principia (20apr21)

git-svn-id: svn://tug.org/texlive/trunk@58927 c570f23f-e606-0410-a88d-b1316a301751

4 files changed, 117 insertions, 297 deletions

diff --git a/Master/texmf-dist/doc/latex/principia/README b/Master/texmf-dist/doc/latex/principia/README
index 05b3abc81d1..83b78ebc293 100644
--- a/Master/texmf-dist/doc/latex/principia/README
+++ b/Master/texmf-dist/doc/latex/principia/README
@@ -2,11 +2,11 @@ principia.sty - a LaTeX2e package for typesetting the "Peanese" notation of Whit
 
 The file principia.sty is the original work of Landon D. C. Elkind (Copyright (c) 2021). It is released under the LaTeX Project Public License 1.3c.
 
-This is principia package Version 1.2 (23/02/2021). Like Versions 1.0-1.1, this version covers typesetting the notations through Volume I of "Principia Mathematica". Version 1.2 has some minor updates. See the file principia.pdf for information on these changes and for further information on how to typeset Peanese symbols in LaTeX with the principia package. 
+This is principia package Version 1.3 (2021/04/19). This version covers typesetting the notations through Sections A and B in Volume I of "Principia Mathematica". See the file principia.pdf for information on these changes and for further information on how to typeset Peanese symbols in LaTeX with the principia package.
 
-Updates to include all notations throughout Volumes II and III are planned. Further information and updates can be found at https://logicalatomist.github.io/principia/
+Changes between version updates can be found at https://logicalatomist.github.io/principia/
 
 Comments and suggestions are welcomed by the package maintainer, signed below.
 
-Landon D. C. Elkind 
-University of Alberta
\ No newline at end of file
+Landon D. C. Elkind
+University of Alberta
diff --git a/Master/texmf-dist/doc/latex/principia/principia.pdf b/Master/texmf-dist/doc/latex/principia/principia.pdf
index 7a86501043f..b0c8da5020a 100644
--- a/Master/texmf-dist/doc/latex/principia/principia.pdf
+++ b/Master/texmf-dist/doc/latex/principia/principia.pdf
diff --git a/Master/texmf-dist/doc/latex/principia/principia.tex b/Master/texmf-dist/doc/latex/principia/principia.tex
index 76618c0b0b9..86d5ce3a223 100644
--- a/Master/texmf-dist/doc/latex/principia/principia.tex
+++ b/Master/texmf-dist/doc/latex/principia/principia.tex
@@ -1,11 +1,13 @@
 \documentclass[12pt]{article}
 \NeedsTeXFormat{LaTeX2e}
-\ProvidesPackage{principia}[2020/10/25 principia package version 1.1] %This package supports typesetting the Peanese notation in Volume I of Whitehead and Russell’s 1910 ``Principia Mathematica". 
+\ProvidesPackage{principia}[2021/04/19 principia package version 1.3] %This is the principia package is for representing notations in Whitehead and Russell's ``Principia Mathematica" close to their appearance in the original.
 %Version 1.0 (superseded by Version 1.1): Covers typesetting of notation through Volume I. 2020/10/24
-%Version 1.1 (updates): fixed the spacing of scope dots around parentheses; fixed spacing of theorem sign; fixed spacing around primitive proposition and definition signs. 2020/10/25
-%Version 1.2 (updates): boldfaced (`thickened') the truth-functional connectives, existential quantifier, set and relation symbols; added numerous commands for typesetting brackets and substitutions into theorems. 2021/02/23
+%Version 1.1 (superseded by Version 1.2) minor updates: fixed the spacing of scope dots around parentheses; fixed spacing of theorem sign; fixed spacing around primitive proposition and definition signs. 2020/10/25
 %Licensed under LaTeX Project Public License 1.3c. 
-%Copyright Landon D. C. Elkind, 2020.  (https://landondcelkind.com/contact/).
+%Version 1.2 (superseded by Version 1.3) (minor updates): boldfaced (`thickened') the truth-functional connectives, existential quantifier, set and relation symbols; added numerous commands for typesetting brackets and substitutions into theorems. 2021/02/25
+%Version 1.3 (minor update): removes package dependency on marvosym; updates Section A and Section B notations. 2021/04/19
+%Licensed under LaTeX Project Public License 1.3c. 
+%Copyright Landon D. C. Elkind, 2021.  (https://landondcelkind.com/contact/).
 
 \usepackage{fullpage}
 \usepackage[T1]{fontenc}
@@ -13,14 +15,89 @@
 \usepackage{setspace}
 
 %Principia package requirements
-\usepackage{principia} %The package itself, and its dependencies:
 \usepackage{amssymb} %This loads the relation domain and converse domain limitation symbols.
 \usepackage{amsmath} %This loads the circumflex, substitution into theorems, \text{}, \mathbf{}, \boldsymbol{}, \overleftarrow{}, \overrightarrow{}, etc.
 \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.
 
