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rec-thy.sty
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% \NeedsTeXFormat{LaTeX2e}
% Release Notes see README
%CHECK DEF OF COMPAT
% POSSIBLE ALT: \mathrel{\rlap{\ensuremath{\not}}\ensuremath{\mid}}
\RequirePackage{expl3}
\RequirePackage{ltxcmds}
\RequirePackage{iftex,ifpdf}
\RequirePackage{suffix}
\RequirePackage{ifmtarg}
\RequirePackage{xifthen}
\RequirePackage{xkeyval}
\RequirePackage{etoolbox}
\RequirePackage{pict2e,picture}
\RequirePackage{xparse}
\def\recthyVersion{4.0}
\ProvidesExplPackage
{rec-thy}
{2024/03/28}
{\recthyVersion}
{Provides commands for writing up recursion theory papers}
\ExplSyntaxOff
% \ProvidesExplPackage{rec-thy}{2020/06/04}{3.5}{Provides commands for writing up recursion theory papers} % Description
% \ProvidesPackage{rec-thy}[2021/02/05 v\recthyVersion Provides commands for writing up recursion theory papers]
\makeatletter
% \newcommand*{\@curpack}{\@currname} %rec-thy.sty
\newcommand*{\@packinfo}[1]{\PackageInfo{rec-thy}{#1}}
\newcommand*{\recthy@strip}[1]{%
\ifcsname #1\endcsname%
\else%
\expandafter\edef\csname #1\endcsname{\expandafter\noexpand\csname @recthy@#1\endcsname}
\fi
}
%leaves us a command \arg defined to do \@recthy@arg
% \ProvidesPackage{\@curpack} %file name is package name
\robustify\(
\robustify\)
%\RequirePackage{mathbbol}}
\ltx@ifpackageloaded{amsmath}{}{\RequirePackage{amsmath}}
% \ltx@ifpackageloaded{amssymb}{}{\RequirePackage{amssymb}}
% \ltx@ifpackageloaded{amsfonts}{}{\RequirePackage{amsfonts}}
\AtBeginDocument{
% \@ifundefined{hyperref}{\providecommand{\texorpdfstring}[2]{def} }
\ltx@ifpackageloaded{mathtools}{}{\RequirePackage{mathtools}}
\ltx@ifpackageloaded{unicode-math}{
\def\@recthy@tpathSYM{\mathbb{f}}
\Umathchardef\@recthy@xnot="3 \symoperators "0338
}{
\ltx@ifpackageloaded{bbm}{\def\@recthy@tpathSYM{\mathbbm{f}}}{\mathbf{f}}
}
% Undertilde doesn't exist in texlive so we remove the dependency and define it again.
\ltx@ifpackageloaded{undertilde}{}{
\newlength\knuthian@fdfive
\def\mathpal@save#1{\let\was@math@style=#1\relax}
\def\utilde#1{\mathpalette\mathpal@save
{\setbox124=\hbox{$\was@math@style#1$}%
\setbox125=\hbox{$\fam=3\global\knuthian@fdfive=\fontdimen5\font$}
\setbox125=\hbox{$\widetilde{\vrule height 0pt depth 0pt width \wd124}$}%
\baselineskip=1pt\relax
\vtop{\copy124\copy125\vskip -\knuthian@fdfive}}}
}
}
% \ifxetex %workaround for bug...hopefully can dispense on later
\ifpdftex
\def\symbf#1{\mathbf{#1}}
\mathchardef\@recthy@mhyphen="2D % Define a "math hyphen"
\else
\def\@recthy@mhyphen{\mathhyphen}
\fi
\def\PMG@arginit{\let\@PMG@parenarg\@PMG@undefined\let\@PMG@braketarg\@PMG@undefined}
\def\@recthy@family{\@currname.\@currext} %The default family for this package...filename.ext
%Define boolean options true if option passed false otherwise
\newif\ifrecthy@nomath \recthy@nomathfalse
\newif\ifrecthy@nosymb \recthy@nosymbfalse
\newif\ifrecthy@nosets \recthy@nosetsfalse
\newif\ifrecthy@noquants \recthy@noquantsfalse
\newif\ifrecthy@nospaces \recthy@nospacesfalse
\newif\ifrecthy@nostrings \recthy@nostringsfalse
\newif\ifrecthy@notrees \recthy@notreesfalse
\newif\ifrecthy@nopair \recthy@nopairfalse
\newif\ifrecthy@nosetrels \recthy@nosetrelsfalse
\newif\ifrecthy@noordinalnotations \recthy@noordinalnotationsfalse
\newif\ifrecthy@nosyntax \recthy@nosyntaxfalse
\newif\ifrecthy@shortsyntax \recthy@shortsyntaxtrue
\newif\ifrecthy@nodegclasses \recthy@nodegclassesfalse
\newif\ifrecthy@noforcing \recthy@noforcingfalse
\newif\ifrecthy@nodegrees \recthy@nodegreesfalse
\newif\ifrecthy@nocomputations \recthy@nocomputationsfalse
\newif\ifrecthy@nostructresets \recthy@nostructresetsfalse
\newif\ifrecthy@noreqhelper \recthy@noreqhelperfalse
\newif\ifrecthy@nosubfun \recthy@nosubfunfalse
\newif\ifrecthy@nopfcases \@ifclassloaded{beamer}{\recthy@nopfcasestrue}{\recthy@nopfcasesfalse}
