% frege.sty - a LaTeX2e package for typesetting begriffsschrift % by Quirin Pamp % % based on begriff.sty released under GNU General Public License % Copyright (C) 2003 by Josh Parsons % with changes made in October 2004 by Richard Heck % and minor changes by Josh Parsons to fix problem with linespacing (May 2005) % % This program is free software; you can redistribute it and/or modify % it under the terms of the GNU General Public License as published by % the Free Software Foundation; either version 2 of the License, or % (at your option) any later version. % % This program is distributed in the hope that it will be useful, % but WITHOUT ANY WARRANTY; without even the implied warranty of % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU % General Public License for more details. % % You should have received a copy of the GNU General Public License % along with this program; if not, write to the Free Software % Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111, % USA (or just search for it online). %%% changes as compared to begriff.sty: % correct relative lengths of various content strokes; % content strokes at middle of line rather than bottom; % greater width for assertion stroke as compared to content stroke; % more intuitive structure of commands (arguments are now given in the same % order as they appear on the left of a completed formula); % the command conditional with empty arguments now only gives the conditional % stroke the other strokes are added as the arguments; % accounting for linewidth so that things remain properly centered even for % a greater linewidth; %%% changes in version 1.1: % added option to locally set \Fbaselength to all basic strokes; % simplified code for \Fbracket in terms of \Fbox; % rearranged code in a more logical order; %%% changes in version 1.2: % added new command \Fargument for typesetting arguments; % added new command \Fstrut to be used in conjunction with \Fargument; % changed \Fbaselength to be the full rather than half the unit length; % fixed a bug where the scalefactor introduced in 1.1 does not always reset; %%% changes in version 1.3: % made the (): in \Fargument user defined, so as to make the option properly % optional (note to self: don't code past midnight); % added a strut to \Fargument so as to produce optically correct centering; % added optional shorthands for all new commands for better flow of usage; % added option bguq for using bguq font (by J.J. Green) for the quantifier; %%% planned changes for future versions: % solving the problem of nested arguments; % the fregean conjunction; % a vertical shorthand stroke as I have seen in Begriffsschrift?!; % scaling with font size; % scaling of bguq character with \Flinewidth; %%% identification: \NeedsTeXFormat{LaTeX2e}% \ProvidesPackage{frege}[2012/08/04 v1.3]% \typeout{Fregean Begriffsschrift: 2012/08/04 v1.3}% %%% package dependencies: \RequirePackage{amssymb}% \RequirePackage{ifthen}% %%% options: % bguq option, if used package bguq must be installed: \newboolean{bguq}% \setboolean{bguq}{false}% \DeclareOption{bguq}{\setboolean{bguq}{true}}% \ProcessOptions\relax% \ifthenelse{\boolean{bguq}}{\RequirePackage[5]{bguq}}{}% %%% variable decleration: \newlength{\temp}% \newlength{\tempp}% \newlength{\Fbaselength}% \setlength{\Fbaselength}{20pt}% 20pt since v1.2 \newlength{\Funitlength}% \newlength{\Flinewidth}% \setlength{\Flinewidth}{0.5pt}% \newlength{\Fspace}% \setlength{\Fspace}{2pt}% \newlength{\Fassertwidth}% \setlength{\Fassertwidth}{3\Flinewidth}% \newlength{\Fraiseheight}% \setlength{\Fraiseheight}{1ex}% \addtolength{\Fraiseheight}{-\Flinewidth}% \newlength{\Fnegsep}% \setlength{\Fnegsep}{3\Flinewidth}% \newlength{\Fnegshort}% \setlength{\Fnegshort}{2\Flinewidth}% \newlength{\Fquantwidth}% \setlength{\Fquantwidth}{6pt}% \newlength{\Fantecedentheight}% \newlength{\Fconsequentdepth}% \newsavebox{\Fantecedent}% \newsavebox{\Fconsequent}% \newlength{\Fantecedentwidth}% \newlength{\Fconsequentwidth}% \newlength{\Fblockwidth}% \newlength{\Fpremiselength}% \newlength{\Fthereforelength}% \newlength{\Fbguqwidth}% since