-\title{\texttt{principia.sty }\\ A \LaTeXe \space Package for Typesetting Whitehead and Russell's \textit{Principia Mathematica} (Version 1.2)}
+%Volume I
+%Mathematical logic
+%The theory of deduction
+%Meta-logical symbols
+\newcommand{\pmfd}{\begin{center} \rule{5cm}{.5pt} \end{center}} %Dividing line between introductory remarks in a starred number and the formal deductions.
+\newcommand{\pmdem}{\textit{Dem}.} %This notation begins a proof.
+\newcommand{\pmdemi}{\indent \pmdem} %This idents the notation that begins a proof.
+\newcommand{\pmhp}{\text{Hp}} %This typesets Hp (short for antecedent), which occurs at the beginning of 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{\pmsubb}[4]{\bigg \lbrack \small \begin{array}{c c} #1, & #3 \\ \hline #2, & #4 \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{\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{\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.
+\newcommand{\pmiddf}{\mathbin{=}}
+\newcommand{\pmdf}{\quad \text{Df}}
+\newcommand{\pmpp}{\quad \text{Pp}}
+
+%Square dots for scope, defined for up to six dots
+\newcommand{\pmdot}{\mathrel{\hbox{\rule{.3ex}{.3ex}}}}
+\newcommand{\pmdott}{\mathrel{\overset{\pmdot}{\pmdot}}}
+\newcommand{\pmdottt}{\pmdott\hspace{.1em}\pmdot}
+\newcommand{\pmdotttt}{\pmdott\hspace{.1em}\pmdott}
+\newcommand{\pmdottttt}{\pmdott\hspace{.1em}\pmdott\hspace{.1em}\pmdot}
+\newcommand{\pmdotttttt}{\pmdott\hspace{.1em}\pmdott\hspace{.1em}\pmdott}
+
+%Logical connectives
+\newcommand{\pmnot}{\mathord{\ooalign{$\boldsymbol{\sim}\mkern.5mu$\hidewidth\cr$\boldsymbol{\sim}$\cr\hidewidth$\mkern.5mu\boldsymbol{\sim}$}}}
+\newcommand{\pmor}{\mathbin{\ooalign{$\boldsymbol{\vee}\mkern.5mu$\hidewidth\cr$\boldsymbol{\vee}$\cr\hidewidth$\mkern.5mu\boldsymbol{\vee}$}}}
+\newcommand{\pmimp}{\mathbin{\ooalign{$\boldsymbol{\supset}\mkern.5mu$\hidewidth\cr$\boldsymbol{\supset}$\cr\hidewidth$\mkern.5mu\boldsymbol{\supset}$}}} %1.01
+\newcommand{\pmand}{\mathrel{\hbox{\rule{.3ex}{.3ex}}}} %3.01
+\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}
+\newcommand{\pmprod}{\mathbin{\ooalign{$\boldsymbol{\wedge}\mkern.5mu$\hidewidth\cr$\boldsymbol{\wedge}$\cr\hidewidth$\mkern.5mu\boldsymbol{\wedge}$}}} %Not in Principia, but added here as a dual of its symbol for disjunction.
+\newcommand{\pmiff}{\mathbin{\ooalign{$\boldsymbol{\equiv}\mkern.5mu$\hidewidth\cr$\boldsymbol{\equiv}$\cr\hidewidth$\mkern.5mu\boldsymbol{\equiv}$}}} %4.01
+
+%The theory of apparent variables
+\newcommand{\pmall}[1]{(#1)}
+\newcommand{\pmsome}[1]{(\text{\raisebox{.5em}{\rotatebox{180}{\textbf{E}}}}#1)} %10.01
+\newcommand{\pmSome}{\text{\raisebox{.5em}{\rotatebox{180}{\textbf{E}}}}}
+
+%Additional defined logic signs
+\newcommand{\pmhat}[1]{\mathbf{\hat{\text{$#1$}}}}
+\newcommand{\pmbreve}[1]{\mathbf{\breve{\text{$#1$}}}}
+\newcommand{\pmcirc}[1]{\mathbf{\dot{\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}}} %*13.02
+\newcommand{\pmiota}{\ooalign{\rotatebox[origin=c]{180}{$\mathbf{\iota}$}\cr\hidewidth\raisebox{.0125em}{\rotatebox[origin=c]{180}{$\mathbf{\iota}$}}\cr\hidewidth\raisebox{.025em}{\rotatebox[origin=c]{180}{$\mathbf{\iota}$}}\cr\hidewidth\raisebox{.0375em}{\rotatebox[origin=c]{180}{$\mathbf{\iota}$}}\cr\hidewidth\raisebox{.05em}{\rotatebox[origin=c]{180}{$\mathbf{\iota}$}}}} %the rotated Greek iota used in definite descriptions
+\newcommand{\pmdsc}[1]{(\pmiota#1)} %*14.01
+\newcommand{\pmDsc}{\pmiota} 
+\newcommand{\pmexists}{\textbf{E}\hspace{.1em}\pmshr} %*14.02
+
+\title{\texttt{principia.sty}\\ A \LaTeXe \space Package for Typesetting Whitehead and Russell's \textit{Principia Mathematica} (Version 1.3)}
 \author{Landon D. C. Elkind \texttt{elkind@ualberta.ca}}
 \date{\today}
 
