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-%This is the principia package is for representing notations in Whitehead and Russell's ``Principia Mathematica" close to their appearance in the original.

-%Copyright (C) 2020 by Landon D. C. Elkind (https://landondcelkind.com/contact/).

-%This program is free software. It may be redistributed and/or modified under the terms of the GNU General Public License as published by the Free Software Foundation, Version 3 or any later version.

-

-%Package Identification

-\NeedsTeXFormat{LaTeX2e}

-\ProvidesPackage{principia}[2020/10/20 principia package version 1.0] %Covers typesetting of notation through Volume I

-

-%Principia package requirements

-\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 The (superseded) graphics package should also work here, but is not recommended.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.

-

-%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}}
\ No newline at end of file