\newif\ifrecthy@beamersupp \@ifclassloaded{beamer}{\recthy@beamersupptrue}{\recthy@beamersuppfalse}
\newif\ifrecthy@noprioritytrees \recthy@noprioritytreesfalse
% \newif\ifrecthy@nosuppprioritytrees \recthy@nosuppprioritytreestrue
\newif\ifrecthy@hyperreqs \recthy@hyperreqstrue
\newif\ifrecthy@nooperators \recthy@nooperatorsfalse
\newif\ifrecthy@fix@typeset \recthy@fix@typesettrue
\newif\ifrecthy@nodoubleangles \recthy@nodoubleanglesfalse
\newif\ifrecthy@stepsenv \recthy@stepsenvfalse
\newif\ifrecthy@shortO \recthy@shortOtrue
\newif\ifrecthy@midincompat \recthy@midincompattrue
\newif\ifrecthy@norsfs \recthy@norsfsfalse
\newif\ifrecthy@nobbm \recthy@nobbmfalse
\DeclareOptionX{nomath}{\recthy@nomathtrue}
\DeclareOptionX{nosymb}{\recthy@nosymbtrue}
\DeclareOptionX{nosets}{\recthy@nosetstrue}
\DeclareOptionX{noquants}{\recthy@noquantstrue}
\DeclareOptionX{nospaces}{\recthy@nospacestrue}
\DeclareOptionX{nostrings}{\recthy@nostringstrue}
\DeclareOptionX{notrees}{\recthy@notreestrue}
\DeclareOptionX{nopair}{\recthy@nopairtrue}
\DeclareOptionX{nosetrels}{\recthy@nosetrelstrue}
\DeclareOptionX{noordinalnotations}{\recthy@noordinalnotationstrue}
\DeclareOptionX{nosyntax}{\recthy@nosyntaxtrue}
\DeclareOptionX{noshortsyntax}{\recthy@shortsyntaxfalse}
\DeclareOptionX{noforcing}{\recthy@noforcingtrue}
\DeclareOptionX{nodegrees}{\recthy@nodegreestrue}
\DeclareOptionX{nocomputations}{\recthy@nocomputationstrue}
\DeclareOptionX{nostructresets}{\recthy@nostructresetstrue}
\DeclareOptionX{noreqhelper}{\recthy@noreqhelpertrue}
\DeclareOptionX{nosubfun}{\recthy@nosubfuntrue}
\DeclareOptionX{nopfcases}{\recthy@nopfcasestrue}
\DeclareOptionX{noprioritytrees}{\recthy@noprioritytreestrue}
\DeclareOptionX{nohyperreqs}{\recthy@hyperreqsfalse}
\DeclareOptionX{nooperators}{\recthy@nooperatorstrue}
\DeclareOptionX{nofixtype}{\recthy@fix@typesetfalse}
\DeclareOptionX{nodoubleangles}{\recthy@nodoubleanglestrue}
\DeclareOptionX{steps}{\recthy@stepsenvtrue}
\DeclareOptionX{noshortO}{\recthy@shortOfalse}
\DeclareOptionX{altcompat}{\recthy@midincompattrue}
\DeclareOptionX{norsfs}{\recthy@norsfstrue}
\DeclareOptionX{nobbm}{\recthy@nobbmtrue}
% \DeclareOptionX{degjoin}{\def\Tjoin{\Tdegjoin}}
\let\@recthy@modulescr\mathcal
\DeclareOptionX{modulescr}[mathcal]{\letcs{\@recthy@modulescr}{#1}}
\let\pmg@casefont\textsc
\DeclareOptionX{pfcasefont}[textsc]{\letcs{\pmg@casefont}{#1}}
\def\@recthy@reqscr{\mathscr}
\DeclareOptionX{reqscr}{\letcs{\@recthy@reqscr}{#1}}
\def\@recthy@recfSYM@default{\phi}
\let\@recthy@recfSYM=\@recthy@recfSYM@default
\def\@recthy@recfnlSYM@default{\Phi}
\let\@recthy@recfnlSYM=\@recthy@recfnlSYM@default
\def\@recthy@useSYM@default{\ltx@ifpackageloaded{unicode-math}{\symbffrak{u}}{\mathfrak{u}}}
\let\@recthy@useSYM=\@recthy@useSYM@default
\DeclareOptionX{recfnlsym}[@recthy@recfnlSYM@default]{\letcs{\@recthy@recfnlSYM}{#1}}
\DeclareOptionX{recfsym}[@recthy@recfSYM@default]{\letcs{\@recthy@recfSYM}{#1}}
\DeclareOptionX{usesym}[@recthy@useSYM@default]{\letcs{\@recthy@useSYM}{#1}}
\newcommand*{\@recthy@llangle}{\langle\!\langle}
\newcommand*{\@recthy@rrangle}{\rangle\!\rangle}
\let\@recthy@llangle@orig=\llangle
\let\@recthy@rrangle@orig=\rrangle
\let\@recthy@EmptyStr=\@recthy@EmptyStr@Default
\let\@recthy@concatSYM=\@recthy@concatSYM@Default
\def\@recthy@langle{\langle}
\def\@recthy@rangle{\rangle}
\let\@recthy@lstrdelim=\@recthy@langle
\let\@recthy@rstrdelim=\@recthy@rangle
\let\@recthy@lcodedelim=\@recthy@llangle
\let\@recthy@rcodedelim=\@recthy@rrangle
\let\@recthy@lpairdelim=\@recthy@langle
\let\@recthy@rpairdelim=\@recthy@rangle
\def\@recthy@concatSYM@Default{\widehat{\phantom{x}}}
\def\@recthy@EmptyStr@Default{\mathopen{\langle}\mathclose{\rangle}}
\let\@recthy@concatSYM\@recthy@concatSYM@Default
\let\@recthy@EmptyStr\@recthy@EmptyStr@Default