@@ -33,9 +110,11 @@ The \texttt{principia} package is designed for typesetting the Peanese notation
 
 In \textit{Principia Mathematica} some symbols occur with an argument and sometimes that same symbol occurs without an argument. For example, `$\pmsome{x}$' occurs in some formulas, but sometimes `$\pmSome$' occurs in the text when they talk about the symbol itself. \texttt{principia} is designed to accommodate these different occurrences of symbols. When a symbol is to occur without an argument, capitalize the first letter following the `\texttt{$\backslash$pm}' part of the command. E.g. \verb|\pmsome{x}| produces $\pmsome{x}$ and \verb|\pmSome| produces `$\pmSome$'. Note the former command requires an argument and the latter command does not. Not all commands in the \texttt{principia} package admit of such dual use because some symbols in \textit{Principia Mathematica} never occur without an argument or do not take an argument in the usual sense. For example, the propositional connectives do not take an `argument' in the way singular or plural descriptions do.
 
-Version 1.2 (and 1.0-1.1) of \texttt{principia} is adequate to typeset all notations throughout Volume I of \textit{Principia} and includes some fixes to spacing, etc. See the package documentation for details. Updates to include all notations throughout Volumes II and III are planned.
+Version 1.3 of \texttt{principia} is adequate to typeset all notations throughout Sections A and B of \textit{Principia}'s Volume I and includes some minor fixes. See the package documentation for details. 
+
+\texttt{principia}'s dependencies are \texttt{amsmath}, \texttt{amssymb}, \texttt{pifont}, and \texttt{graphicx}. Make sure to load these package by typing \texttt{$\backslash$usepackage\{graphicx\}}, etc., into the document preamble. 
 
-\texttt{principia}'s dependencies are \texttt{amsmath}, \texttt{amssymb}, \texttt{pifont}, \texttt{marvosym}, and \texttt{graphicx}. Make sure to load these package by typing \texttt{$\backslash$usepackage\{graphicx\}}, etc., into the document preamble. To load \texttt{principia}, type \texttt{$\backslash$usepackage\{principia\}} in the document's preamble.
+To load \texttt{principia}, type \texttt{$\backslash$usepackage\{principia\}} in the document's preamble.
 
