, & #5, & #7 \end{array}  \bigg \rbrack} %This is the substitution command.

+\newcommand{\pmSubbbb}[9]{\bigg \lbrack \normalsize #1 \text{ } \small \begin{array}{c c c c} #1, & #3, & #5, & #7 \\ \hline #2, & #4, & #6, & #8 \end{array} \bigg \rbrack} %This is the substitution command.

+\newcommand{\pmsUb}[2]{\small \begin{array}{c} #1 \\ \hline #2 \end{array}} %This is the substitution command.

+\newcommand{\pmsUbb}[4]{\small \begin{array}{c c} #1, & #3 \\ \hline #2, & #4 \end{array}} %This is the substitution command.

+\newcommand{\pmsUbbb}[6]{\small \begin{array}{c c c} #1, & #3, & #5 \\ \hline #2, & #4, & #6 \end{array}} %This is the substitution command.

+\newcommand{\pmsUbbbb}[8]{\small \begin{array}{c c c c} #1, & #3, & #5, & #7 \\ \hline #2, & #4, & #6, & #8 \end{array}} %This is the substitution command.

+\newcommand{\pmSUb}[3]{\normalsize #1 \text{ } \small \begin{array}{c} #2 \\ \hline #3 \end{array}} %This is the substitution command.

+\newcommand{\pmSUbb}[5]{\normalsize #1 \text{ } \small \begin{array}{c c} #2, & #4 \\ \hline #3, & #5 \end{array}} %This is the substitution command.

+\newcommand{\pmSUbbb}[7]{\normalsize #1 \text{ } \small \begin{array}{c c c} #2, & #4, & #6 \\ \hline #3, & #5, & #7 \end{array}} %This is the substitution command.

+\newcommand{\pmSUbbbb}[9]{\normalsize #1 \text{ } \small \begin{array}{c c c c} #1, & #3, & #5, & #7 \\ \hline #2, & #4, & #6, & #8 \end{array}} %This is the substitution command.

 \newcommand{\pmthm}{\mathpunct{\text{\scalebox{.5}[1]{$\boldsymbol\vdash$}}}} %This is the theorem sign.

 \newcommand{\pmast}{\text{\resizebox{!}{.75\height}{\ding{107}}}} %This is the sign introducing a theorem number.

 \newcommand{\pmcdot}{\text{\raisebox{.05cm}{$\boldsymbol\cdot$}}} %This is a sign introducing a theorem sub-number.

@@ -198,9 +210,10 @@
 \newcommand{\pmSele}{\pmcin_{\Delta}}

 \newcommand{\pmself}[1]{F_{\small\Delta}\mathbf{`}#1}

 \newcommand{\pmSelf}{F_{\Delta}}

+\newcommand{\pmex}[1]{\text{Cls} \mathop{\text{excl}}\mathbf{`}#1}

 \newcommand{\pmexc}{\text{Cls}^2 \mathop{\text{excl}}}

 \newcommand{\pmexcc}[1]{\text{Cl} \mathop{\text{excl}}\textbf{`}#1}

-\newcommand{\pmexcn}{\text{Cls} \mathop{\text{ex}}^2 \mathop{\text{excl}}}

+\newcommand{\pmexcn}{\text{Cls} \mathop{\text{ex}^2} \mathop{\text{excl}}}

 \newcommand{\pmselc}[2]{#1 \mathrel{\rotatebox[origin=c]{270}{$\boldsymbol{\mapsto}$}} #2}

 \newcommand{\pmmultr}{\mathop{\text{Rel}} \mathop{\text{Mult}}}

 \newcommand{\pmmultc}{\mathop{\text{Cls}^2} \mathop{\text{Mult}}}

@@ -231,4 +244,9 @@
 \newcommand{\pmNc}{\text{Nc}}

 \newcommand{\pmNC}{\text{NC}}

 \newcommand{\pmnoc}[1]{\text{N}_0\text{c}\textbf{`}#1}

-\newcommand{\pmNoc}{\text{N}_0\text{c}}
\ No newline at end of file
+\newcommand{\pmNoc}{\text{N}_0\text{c}}

+\newcommand{\pmnocind}[1]{\text{N}_0\text{Cinduct}\textbf{`}#1}

+\newcommand{\pmNocind}{\text{N}_0\text{Cinduct}}

+

+\newcommand{\pmclsrefl}{\text{Cls} \mathop{\text{refl}}} 

+\newcommand{\pmncrefl}{\text{NC} \mathop{\text{refl}}} 
\ No newline at end of file