\DeclareOptionX{emptystr}[@recthy@EmptyStr@Default]{\letcs{\@recthy@EmptyStr}{#1}}
\DeclareOptionX{concatsym}[@recthy@concatSYM@Default]{\letcs{\@recthy@concatSYM}{#1}}
\DeclareOptionX{lstrdelim}[@recthy@langle]{\letcs{\@recthy@lstrdelim}{#1}}
\DeclareOptionX{rstrdelim}[@recthy@rangle]{\letcs{\@recthy@rstrdelim}{#1}}
\DeclareOptionX{lcodedelim}[@recthy@langle]{\letcs{\@recthy@lcodedelim}{#1}}
\DeclareOptionX{rcodedelim}[@recthy@rangle]{\letcs{\@recthy@rcodedelim}{#1}}
\DeclareOptionX{lpairdelim}[@recthy@llangle]{\letcs{\@recthy@lpairdelim}{#1}}
\DeclareOptionX{rpairdelim}[@recthy@rrangle]{\letcs{\@recthy@rpairdelim}{#1}}
% \AtBeginDocument{\@ifundefined{hyperref}{\newcommand*{\texorpdfstring}[2]{#1}}{}}
% \ProcessOptions*
% \ProcessOptionsX<\@recthy@family>
\ProcessOptionsX
\ifrecthy@norsfs
\else
\ltx@ifpackageloaded{unicode-math}{}{\RequirePackage{mathrsfs}}
\fi
\ifrecthy@nobbm
\else
\ltx@ifpackageloaded{unicode-math}{}{\RequirePackage{bbm}}
\fi
%misc tools
\def\@recthy@ignorespacesandallparsafterend{\ifhmode\unskip\fi
\aftergroup\@recthy@useignorespacesandallpars}
\def\@recthy@useignorespacesandallpars#1\ignorespaces\fi{%
#1\fi\@recthy@ignorespacesandallpars}
\def\@recthy@ignorespacesandallpars{%
\@ifnextchar\par
{\expandafter\@recthy@ignorespacesandallpars\@gobble}%
{}%
}
\ifrecthy@fix@typeset
%Defining \overbar
\let\save@mathaccent\mathaccent
\newcommand*\if@single[3]{%
\setbox0\hbox{${\mathaccent"0362{#1}}^H$}%
\setbox2\hbox{${\mathaccent"0362{\kern0pt#1}}^H$}%
\ifdim\ht0=\ht2 #3\else #2\fi
}
%The bar will be moved to the right by a half of \macc@kerna, which is computed by amsmath:
\newcommand*\rel@kern[1]{\kern#1\dimexpr\macc@kerna}
%If there's a superscript following the bar, then no negative kern may follow the bar;
%an additional {} makes sure that the superscript is high enough in this case:
\providecommand*\overbar{\relax}
\renewcommand*\overbar[1]{\@ifnextchar^{{\over@bar{#1}{0}}}{\over@bar{#1}{1}}}
%Use a separate algorithm for single symbols:
\newcommand*\over@bar[2]{\if@single{#1}{\over@bar@{#1}{#2}{1}}{\over@bar@{#1}{#2}{2}}}
\newcommand*\over@bar@[3]{%
\begingroup
\def\mathaccent##1##2{%
%Enable nesting of accents:
\let\mathaccent\save@mathaccent
%If there's more than a single symbol, use the first character instead (see below):
\if#32 \let\macc@nucleus\first@char \fi
%Determine the italic correction:
\setbox\z@\hbox{$\macc@style{\macc@nucleus}_{}$}%
\setbox\tw@\hbox{$\macc@style{\macc@nucleus}{}_{}$}%
\dimen@\wd\tw@
\advance\dimen@-\wd\z@
%Now \dimen@ is the italic correction of the symbol.
\divide\dimen@ 3
\@tempdima\wd\tw@
\advance\@tempdima-\scriptspace
%Now \@tempdima is the width of the symbol.
\divide\@tempdima 10
\advance\dimen@-\@tempdima
%Now \dimen@ = (italic correction / 3) - (Breite / 10)
\ifdim\dimen@>\z@ \dimen@0pt\fi
%The bar will be shortened in the case \dimen@<0 !
\rel@kern{0.6}\kern-\dimen@
\if#31
\overline{\rel@kern{-0.6}\kern\dimen@\macc@nucleus\rel@kern{0.4}\kern\dimen@}%
\advance\[email protected]\dimexpr\macc@kerna
%Place the combined final kern (-\dimen@) if it is >0 or if a superscript follows:
\let\final@kern#2%
\ifdim\dimen@<\z@ \let\final@kern1\fi
\if\final@kern1 \kern-\dimen@\fi
\else
\overline{\rel@kern{-0.6}\kern\dimen@#1}%
\fi
}%
\macc@depth\@ne
\let\math@bgroup\@empty \let\math@egroup\macc@set@skewchar
\mathsurround\z@ \frozen@everymath{\mathgroup\macc@group\relax}%
\macc@set@skewchar\relax
\let\mathaccentV\macc@nested@a
%The following initialises \macc@kerna and calls \mathaccent:
\if#31
\macc@nested@a\relax111{#1}%
\else
%If the argument consists of more than one symbol, and if the first token is
%a letter, use that letter for the computations:
\def\gobble@till@marker##1\endmarker{}%
\futurelet\first@char\gobble@till@marker#1\endmarker
\ifcat\noexpand\first@char A\else
\def\first@char{}%