 \noindent \begin{tabular}{@{}p{3cm} | p{5cm} | p{8.25cm}}
 	\textbf{Symbol} & \textbf{\LaTeX command} & \textbf{Notes} \\ \hline
@@ -70,105 +149,7 @@ Version 1.2 (and 1.0-1.1) of \texttt{principia} is adequate to typeset all notat
 \noindent \begin{tabular}{@{}p{3cm} | p{5cm} | p{8.25cm}}
 	$=$, $\pmnid$ & \verb|=|, \verb|\pmnid| & Identity and its negation. \\
 	$\pmdsc{x}$ & \verb|\pmdsc{x}| & Definite description. \\
-	$\pmexists$ & \verb|\pmexists| & Existence. \\
-	$\pmcls{z}{\psi z}$ & \verb|\pmcls{z}{\psi z}| & The class of $z$s satisfying $\psi$. \\
-	$\pmcin$ & \verb|\pmcin| & The class membership symbol. \\
-	$\pmClsn{n}$, $\pmCls$ &  \verb|\pmClsn{n}|, \verb|\pmCls| & The class of classes of individuals. \\
-	 $\pmscl{\alpha}$, $\pmsCl$ & \verb|\pmscl{\alpha}|, \verb|\pmsCl| & The subclasses of a class $\alpha$. \\
-	 $\pmsrl{R}$, $\pmsRl$ & \verb|\pmsrl{R}|, \verb|\pmsRl| & The sub-relations of a relation $R$. \\
-	$\pmcuni$ & \verb|\pmcuni| & The universal class. \\
-	$\pmcnull$ & \verb|\pmcnull| & The null class. \\
-	$\pmcexists$ & \verb|\pmcexists| & The existence of a class. \\
-	$\pmccmp{\alpha}$ & \verb|\pmccmp{\alpha}| & This command requires one argument. \\
-	$\pmcmin{\alpha}{\beta}$ & \verb|\pmcmin{\alpha}{\beta}| & This command requires two arguments. \\
-	$\pmccup$ & \verb|\pmccup| & Class union. \\
-	$\pmccap$ & \verb|\pmccap| & Class intersection. \\
-	$\pmcinc$ & \verb|\pmcinc| & Class inclusion. \\
-	$\pmrel{x}{y}{\phi(x,y)}$ & \verb|\pmrel{x}{y}{\phi(x,y)}| & The relation in extension given by $\phi$. \\
-	$\pmrele{a}{x}{y}{R}{b}$ & \verb|\pmrele{a}{x}{y}{R}{b}| & This command requires five arguments. \\
-	$\pmrelep{a}{R}{b}$ & \verb|\pmrelep{a}{R}{b}| & This command requires three arguments. \\
-	$\pmrin$ & \verb|\pmrin| & The relation membership symbol. \\
-	$\pmReln{n}$, $\pmRel$ & \verb|\pmReln{n}|, \verb|\pmRel| & The class of relations ($n$-many `of relations'). \\
-	$\pmruni$ & \verb|\pmruni| & The universal relation. \\
-	$\pmrnull$ & \verb|\pmrnull| & The null relation. \\
-	$\pmrexists$ & \verb|\pmrexists| & This symbol prefixes relations. \\
-	$\pmrcmp{R}$ & \verb|\pmrcmp{\alpha}| & This command requires one argument. \\
-	$\pmrmin{R}{S}$ & \verb|\pmcmin{R}{S}| & This command requires two arguments. \\
-	$\pmrcup$ & \verb|\pmrcup| & Relation union. \\
-	$\pmrcap$ & \verb|\pmrcap| & Relation intersection. \\
-	$\pmrinc$ & \verb|\pmrinc| & Relation inclusion. \\
-	$\pmcrel{R}$ & \verb|\pmcrel{R}| & The converse of a relation. \\
-	$\pmCnv$ & \verb|\pmCnv| & The command for `Cnv'. \\
-	$\pmdscf{R}{x}$ & \verb|\pmdscf{R}{x}| & A singular descriptive function. \\
-	$\pmdscff{R}{\beta}$ & \verb|\pmdscff{R}{\beta}| & A plural descriptive function. \\
-	$\pmdscfff{R}{\kappa}$ & \verb|\pmdscfff{R}{\kappa}| & A plural descriptive function.   \\
-	$\pmdscfe{R}{\beta}$ & \verb|\pmdscfe{R}{\beta}| & The existence of a plural descriptive function.
-\end{tabular}
-
-\noindent \begin{tabular}{@{}p{3cm} | p{5cm} | p{8.25cm}}
-	$\pmdscfr{R}{x}$, `$\pmdscfR{R}$'& \verb|\pmdscfr{R}{x}|, \verb|\pmdscfR{R}| & The relation of $\pmdscfr{R}{\beta}$ to $\beta$. \\
-	$\pmdm{R}$, $\pmDm$ & \verb|\pmdm{R}|, \verb|\pmDm| & The domain of a relation $R$.  \\
-	$\pmcdm{R}$, $\pmCdm$ & \verb|\pmcdm{R}|, \verb|\pmCdm| & The converse domain of a relation $R$. \\
-	$\pmcmp{R}$, $\pmCmp$ & \verb|\pmcmp{R}|, \verb|\pmCmp| & The campus of a relation $R$.  \\
-	$\pmfld{R}$, $\pmFld$ & \verb|\pmfld{R}|, \verb|\pmFld| & The field of a relation $R$. \\
-	$\pmrrf{R}{x}$, $\pmRrf{R}$ & \verb|\pmrrf{R}{x}|, \verb|\pmRrf{R}| & The referents of a given relation. \\
-	$\pmrrl{R}{x}$, $\pmRrl{R}$ & \verb|\pmrrl{R}{x}|, \verb|\pmRrl{R}| & The relata of a given relation. \\
-	$\pmsg{R}$, $\pmSg$ & \verb|\pmsg{R}|, \verb|\pmSg| &  \\
-	$\pmgs{R}$, $\pmGs$ & \verb|\pmgs{R}|, \verb|\pmGs| &  \\
-	$\pmrprd{R}{S}$, $\pmRprd$ & \verb|\pmrprd{R}{S}|, \verb|\pmrprd| &  The relative product of $R$ and $S$. \\
-	$\pmrprdn{R}{n}$ & \verb|\pmrprdn{R}{n}| & The $n$th relative product of $R$. \\
-	$\pmrprdd{R}{S}$, $\pmRprdd$ & \verb|\pmrprdd{R}{S}|, \verb|\pmrprdd| &  The double relative product of $R$ and $S$. \\
-	$\pmrlcd{\alpha}{R}$ & \verb|\pmrld{\alpha}{R}| & The limitation of $R$'s domain to $\alpha$. \\
-	$\pmrlcd{R}{\beta}$ & \verb|\pmrld{R}{\beta}| & The limitation of $R$'s converse domain to $\beta$. \\
-	$\pmrlf{\alpha}{R}{\beta}$ & \verb|\pmrlf{\alpha}{R}{\beta}| & The limitation of $R$'s field to $\alpha$ and $\beta$, resp. \\ 
-	$\pmrlF{P}{\alpha}$ & \verb|\pmrlF{\alpha}{R}{\beta}| & The limitation of $P$'s field to $\alpha$. \\ 
-	$\pmrl{\alpha}{\beta}$ & \verb|\pmrl{\alpha}{\beta}| & The relation made of all $x$s in $\alpha$ and $y$s in $\beta$. \\