\fi
\macc@nested@a\relax111{\first@char}%
\fi
\endgroup
}
\else
\@packinfo{Not loading Fix Typesetting}
\fi
%Strings
\newcommand*{\@recthy@pair}[2]{\mathopen{\@recthy@lpairdelim} #1, #2 \mathclose{\@recthy@rpairdelim}}
\newcommand*{\@recthy@str}[1]{\mathopen{\@recthy@lstrdelim}#1\mathclose{\@recthy@rstrdelim}}
\newcommand*{\@recthy@code}[1]{\mathopen{\@recthy@lcodedelim}#1\mathclose{\@recthy@rcodedelim}}
\let\godelpair=\@recthy@pair
\ifrecthy@nopair
\@packinfo{No redefining pair.}
\else
\@packinfo{pair=godelpair.}
\let\pair=\@recthy@pair
\fi
\newcommand{\succprec@recthy}{\mathrel{\mathpalette\succ@prec@recthy{\succ\prec}}}
\newcommand{\precsucc@recthy}{\mathrel{\mathpalette\succ@prec@recthy{\prec\succ}}}
\newcommand{\nsuccprec@recthy}{\ltx@ifpackageloaded{unicode-math}{\succprec@recthy\!\@recthy@xnot}{\not\succprec@recthy}}
\newcommand{\nprecsucc@recthy}{\ltx@ifpackageloaded{unicode-math}{\precsucc@recthy\!\@recthy@xnot}{\not\precsucc@recthy}}
\newcommand{\succ@prec@recthy}[2]{\succ@@prec@recthy#1#2}
\newcommand{\succ@@prec@recthy}[3]{%
\vcenter{\m@th\offinterlineskip
\sbox\z@{$#1#3$}%
\hbox{$#1#2$}\kern-0.4\ht\z@\box\z@
}%
}
\def\defaultincompatsymb@recthy{\mathrel{\mid}}
\def\defaulcompatSymb@recthy{\mathrel{\,\not|\,}}
\let\ncompatsymb@recthy=\nsuccprec@recthy
\ifrecthy@midincompat
\@packinfo{Using mid as incompat symbol}
\let\compatsymb@recthy=\defaulcompatSymb@recthy
\let\incompatsymb@recthy=\defaultincompatsymb@recthy
\else
\@packinfo{Using precc over succ as compat symbol}
\let\compatsymb@recthy=\succprec@recthy
\let\incompatsymb@recthy=\nsuccprec@recthy
\fi
\NewDocumentCommand{\incompat@recthy}{o}{\incompatsymb@recthy\IfValueTF{#1}{_{#1}}{}}
\NewDocumentCommand{\compat@recthy}{o}{{\compatsymb@recthy\IfValueTF{#1}{_{#1}}{}}}
\ifrecthy@nostrings
\@packinfo{No strings loading.}
\else
\@packinfo{Strings loading.}
% \appto{\recthy@rollback@threeSix}{\newcommand*{\closedn}[1]{{#1}^\blacktriangledown}}
\let\code=\@recthy@code
\let\str=\@recthy@str
\newcommand*{\EmptyStr}{\@recthy@EmptyStr}
\newcommand*{\estr}{\@recthy@EmptyStr}
\newcommand*{\decode}[2]{\left(#1\right)_{#2}}
\newcommand*{\godelnum}[1]{\left\ulcorner #1 \right\urcorner}
\let\cornerquote=\godelnum
\newcommand*{\concat}{\@recthy@concatSYM}
\WithSuffix\def\concat[#1]{\concat\str{#1}}
\newcommand*{\strpred}[1]{{#1}^{-}}
\providecommand*{\lh}[2][]{\@recthy@abs{#2}_{#1}} %% Gives length of a string
\providecommand*{\incompat}{\incompat@recthy} %incompatible stringes FIX SPACING
% \providecommand*{\incomp}{\incompat@recthy}
\providecommand*{\compat}{\compat@recthy}
\let\succprec=\succprec@recthy
\let\nsuccprec=\nsuccprec@recthy
\let\precsucc=\precsucc@recthy
\let\nprecsucc=\nprecsucc@recthy
% \providecommand*{\nincompat}{\compat@recthy}
% \providecommand*{\nincomp}{\compat@recthy}
% \newcommand*{\setcol}[2]{{#1}^{[#2]}}
\ExplSyntaxOn %thx stackexghance
\NewDocumentCommand \setcol {m m}
{
\bool_lazy_and:nnTF
{ \int_compare_p:nNn { \tl_count:n {#1} } = 3 }
{ \tl_if_head_eq_meaning_p:nN {#1} \setcol }
{
\pgerdes_setcol_special:nnnn #1 {#2}
}
{
\pgerdes_setcol_normal:nn {#1} {#2}
}
}
\cs_new:Npn \pgerdes_setcol_special:nnnn #1 #2 #3 #4
{
{#2} \sp { [#3] [#4] }
}
\cs_new:Npn \pgerdes_setcol_normal:nn #1 #2
{
{#1} \sp { [#2] }
}
\ExplSyntaxOff
\fi
\ifrecthy@noprioritytrees
\@packinfo{Not loading Priority Tree Helper}
\else
\@packinfo{Loading Priority Tree Helper.}
\providecommand{\PriorityTree}{\mathbb{T}}
\providecommand{\tpath}[1][]{\ifthenelse{\isempty{#1}}{\@recthy@tpathSYM}{\@recthy@tpathSYM_{#1}}}
\providecommand{\leftof}{\mathbin{<_L}}
\providecommand{\leftofeq}{\mathbin{\leq_L}}
\providecommand{\rightof}{\mathbin{>_L}}
\providecommand{\rightofeq}{\mathbin{\geq_L}}
\providecommand{\nleftof}{\mathbin{\nless_L}}
\providecommand{\nleftofeq}{\mathbin{\nleq_L}}
\providecommand{\nrightof}{\mathbin{\ngtr_L}}
\providecommand{\nrightofeq}{\mathbin{\ngeq_L}}
\NewDocumentCommand{\PriorityTreeModule}{mO{}m}{\ensuremath{{\@recthy@modulescr{#1}}^{#2}_{#3} }}
\let\module=\PriorityTreeModule
\fi
\ifrecthy@nopfcases
\@packinfo{Not loading Proof Cases Helper}
\else
\@packinfo{Loading Proof Cases Helper.}
\RequirePackage{enumitem}
\ltx@ifpackageloaded{cleveref}{
\crefformat{pfcasesnonumi}{#2case~#1#3}
\Crefformat{pfcasesnonumi}{#2Case~#1#3}
\crefformat{pfcasesnonumii}{#2subcase~#1#3}
\Crefformat{pfcasesnonumii}{#2Subcase~#1#3}
\crefformat{pfcasesnonumiii}{#2subsubcase~#1#3}
\Crefformat{pfcasesnonumiii}{#2Subsubcase~#1#3}
\crefformat{pfcasesnumberedi}{#2case~#1#3}
\Crefformat{pfcasesnumberedi}{#2Case~#1#3}
\crefformat{pfcasesnumberedii}{#2case~#1#3}
\Crefformat{pfcasesnumberedii}{#2Case~#1#3}
\crefformat{pfcasesnumberediii}{#2case~#1#3}
\Crefformat{pfcasesnumberediii}{#2Case~#1#3}
}{}
\newlist{pfcasesnonum}{enumerate}{3}
\setlist[pfcasesnonum]{
label={\pmg@casefont{Case}},
align=left,
left=0pt .. 1.5em,
itemindent=*
}
\setlist[pfcasesnonum,1]{
before=\def\pfcasecounter@pmg{pfcasesnonumi},
}
\setlist[pfcasesnonum,2]{
before=\def\pfcasecounter@pmg{pfcasesnonumii},
}
\setlist[pfcasesnonum,3]{
before=\def\pfcasecounter@pmg{pfcasesnonumiii},
}
\newlist{pfcasesnumbered}{enumerate}{3}
\setlist[pfcasesnumbered]{
align=left,
left=0pt .. 1.5em,
itemindent=*
}
% \setlist[pfcasesnumbered]{
% align=left,
% labelsep=0pt,
% itemindent=!,
% leftmargin=2em,
% labelindent=0pt,
% labelwidth=0pt
% }
\setlist[pfcasesnumbered,1]{
before=\def\pfcasecounter@pmg{pfcasesnumberedi},
label={{\pmg@casefont{Case}}~\arabic*},
ref={\arabic*},
}
\setlist[pfcasesnumbered,2]{
before=\def\pfcasecounter@pmg{pfcasesnumberedii},
label={{\pmg@casefont{Case}}~\arabic{pfcasesnumberedi}\alph*},
ref={\arabic{pfcasesnumberedi}\alph*},
labelindent=-1em,
}
\setlist[pfcasesnumbered,3]{
before=\def\pfcasecounter@pmg{pfcasesnumberediii},
label={{\pmg@casefont{Case}}~\arabic{pfcasesnumberedi}\alph{pfcasesnumberedii}.\roman*},
ref={\arabic{pfcasesnumberedi}\alph{pfcasesnumberedii}.\roman*},
labelindent=-1em,
}
\def\@recthy@cases@labelindent{0pt}
\newenvironment{pfcases*}{
\def\@recthy@cases@labelindent{-1em}
\ProvideDocumentCommand{\case}{r[]}{
\def\thiscase{~##1}%
\item~##1\textbf{:} %
\ltx@ifpackageloaded{cleveref}{%
\cref@constructprefix{pfcases}{\cref@result}%
\protected@xdef\cref@currentlabel{[\pfcasecounter@pmg][][\cref@result]##1}}{} \protected@edef\@currentlabel{##1}\ignorespaces}
\begin{pfcasesnonum}\def\@recthy@cases@labelindent{1em}\ignorespaces}{\end{pfcasesnonum}\ignorespacesafterend}
\newenvironment{pfcases}{
\ProvideDocumentCommand{\case}{o}{
\IfNoValueTF{##1}{
\def\thiscase{}\item\!\!\textbf{:} \allowbreak%\linebreak[1]%
}{
\def\thiscase{~##1}\item~##1\textbf{:} \allowbreak%\linebreak[1]%
}
\ltx@ifpackageloaded{cleveref}{%
\cref@constructprefix{\pfcasecounter@pmg}{\cref@result}%
\protected@xdef\cref@currentlabel{[\pfcasecounter@pmg][][\cref@result]\csname the\pfcasecounter@pmg \endcsname}}{}\ignorespaces}
\begin{pfcasesnumbered}[labelindent=\@recthy@cases@labelindent]\def\@recthy@cases@labelindent{-1em}\ignorespaces}{\end{pfcasesnumbered}\ignorespacesafterend}
\fi
\ifrecthy@nosubfun
\@packinfo{Not loading subfun defs.}
\else
\@packinfo{Loading subfun defs.}
%DOCUMENT ME
\newcommand{\@pnrelbar}{%
\linethickness{\dimen2}%
\sbox\z@{$\m@th\prec$}%
\dimen@=1.1\ht\z@
\begin{picture}(\dimen@,.4ex)
\roundcap
\put(0,.2ex){\line(1,0){\dimen@}}
\put(\dimexpr 0.5\[email protected]\relax,0){\line(1,1){.4ex}}
\end{picture}%
}
\newcommand{\@snrelbar}{%
\linethickness{\dimen2}%
\sbox\z@{$\m@th\succ$}%
\dimen@=1.1\ht\z@
\begin{picture}(\dimen@,.4ex)
\roundcap
\put(0,.2ex){\line(1,0){\dimen@}}
\put(\dimexpr 0.5\[email protected]\relax,0){\line(1,1){.4ex}}
\end{picture}%
}
\newcommand{\@precneq}{\mathrel{\vcenter{\hbox{\text{\prec@neq}}}}}