-	$\pmop$ & \verb|\pmop| & The operation symbol. \\
-	$\pmopc{\alpha}{y}$ & \verb|\pmopc{\alpha}{y}| & The relation of $x$s in $\alpha$ taken to $y$ by $\pmop$. \\
-	$\pmccsum{\alpha}$ & \verb|\pmccsum{\alpha}| & The sum of a class of classes. \\
-	$\pmccprd{\alpha}$ & \verb|\pmccprd{\alpha}| & The product of a class of classes. \\
-	$\pmcrsum{\alpha}$ & \verb|\pmcrsum{\alpha}| & The sum of a class of relations. \\
-	$\pmcrprd{\alpha}$ & \verb|\pmcrprd{\alpha}| & The product of a class of relations. \\
-	$\pmrid$, $\pmrdiv$ & \verb|\pmrid|, \verb|\pmrdiv| & The relations of identity and diversity. \\
-	$\pmcunit{x}$, $\pmcUnit$ & \verb|\pmcunit{x}|, \verb|\pmcUnit| & The unit class. \\
-	$\pmcunits{\alpha}$ & \verb|\pmcunits{\alpha}| & The sum of unit classes of $\alpha$'s elements. \\
-	$\pmrn{n}$ & \verb|\pmrn{n}| & The ordinal number $n$. \\
-	$\pmdn{n}$ & \verb|\pmdn{n}| & The class of relations equal to an $n$-tuple. \\
-	$\pmoc{x}{y}$ & \verb|\pmoc{x}{y}| & The ordinal number restricted to $R=(x,y)$. \\
-	$\pmrt{x}$, $\pmrti{n}{x}$ & \verb|\pmrt{x}|, \verb|\pmrti{n}{x}| & The relative type of $x$ ($n$-many `type of's). \\
-	$\pmrtc{n}{\alpha}$ & \verb|\pmrtc{n}{\alpha}| & The relative type of $\alpha$ ($n$-many `type of's). \\
-	$\pmrtri{n}{R}$, $\pmrtrc{n}{R}$ & \verb|\pmrtri{n}{R}|,  \verb|\pmrtrc{n}{R}| & The relative type of (with $n$-many `type of's) $R$ from individuals to individuals, or from classes to classes. `$nm$' can replace `$n$'. 
-\end{tabular}
-
-\noindent \begin{tabular}{@{}p{3cm} | p{5cm} | p{8.25cm}}
-	$\pmrtric{n}{m}{R}$, $\pmrtrci{n}{m}{R}$ & \verb|\pmrtric{n}{R}|,  \verb|\pmrtrci{n}{R}| & The relative type of $R$ from individuals to classes, or from classes to individuals. \\
-	$\pmrtdi{\alpha}{x}$, $\pmrtdri{R}{(x,y)}$ & \verb|\pmrtdi{\alpha}{x}|, \verb|\pmrtdri{R}{(x,y)}| & The result of determining that the members of $\alpha$ ($R$) belong to the relative type of $x$ (in the domain, and of $y$ in the converse domain). \\
-	$\pmrtdc{\alpha}{x}$, $\pmrtdrc{R}{x,y}$ & \verb|\pmrtdc{\alpha}{x}|, \verb|\pmrtdrc{R}{x,y}| & The result of determining that the members of $\alpha$ ($R$) belong to the relative type of $\pmrt{x}$ (in the domain, and of $\pmrt{y}$ in the converse domain). \\
-	$\pmrdc{\alpha}{\beta}$ & \verb|\pmrdc{\alpha}{\beta}| & The class of relations $R$ with domain contained in $\alpha$ and converse domain in $\beta$.  \\
-	$\pmoneone$, $\pmonemany$, $\pmmanyone$ &  \verb|\pmoneone|, \verb|\pmonemany|, \verb|\pmmanyone| & The class of one-one, or one-many, or many-one, relations. Note \verb|\pmrdc| can be used here. \\
-	$\pmsm$, $\pmsmbar$ & \verb|\pmsm|, \verb|\pmsmbar| & The similarity relation. \\
-	$\pmselp{\kappa}$, $\pmSelp$ & \verb|\pmselp{\kappa}|, \verb|\pmSelp| &  The $P$-selections from $\kappa$ \\
-	$\pmsele{\kappa}$, $\pmSele$ & \verb|\pmsele{\kappa}|, \verb|\pmSele| &  The $\pmcin$-selections from $\kappa$ \\
-	$\pmself{\kappa}$, $\pmSelf$ & \verb|\pmself{\kappa}|, \verb|\pmSelf| &  The $F$-selections from $\kappa$ \\
-	$\pmexc$ & \verb|\pmexc| & The class of pairwise-disjoint classes. \\
-	$\pmexcn$ & \verb|\pmexcn| & The class of pairwise-disjoint non-null classes. \\
-	$\pmexcc{\gamma}$ & \verb|\pmexcc{\gamma}| & A class of mutually exclusive classes in $\gamma$. \\
-	$\pmselc{P}{y}$ & \verb|\pmselc{P}{y}| & The class of couples $(y, \pmdscf{P}{y})$. \\
-	$\pmmultc$ & \verb|\pmmultc| & The class of multipliable classes. \\
-	$\pmmultr$ & \verb|\pmmultr| & The class of multipliable relations. \\
-	$\pmmultax$ & \verb|\pmmultax| & The multiplicative axiom. \\
-	$\pmanc{R}$, $\pmancc{R}$ & \verb|\pmanc{R}|, \verb|\pmancc{R}| & The ancestral and its converse. \\
-	$\pmrst{R}$, $\pmrts{R}$ & \verb|\pmrst{R}|, \verb|\pmrts{R}| & The powers of the ancestral and its converse. \\
-	$\pmmin{P}$, $\pmmax{P}$ & \verb|\pmmin{P}|, \verb|\pmmax{P}| & The minimum and maximum under $P$. \\
-	$\pmpot{R}$, $\pmpotid{R}$ & \verb|\pmpot{R}|, \verb|\pmpotid{R}| & The products (strict and not) of an ancestral. \\
-	 $\pmpo{R}$ & \verb|\pmpo{R}| & The product of a class of ancestrals $R$. \\
-	 $\pmB$ & \verb|\pmB| & The relation of beginning under $P$. \\
-	$\pmgen{P}$ & \verb|\pmgen{P}| & The generation of $P$. \\
-	$\pmefr{P}{Q}$ & \verb|\pmefr{P}{Q}| & The equi-factor relation. \\
-	$\pmipr{R}{x}$ & \verb|\pmipr{R}{x}| &  The non-distinct posterity of $x$ under $R$. \\
-	$\pmjpr{R}{x}$ & \verb|\pmjpr{R}{x}| &  The distinct posterity of $x$ under $R$. \\
-	$\pmfr{R}{x}$ & \verb|\pmfr{R}{x}| & The ancestry and posterity of $x$ under $R$. \\
-	$\pmnc{\kappa}$, $\pmNc$ & \verb|\pmnc{\kappa}|, \verb|\pmNc| & The cardinal number of $\kappa$.
+	$\pmexists$ & \verb|\pmexists| & Existence. 
 \end{tabular}
 