\newcommand{\prec@neq}{%
\dimen2=\f@size\dimexpr.04pt\relax
\oalign{%
\noalign{\kern\dimexpr.2ex-.5\dimen2\relax}
$\m@th\prec$\cr
\noalign{\kern-.5\dimen2}
\hidewidth\@pnrelbar\hidewidth\cr
}%
}
\newcommand{\@succneq}{\mathrel{\vcenter{\hbox{\text{\succ@neq}}}}}
\newcommand{\succ@neq}{%
\dimen2=\f@size\dimexpr.04pt\relax
\oalign{%
\noalign{\kern\dimexpr.2ex-.5\dimen2\relax}
$\m@th\prec$\cr
\noalign{\kern-.5\dimen2}
\hidewidth\@snrelbar\hidewidth\cr
}%
}
\NewDocumentCommand{\subfun}{o}{\prec\IfNoValueTF{#1}{}{_{#1}}}
\NewDocumentCommand{\supfun}{o}{\succ\IfNoValueTF{#1}{}{_{#1}}}
\NewDocumentCommand{\nsubfun}{o}{\nprec\IfNoValueTF{#1}{}{_{#1}}}
\NewDocumentCommand{\nsupfun}{o}{\nsucc\IfNoValueTF{#1}{}{_{#1}}}
\NewDocumentCommand{\subfuneq}{o}{\preceq\IfNoValueTF{#1}{}{_{#1}}}
\NewDocumentCommand{\subfunneq}{o}{\@precneq\IfNoValueTF{#1}{}{_{#1}}}
\NewDocumentCommand{\supfuneq}{o}{\succeq\IfNoValueTF{#1}{}{_{#1}}}
\NewDocumentCommand{\supfunneq}{o}{\@succneq\IfNoValueTF{#1}{}{_{#1}}}
\NewDocumentCommand{\nsubfuneq}{o}{\npreceq\IfNoValueTF{#1}{}{_{#1}}}
\NewDocumentCommand{\nsupfuneq}{o}{\nsucceq\IfNoValueTF{#1}{}{_{#1}}}
\fi
\newcommand*{\@pmg@saveeqstate}{\let\@origif@fleqn@pmg=\if@fleqn \let\@origiftagsleft@pmg=\iftagsleft@}
\newcommand*{\@pmg@restoreeqstate}{ \let\if@fleqn=\@origif@fleqn@pmg\let\iftagsleft@=\@origiftagsleft@pmg}
\ifrecthy@noreqhelper
\@packinfo{Not loading requirement assist.}
\else
\@packinfo{Loading requirement assist.}
% \newcommand*{\req@beamer}[3][]{\ensuremath{\@recthy@reqscr{#2}^{#1}_{#3}}}
\newcommand*{\req@orig}[3]{\ensuremath{\@ifmtarg{#1}{\@recthy@reqscr{#2}_{#3}}{\@recthy@reqscr{#2}_{#3}^{#1}}}}
\NewDocumentCommand{\req@nohref}{sO{}mO{}m}{\req@orig{#2#4}{#3}{#5}}
\NewDocumentCommand{\req@href}{O{}mO{}m}{\hyperref[\detokenize{req:#2@#1#3}]{\req@orig{#1#3}{#2}{#4}}}
\NewDocumentCommand\req@href@star{s}{\IfBooleanTF#1{\req@nohref}{\req@href}}
\newcommand{\req}{\req@nohref}
\ifrecthy@hyperreqs
\AtBeginDocument{\@ifundefined{hyperref}{}{\let\req=\req@href@star}}
\fi
\newtagform{colon}{}{:}
\NewDocumentCommand{\refreq}{O{}mO{}}{\ref{\detokenize{req:#2@#1#3}}}
\NewDocumentCommand{\require@nested}{sO{}mO{}m}{%
\tag{\req@nohref[#2#4]{#3}{#5}}\IfBooleanTF{#1}{}{\label{\detokenize{req:#3@#2#4}}}%
}
\ifrecthy@beamersupp
\AtBeginDocument{
\theoremstyle{plain}
\newtheorem{reqsblock@recthy}{Requirements}
\newtheorem{reqblock@recthy}{Requirement}
\let\OLDreqsblock@recthy=\reqsblock@recthy
\let\OLDreqblock@recthy=\reqblock@recthy
\def\reqsblock@recthy{%
\setbeamercolor{block title}{fg=white,bg=Maroon}%
\setbeamercolor{block body}{fg=black,bg=Maroon!10}\OLDreqsblock@recthy
}
\def\reqblock@recthy{%
\setbeamercolor{block title}{fg=white,bg=Maroon}%
\setbeamercolor{block body}{fg=black,bg=Maroon!10}\OLDreqblock@recthy
}
}
\NewDocumentCommand{\require@beamer}{sO{}mO{}m}{\tag{$\@ifmtarg{#2#4}{\mathscr{#3}_{#5}}{\mathscr{#3}_{#5}^{#2#4}}$} \IfBooleanTF{#1}{}{\label{\detokenize{req:#3@#2#4}}} & }
\NewDocumentEnvironment{requirements}{d<>b}{\IfValueTF{#1}{\begin{reqsblock@recthy}<#1>}{\begin{reqsblock@recthy}}%
\setlength{\abovedisplayskip}{0pt}%
\setlength{\belowdisplayskip}{0pt}%
\begin{requirements*}
#2
\end{requirements*}
\end{reqsblock@recthy}}{}
\NewDocumentEnvironment{requirement}{d<>b}{\IfValueTF{#1}{\begin{reqblock@recthy}<#1>}{\begin{reqblock@recthy}}%
\setlength{\abovedisplayskip}{0pt}%
\setlength{\belowdisplayskip}{0pt}%
\begin{requirements*}
#2
\end{requirements*}
\end{reqblock@recthy}}{}
\NewDocumentEnvironment{requirements*}{b}{\usetagform{colon} %
\let\myhalign\halign%
\def\halign{\let\mylb\\ \renewcommand{\\}{& \mylb}\myhalign}%
\let\require=\require@beamer %
\begin{flalign*}%
#1
\end{flalign*}}{\ignorespacesafterend}%\@recthy@ignorespacesandallparsafter}