 \end{document}
\ No newline at end of file
diff --git a/Master/texmf-dist/tex/latex/principia/principia.sty b/Master/texmf-dist/tex/latex/principia/principia.sty
index 14a99d9fa3b..421a0b65ab7 100644
--- a/Master/texmf-dist/tex/latex/principia/principia.sty
+++ b/Master/texmf-dist/tex/latex/principia/principia.sty
@@ -1,18 +1,24 @@
 %Package Identification
 \NeedsTeXFormat{LaTeX2e}
-\ProvidesPackage{principia}[2020/10/25 principia package version 1.1] %This is the principia package is for representing notations in Whitehead and Russell's ``Principia Mathematica" close to their appearance in the original.
+\ProvidesPackage{principia}[2021/04/19 principia package version 1.3] %This is the principia package is for representing notations in Whitehead and Russell's ``Principia Mathematica" close to their appearance in the original.
 %Version 1.0 (superseded by Version 1.1): Covers typesetting of notation through Volume I. 2020/10/24
-%Version 1.1 (updates): fixed the spacing of scope dots around parentheses; fixed spacing of theorem sign; fixed spacing around primitive proposition and definition signs. 2020/10/25
+%Version 1.1 (superseded by Version 1.2) minor updates: fixed the spacing of scope dots around parentheses; fixed spacing of theorem sign; fixed spacing around primitive proposition and definition signs. 2020/10/25
 %Licensed under LaTeX Project Public License 1.3c. 
-%Copyright Landon D. C. Elkind, 2020.  (https://landondcelkind.com/contact/).
+%Version 1.2 (superseded by Version 1.3) (minor updates): boldfaced (`thickened') the truth-functional connectives, existential quantifier, set and relation symbols; added numerous commands for typesetting brackets and substitutions into theorems. 2021/02/25
+%Version 1.3 (minor update): removes package dependency on marvosym; updates Section A notation; removes other notations (corrected extension pending). 2021/04/19
+%Licensed under LaTeX Project Public License 1.3c. 
+%Copyright Landon D. C. Elkind, 2021  (https://landondcelkind.com/contact/).
 