% \NewDocumentEnvironment{BeamerRequire}{d<>O{}mO{}m}{\IfValueTF{#1}{\begin{reqblock@recthy}<#1>}{\begin{reqblock@recthy}}%
% \setlength{\abovedisplayskip}{0pt}%
% \setlength{\belowdisplayskip}{0pt}%
% \begin{requirement}{\req@nohref[#2#4]{#3}{#5}} \label{\detokenize{req:#3@#2#4}}%
% }{
% \end{requirement}%
% \vspace*{-.3cm}%
% \end{reqblock@recthy}%
% }
% \NewDocumentEnvironment{BeamerRequire*}{d<>O{}mO{}m}{\IfValueTF{#1}{\begin{reqblock@recthy}<#1>}{\begin{reqblock@recthy}}%
% \setlength{\abovedisplayskip}{0pt}%
% \setlength{\belowdisplayskip}{0pt}%
% \begin{requirement}{\req@nohref[#2#4]{#3}{#5}}
% }{
% \end{requirement}%
% \vspace*{-.3cm}%
% \end{reqblock@recthy}%
% }
\else
\newenvironment{requirement}[1]{
\@pmg@saveeqstate
\@fleqntrue
\setlength\@mathmargin{1.5cm}
\tagsleft@true
\usetagform{colon}
\begin{equation}\tag{#1}
}{
\end{equation}
\@pmg@restoreeqstate
\usetagform{default}
% \let\maketag@@@=\maketag@@@orig@pmg
}
\NewDocumentEnvironment{require}{O{}mO{}m}{
\begin{requirement}{\req@nohref[#1#3]{#2}{#4}} \label{\detokenize{req:#2@#1#3}}%
}{
\end{requirement}%
}
\NewDocumentEnvironment{require*}{O{}mO{}m}{
\begin{requirement}{\req@nohref[#1#3]{#2}{#4}}
}{
\end{requirement}%
}
\NewDocumentEnvironment{requirements}{}{%
\@pmg@saveeqstate%
\@fleqntrue%
\setlength\@mathmargin{1.5cm}%
\tagsleft@true%
\usetagform{colon}%
\let\require=\require@nested%
\gather
}{\endgather%
\@pmg@restoreeqstate%
\usetagform{default}%
\ignorespacesafterend}
\fi
\fi
\ifrecthy@nostructresets
\@packinfo{Not loading r.e. subset commands}
\else
\@packinfo{Loading r.e. subset commands}
%%TODO: This stuff should be in a different section
% \let\@orig@setminus=\setminus
\newcommand*{\promptdif}{\@orig@setminus_{\downarrow}}
\let\setbefore=\promptdif
\let\promptminus=\promptdif
\let\promptsetminus=\promptdif
\newcommand*{\splitof}{\sqsubset}
\newcommand*{\splitby}{\sqsupset}
%%TODO depreciate capital S for commands...and generally remove the R and D stuff
\newcommand*{\strcE}{\ensuremath{\mathscr{E}}}
\WithSuffix\def\strcE*{\ensuremath{\mathscr{E}^{*}}}
% \let\strcE\StrcE
\newcommand*{\strcL}[1]{\mathscr{L}(#1)}
\newcommand*{\strcStarL}[1]{\mathscr{L}^{*}(#1)}
\WithSuffix\def\strcL*{\StrcStarL}
% \let\strcR=\StrcR
% \let\strcD=\StrcD
\fi
% \newcommand*{\@recthy@abs}[1]{\lvert#1\rvert}
\DeclarePairedDelimiter\@recthy@abs{\lvert}{\rvert}
\newcommand*{\@recthy@ensuretext}[1]{\ensuremath{\text{#1}}}
\ifrecthy@nomath
\@packinfo{No math loading.}
\else
\@packinfo{math loading.}
\providecommand*{\eqdef}{\overset{\text{\tiny def}}{=}} %\newcommand*{\eqdef}{\ensuremath{=\limits_{\text{\tiny def}}}}
\providecommand*{\iffdef}{\stackrel{\text{\tiny def}}{\iff}}
\ifdefined\aut
\else
\DeclareMathOperator{\aut}{Aut}
\fi
\ifdefined\Ord
\else
\DeclareMathOperator{\Ord}{Ord}
\fi
\DeclarePairedDelimiter\ceil{\lceil}{\rceil}
\DeclarePairedDelimiter\floor{\lfloor}{\rfloor}
\recthy@strip{abs}
\ifdefined\dom
\else
\DeclareMathOperator{\dom}{dom}
\fi
\ifdefined\rng
\else
\DeclareMathOperator{\rng}{rng}
\fi
\providecommand*{\restr}[1]{\mathpunct{\restriction_{#1}}}
\providecommand*{\ordpair}[2]{\left( #1, #2 \right) }
%%%%%%%%Function commands
\providecommand*{\maps}[2]{\mathop{:}#1\mapsto #2}
\providecommand*{\compfunc}{\mathbin{\circ}}
\ifdefined\compose
\else
\let\compose=\compfunc
\fi
\ltx@ifpackageloaded{unicode-math}{
\newcommand{\pmapsto}{\mathrel{\nvrightarrow}}
\newcommand{\pmapsfrom}{\mathrel{\nvleftarrow}}
}{
% \newcommand{\pmapsto}{}% just for safety
% \newcommand{\pmapsfrom}{}% just for safety
\DeclareRobustCommand{\pmapsto}{\mathrel{\mathpalette\p@to@gets\to}}
\DeclareRobustCommand{\pmapsfrom}{\mathrel{\mathpalette\p@to@gets\gets}}
\newcommand{\p@to@gets}[2]{%
\ooalign{\hidewidth$\m@th#1\mapstochar\mkern5mu$\hidewidth\cr$\m@th#1\to$\cr}%
}
}
\newcommand{\fpmapsto}{\mathrel{\pmapsto_{< \infty}}}
\newcommand{\fpmapsfrom}{\mathrel{\pmapsfrom_{< \infty}}}