 %Principia package requirements
 \RequirePackage{amssymb} %This loads the relation domain and converse domain limitation symbols.
 \RequirePackage{amsmath} %This loads the circumflex, substitution into theorems, \text{}, \mathbf{}, \boldsymbol{}, \overleftarrow{}, \overrightarrow{}, etc.
 \RequirePackage{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.
-\RequirePackage{marvosym} %This loads the male and female symbol.
 \RequirePackage{pifont} %This loads the symbols such as the eight-pointed asterisk.
+%The \Female and \Male symbols are imported directly from Marvosym.
 
+%Volume I
+%Mathematical logic
+%The theory of deduction
 %Meta-logical symbols
 \newcommand{\pmfd}{\begin{center} \rule{5cm}{.5pt} \end{center}} %Dividing line between introductory remarks in a starred number and the formal deductions.
 \newcommand{\pmdem}{\textit{Dem}.} %This notation begins a proof.
@@ -54,22 +60,26 @@
 
 %Logical connectives
 \newcommand{\pmnot}{\mathord{\ooalign{$\boldsymbol{\sim}\mkern.5mu$\hidewidth\cr$\boldsymbol{\sim}$\cr\hidewidth$\mkern.5mu\boldsymbol{\sim}$}}}
-\newcommand{\pmimp}{\mathbin{\ooalign{$\boldsymbol{\supset}\mkern.5mu$\hidewidth\cr$\boldsymbol{\supset}$\cr\hidewidth$\mkern.5mu\boldsymbol{\supset}$}}}
-\newcommand{\pmiff}{\mathbin{\ooalign{$\boldsymbol{\equiv}\mkern.5mu$\hidewidth\cr$\boldsymbol{\equiv}$\cr\hidewidth$\mkern.5mu\boldsymbol{\equiv}$}}}
 \newcommand{\pmor}{\mathbin{\ooalign{$\boldsymbol{\vee}\mkern.5mu$\hidewidth\cr$\boldsymbol{\vee}$\cr\hidewidth$\mkern.5mu\boldsymbol{\vee}$}}}
-\newcommand{\pmprod}{\mathbin{\ooalign{$\boldsymbol{\wedge}\mkern.5mu$\hidewidth\cr$\boldsymbol{\wedge}$\cr\hidewidth$\mkern.5mu\boldsymbol{\wedge}$}}}
-\newcommand{\pmall}[1]{(#1)}
-\newcommand{\pmsome}[1]{(\text{\raisebox{.5em}{\rotatebox{180}{\textbf{E}}}}#1)}
-\newcommand{\pmSome}{\text{\raisebox{.5em}{\rotatebox{180}{\textbf{E}}}}}
-\newcommand{\pmand}{\mathrel{\hbox{\rule{.3ex}{.3ex}}}}
+\newcommand{\pmimp}{\mathbin{\ooalign{$\boldsymbol{\supset}\mkern.5mu$\hidewidth\cr$\boldsymbol{\supset}$\cr\hidewidth$\mkern.5mu\boldsymbol{\supset}$}}} %1.01
+\newcommand{\pmand}{\mathrel{\hbox{\rule{.3ex}{.3ex}}}} %3.01
 \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}
+\newcommand{\pmprod}{\mathbin{\ooalign{$\boldsymbol{\wedge}\mkern.5mu$\hidewidth\cr$\boldsymbol{\wedge}$\cr\hidewidth$\mkern.5mu\boldsymbol{\wedge}$}}} %Not in Principia, but added here as a dual of its symbol for disjunction.
+\newcommand{\pmiff}{\mathbin{\ooalign{$\boldsymbol{\equiv}\mkern.5mu$\hidewidth\cr$\boldsymbol{\equiv}$\cr\hidewidth$\mkern.5mu\boldsymbol{\equiv}$}}} %4.01
+
+%The theory of apparent variables
+\newcommand{\pmall}[1]{(#1)}
+\newcommand{\pmsome}[1]{(\text{\raisebox{.5em}{\rotatebox{180}{\textbf{E}}}}#1)} %10.01
+\newcommand{\pmSome}{\text{\raisebox{.5em}{\rotatebox{180}{\textbf{E}}}}}
 
 %Additional defined logic signs
 \newcommand{\pmhat}[1]{\mathbf{\hat{\text{$#1$}}}}
+\newcommand{\pmbreve}[1]{\mathbf{\breve{\text{$#1$}}}}
+\newcommand{\pmcirc}[1]{\mathbf{\dot{\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
@@ -77,179 +87,8 @@
 \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{\pmnid}{\mathrel{\ooalign{$=$\cr\hidewidth\footnotesize\rotatebox[origin=c]{210}{\textbf{/}}\hidewidth\cr}}} %*13.02
 \newcommand{\pmiota}{\ooalign{\rotatebox[origin=c]{180}{$\mathbf{\iota}$}\cr\hidewidth\raisebox{.0125em}{\rotatebox[origin=c]{180}{$\mathbf{\iota}$}}\cr\hidewidth\raisebox{.025em}{\rotatebox[origin=c]{180}{$\mathbf{\iota}$}}\cr\hidewidth\raisebox{.0375em}{\rotatebox[origin=c]{180}{$\mathbf{\iota}$}}\cr\hidewidth\raisebox{.05em}{\rotatebox[origin=c]{180}{$\mathbf{\iota}$}}}} %the rotated Greek iota used in definite descriptions
 \newcommand{\pmdsc}[1]{(\pmiota#1)} %*14.01
-\newcommand{\pmDsc}{\pmiota} %*14.01
-\newcommand{\pmexists}{\textbf{E}\hspace{.1em}\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}{\textbf{E}}}}\hspace{-.1em}\mathop{\pmshr}}
-\newcommand{\pmccmp}[1]{\boldsymbol{-}#1}
-\newcommand{\pmcmin}[2]{#1\boldsymbol{-}#2}
-\newcommand{\pmcin}{\mathop{\boldsymbol{\epsilon}}}
-\newcommand{\pmccup}{\mathop{\ooalign{\scalebox{1.3}[1.75]{$\put(3, 2.5){\oval(4,4)[b]}\phantom{\circ}$}\cr\hidewidth\hspace{.1em}\scalebox{1.3}[1.75]{$\put(3, 2.5){\oval(4,4)[b]}\phantom{\circ}$}\cr\hidewidth\hspace{.2em}\scalebox{1.3}[1.75]{$\put(3, 2.5){\oval(4,4)[b]}\phantom{\circ}$}\cr\hidewidth\hspace{.3em}\scalebox{1.3}[1.75]{$\put(3, 2.5){\oval(4,4)[b]}\phantom{\circ}$}\cr\hidewidth\hspace{.4em}\scalebox{1.3}[1.75]{$\put(3, 2.5){\oval(4,4)[b]}\phantom{\circ}$}\cr\hidewidth\hspace{.5em}\scalebox{1.3}[1.75]{$\put(3, 2.5){\oval(4,4)[b]}\phantom{\circ}$}\cr\hidewidth\hspace{.6em}\scalebox{1.3}[1.75]{$\put(3, 2.5){\oval(4,4)[b]}\phantom{\circ}$}}}}
-\newcommand{\pmccap}{\mathop{\ooalign{\scalebox{1.3}[1.75]{$\put(3, 2){\oval(4,1)[t]}\phantom{\circ}$}\cr\hidewidth\hspace{.1em}\scalebox{1.3}[1.75]{$\put(3, 2){\oval(4,1)[t]}\phantom{\circ}$}\cr\hidewidth\hspace{.2em}\scalebox{1.3}[1.75]{$\put(3, 2){\oval(4,1)[t]}\phantom{\circ}$}\cr\hidewidth\hspace{.3em}\scalebox{1.3}[1.75]{$\put(3, 2){\oval(4,1)[t]}\phantom{\circ}$}\cr\hidewidth\hspace{.4em}\scalebox{1.3}[1.75]{$\put(3, 2){\oval(4,1)[t]}\phantom{\circ}$}\cr\hidewidth\hspace{.5em}\scalebox{1.3}[1.75]{$\put(3, 2){\oval(4,1)[t]}\phantom{\circ}$}\cr\hidewidth\hspace{.6em}\scalebox{1.3}[1.75]{$\put(3, 2){\oval(4,1)[t]}\phantom{\circ}$}}}}
-\newcommand{\pmcinc}{\mathop{\ooalign{$\boldsymbol{\subset}$\cr\hidewidth$\hspace{.1em}\boldsymbol{\subset}$\cr\hidewidth$\hspace{.15em}\boldsymbol{\subset}$\cr\hidewidth$\hspace{.2em}\boldsymbol{\subset}$}}}
-
-%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{\boldsymbol{\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{\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{\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}}
-\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
+\newcommand{\pmDsc}{\pmiota} 
+\newcommand{\pmexists}{\textbf{E}\hspace{.1em}\pmshr} %*14.02
\ No newline at end of file