\newcommand{\ParFuncs}[2]{{#2}^{\subset #1}}
\newcommand{\FinParFuncs}[2]{{#2}^{\subset_{< \infty} #1}}
\recthy@strip{ensuretext}
\providecommand{\quotient}{\quotient@recthy}
\fi
\ifrecthy@nooperators
\@packinfo{No operators loading.}
\else
\@packinfo{Operators loading.}
\providecommand*{\Land}{\mathop{\bigwedge}}
\providecommand*{\Lor}{\mathop{\bigvee}}
\providecommand*{\LLand}{\mathop{\bigwedge\mkern-15mu\bigwedge}}
\providecommand*{\LLor}{\mathop{\bigvee\mkern-15mu\bigvee}}
%save MnVersion in case wanted
\AtBeginDocument{
\let\Join=\@recthy@Join
}
\ifdefined\xor
\else
\DeclareMathOperator{\xor}{xor}
\fi
\fi
\ifrecthy@nosymb
\@packinfo{No Special Symbols Loading.}
\newcommand*{\ndownarrow}{\mathpunct{\mkern-4mu{\arrownot\mkern 4mu \downarrow}}}
\else
\ltx@ifpackageloaded{MnSymbol}{}{
\DeclareFontFamily{OMX}{MnSymbolE}{}
\DeclareFontFamily{U} {MnSymbolB}{}
\DeclareSymbolFont{MnSyB} {U} {MnSymbolB}{m}{n}
\DeclareSymbolFont{MnLargeSymbols}{OMX}{MnSymbolE}{m}{n}
\SetSymbolFont{MnLargeSymbols}{bold}{OMX}{MnSymbolE}{b}{n}
\DeclareFontShape{OMX}{MnSymbolE}{m}{n}{
<-6> MnSymbolE5
<6-7> MnSymbolE6
<7-8> MnSymbolE7
<8-9> MnSymbolE8
<9-10> MnSymbolE9
<10-12> MnSymbolE10
<12-> MnSymbolE12
}{}
\DeclareFontShape{OMX}{MnSymbolE}{b}{n}{
<-6> MnSymbolE-Bold5
<6-7> MnSymbolE-Bold6
<7-8> MnSymbolE-Bold7
<8-9> MnSymbolE-Bold8
<9-10> MnSymbolE-Bold9
<10-12> MnSymbolE-Bold10
<12-> MnSymbolE-Bold12
}{}
\DeclareFontShape{U}{MnSymbolB}{m}{n}{
<-6> MnSymbolB5
<6-7> MnSymbolB6
<7-8> MnSymbolB7
<8-9> MnSymbolB8
<9-10> MnSymbolB9
<10-12> MnSymbolB10
<12-> MnSymbolB12}{}
\DeclareFontShape{U}{MnSymbolB}{b}{n}{
<-6> MnSymbolB-Bold5
<6-7> MnSymbolB-Bold6
<7-8> MnSymbolB-Bold7
<8-9> MnSymbolB-Bold8
<9-10> MnSymbolB-Bold9
<10-12> MnSymbolB-Bold10
<12-> MnSymbolB-Bold12}{}
\DeclareSymbolFont{MnSyA} {U} {MnSymbolA}{m}{n}
\DeclareFontFamily{U} {MnSymbolA}{}
\DeclareFontShape{U}{MnSymbolA}{m}{n}{
<-6> MnSymbolA5
<6-7> MnSymbolA6
<7-8> MnSymbolA7
<8-9> MnSymbolA8
<9-10> MnSymbolA9
<10-12> MnSymbolA10
<12-> MnSymbolA12}{}
\DeclareFontShape{U}{MnSymbolA}{b}{n}{
<-6> MnSymbolA-Bold5
<6-7> MnSymbolA-Bold6
<7-8> MnSymbolA-Bold7
<8-9> MnSymbolA-Bold8
<9-10> MnSymbolA-Bold9
<10-12> MnSymbolA-Bold10
<12-> MnSymbolA-Bold12}{}
\DeclareMathDelimiter{\@recthy@ulcorner}
{\mathopen}{MnLargeSymbols}{'036}{MnLargeSymbols}{'036}
\DeclareMathDelimiter{\@recthy@urcorner}
{\mathclose}{MnLargeSymbols}{'043}{MnLargeSymbols}{'043}
\let\ulcorner=\@recthy@ulcorner
\let\urcorner=\@recthy@urcorner
\DeclareMathSymbol{\ndownarrow}{\mathpunct}{MnSyB}{3}
\DeclareMathDelimiter{\@recthy@ulcorner}
{\mathopen}{MnLargeSymbols}{'036}{MnLargeSymbols}{'036}
\DeclareMathDelimiter{\@recthy@urcorner}
{\mathclose}{MnLargeSymbols}{'043}{MnLargeSymbols}{'043}
\DeclareMathSymbol{\Searrow}{\mathrel}{MnSyA}{15}
\DeclareMathSymbol{\nSearrow}{\mathrel}{MnSyB}{15}
}
\ifrecthy@nodoubleangles
\else
\let\llangle=\@recthy@llangle
\let\rrangle=\@recthy@rrangle
\fi
\fi
\NewDocumentCommand{\REA}{d()o}{\ensuremath{\IfValueTF{#2}{#2 \@recthy@mhyphen}{}\text{REA}\IfValueTF{#1}{(#1)}{}}}
\NewDocumentCommand{\CEA}{d()o}{\ensuremath{\IfValueTF{#2}{#2 \@recthy@mhyphen}{}\text{CEA}\IfValueTF{#1}{(#1)}{}}}
% Set stuff
\NewDocumentCommand{\@recthy@set}{m!G{}}{{\let\st=\mid\left\{#1 \ifthenelse{\isempty{#2}}{}{\mid #2} \right\}}}
% \def\@recthy@set#1{\def\@set@argi@pmg{#1}\@ifnextchar\bgroup\@setst@pmg\@setplain@pmg}
% \newcommand*{\@setst@pmg}[1]{\ifthenelse{\isempty{#1}}{\@setplain@pmg}{\left \{ \@set@argi@pmg \middle | #1\right \}}}
% \newcommand*{\@setplain@pmg}{\left \{ \@set@argi@pmg \right \}}
% \newcommand*{\@recthy@set}[2]{\ifthenelse{\isempty{#2}}{\left \{ #1 \right \}}{\left \{ #1 \middle | #2\right \}} }
% \DeclareOptionX{setminussym}[@recthy@defaultsetminusSYM]{\edef\@recthy@setminusSYM{\expandafter\noexpand\csname #1 \endcsname}}