v1.3 \ifthenelse{\boolean{bguq}}{\setlength{\Fbguqwidth}{\bguqwidth}}{}% %%% shorthand commands since v1.3: \newcommand{\Fb}[1]{\Fbox{#1}}% \newcommand{\Fbb}[1]{\Fbracket{#1}}% \newcommand{\Fcdt}[3][]{\Fconditional[#1]{#2}{#3}}% \newcommand{\Farg}[4][]{\Fargument[#1]{#2}{#3}{#4}}% \newcommand{\Fs}[1][1]{\Fstrut[#1]}% \newcommand{\F}[1][1]{\Fcontent[#1]}% \newcommand{\Fn}[1][1]{\Fncontent[#1]}% \newcommand{\Fnn}[1][1]{\Fnncontent[#1]}% \newcommand{\Fa}[1][1]{\Facontent[#1]}% \newcommand{\Fan}[1][1]{\Fancontent[#1]}% \newcommand{\Fann}[1][1]{\Fanncontent[#1]}% \newcommand{\Fq}[1][1]{\Fquant[#1]}% \newcommand{\Fnq}[1][1]{\Fnquant[#1]}% \newcommand{\Fnnq}[1][1]{\Fnnquant[#1]}% \newcommand{\Fqn}[1][1]{\Fquantn[#1]}% \newcommand{\Fqnn}[1][1]{\Fquantnn[#1]}% \newcommand{\Fnqn}[1][1]{\Fnquantn[#1]}% \newcommand{\Fnnqn}[1][1]{\Fnnquantn[#1]}% \newcommand{\Fnqnn}[1][1]{\Fnquantnn[#1]}% \newcommand{\Fnnqnn}[1][1]{\Fnnquantnn[#1]}% \newcommand{\Faq}[1][1]{\Faquant[#1]}% \newcommand{\Fanq}[1][1]{\Fanquant[#1]}% \newcommand{\Fannq}[1][1]{\Fannquant[#1]}% \newcommand{\Faqn}[1][1]{\Faquantn[#1]}% \newcommand{\Faqnn}[1][1]{\Faquantnn[#1]}% \newcommand{\Fanqn}[1][1]{\Fanquantn[#1]}% \newcommand{\Fannqn}[1][1]{\Fannquantn[#1]}% \newcommand{\Fanqnn}[1][1]{\Fanquantnn[#1]}% \newcommand{\Fannqnn}[1][1]{\Fannquantnn[#1]}% %%% main body/new commands: % boxing complex expressions with a centered baseline: \newcommand{\Fbox}[1]{% \settowidth{\temp}{\ensuremath{#1}}% \settoheight{\tempp}{\ensuremath{#1}}% \addtolength{\tempp}{3pt}% visual approximation may not scale right \parbox{\temp}{\rule{0pt}{\tempp}\ensuremath{#1}}% }% % bracketed Fbox v1.1: \newcommand{\Fbracket}[1]{\ensuremath{\left(\Fbox{#1}\right)}}% % conditional stroke \Fconditional[content]{consequent}{antecedent}: \newcommand{\Fconditional}[3][]% {% \unskip% \sbox{\Fconsequent}{% \rule[-0.3\baselineskip]{0pt}{0.3\baselineskip}% this is a strut \ensuremath{#2}}% \settodepth{\Fconsequentdepth}{% \rule[-0.3\baselineskip]{0pt}{0.3\baselineskip}% this is a strut \ensuremath{#2}}% \sbox{\Fantecedent}{% \rule{0pt}{\baselineskip}% this is a strut \rule[-0.3\baselineskip]{0pt}{0.3\baselineskip}% this is a strut \ensuremath{#3}}% \settoheight{\Fantecedentheight}{% \rule{0pt}{\baselineskip}% \rule[-0.3\baselineskip]{0pt}{0.3\baselineskip}% this is a strut \ensuremath{#3}}% \setlength{\temp}{\lineskip}% \addtolength{\temp}{\Fantecedentheight}% \addtolength{\temp}{\Fconsequentdepth}% \setlength{\tempp}{\temp}% \addtolength{\tempp}{-\Fraiseheight}% \mbox{% \ensuremath{#1\unskip}% \kern-\Flinewidth% \rule[-\tempp]{\Flinewidth}{\temp}% \settowidth{\Fconsequentwidth}{\usebox{\Fconsequent}}% find width \settowidth{\Fantecedentwidth}{\usebox{\Fantecedent}}% find width \settoheight{\temp}{\mbox{% compare and find longer of two widths \rule{0pt}{\Fconsequentwidth}% \rule{0pt}{\Fantecedentwidth}}}% \parbox[t]{\temp}{\usebox{\Fconsequent}\\\usebox{\Fantecedent}}}% }% % argument presentation \Fargument[premise 0]{premise 1}{premise 2}{conclusion} v1.2 \newcommand{\Fargument}[4][]% {% \settowidth{\Fantecedentwidth}{\ensuremath{#2}}% \settowidth{\Fconsequentwidth}{\ensuremath{#3}}% \settoheight{\Fblockwidth}{\mbox{% \rule{0pt}{\Fantecedentwidth}% \rule{0pt}{\Fconsequentwidth}}}% \setlength{\Fthereforelength}{\Fblockwidth}% \addtolength{\Fthereforelength}{1em}% \settowidth{\Fpremiselength}{\ensuremath{#1}}% \mbox{% \raisebox{.69\baselineskip}{\ensuremath{#1}}% \hskip .5em% \parbox[b]{\Fblockwidth}{% \ensuremath{#2}\\% \rule{0pt}{1\baselineskip}\ensuremath{#3}\\% \makebox[\Fblockwidth]{% \rule{0pt}{1.3\baselineskip}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{0.65\baselineskip}% \addtolength{\temp}{0.5\lineskip}% \rule[\temp]{\Fthereforelength}{\Flinewidth}}}% \kern-\Fblockwidth% \ensuremath{#4}% \rule{0.5\Fpremiselength}{0pt}}% }% % strut (for use with argument) v1.2: \newcommand{\Fstrut}[1][1]% {% \setlength{\Funitlength}{\Fbaselength}% \setlength{\Fbaselength}{#1\Fbaselength}% \rule[\Fraiseheight]{\Fbaselength}{0pt}% \setlength{\Fbaselength}{\Funitlength}% }% % content stroke: \newcommand{\Fcontent}[1][1]% {% \setlength{\Funitlength}{\Fbaselength}% \setlength{\Fbaselength}{#1\Fbaselength}% \unskip% \rule[\Fraiseheight]{\Fbaselength}{\Flinewidth}% \setlength{\Fbaselength}{\Funitlength}% \hskip\Fspace% }% % negated content stroke: \newcommand{\Fncontent}[1][1]% {% \setlength{\Funitlength}{\Fbaselength}% \setlength{\Fbaselength}{#1\Fbaselength}% \unskip% \setlength{\temp}{.5\Fbaselength}% \addtolength{\temp}{-0.5\Flinewidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \setlength{\temp}{.5\Fbaselength}% \addtolength{\temp}{-0.5\Flinewidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\Fbaselength}{\Funitlength}% \hskip\Fspace% }% % twice negated content stroke: \newcommand{\Fnncontent}[1][1]% {% \setlength{\Funitlength}{\Fbaselength}% \setlength{\Fbaselength}{#1\Fbaselength}% \unskip% \setlength{\temp}{.5\Fbaselength}% \addtolength{\temp}{-0.5\Fnegsep}% \addtolength{\temp}{-\Flinewidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \rule[\Fraiseheight]{\Fnegsep}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \setlength{\temp}{.5\Fbaselength}% \addtolength{\temp}{-0.5\Fnegsep}% \addtolength{\temp}{-\Flinewidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\Fbaselength}{\Funitlength}% \hskip\Fspace% }% % asserted content stroke: \newcommand{\Facontent}[1][1]% {% \setlength{\Funitlength}{\Fbaselength}% \setlength{\Fbaselength}{#1\Fbaselength}% \unskip% \setlength{\temp}{2\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \rule{\Fassertwidth}{\temp}% \setlength{\temp}{\Fbaselength}% \addtolength{\temp}{-\Fassertwidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\Fbaselength}{\Funitlength}% \hskip\Fspace% }% % asserted negated content stroke: \newcommand{\Fancontent}[1][1]% {% \setlength{\Funitlength}{\Fbaselength}% \setlength{\Fbaselength}{#1\Fbaselength}% \unskip% \setlength{\temp}{2\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \rule{\Fassertwidth}{\temp}% \setlength{\temp}{.5\Fbaselength}% \addtolength{\temp}{-\Fassertwidth}% \addtolength{\temp}{-0.5\Flinewidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \setlength{\temp}{.5\Fbaselength}% \addtolength{\temp}{-0.5\Flinewidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\Fbaselength}{\Funitlength}% \hskip\Fspace% }% % asserted twice negated content stroke: \newcommand{\Fanncontent}[1][1]% {% \setlength{\Funitlength}{\Fbaselength}% \setlength{\Fbaselength}{#1\Fbaselength}% \unskip% \setlength{\temp}{2\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \rule{\Fassertwidth}{\temp}% \setlength{\temp}{.5\Fbaselength}% \addtolength{\temp}{-\Fassertwidth}% \addtolength{\temp}{-\Fnegshort}% \addtolength{\temp}{-\Flinewidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \rule[\Fraiseheight]{\Fnegsep}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \setlength{\temp}{.5\Fbaselength}% \addtolength{\temp}{-0.5\Fnegsep}% \addtolength{\temp}{-\Flinewidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\Fbaselength}{\Funitlength}% \hskip\Fspace% }% % universal quantifier: \newcommand{\Fquant}[2][1]% {% \ifthenelse{\boolean{bguq}}% {% \setlength{\Funitlength}{\Fbaselength}% \setlength{\Fbaselength}{#1\Fbaselength}% \unskip% \setlength{\temp}{0.5\Fbaselength}% \addtolength{\temp}{-0.5\Fbguqwidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \raisebox{\temp}{\ensuremath{\bguq}}% \kern-\Fbguqwidth% \raisebox{\temp}% {\makebox[\Fbguqwidth]{\ensuremath{\scriptstyle\mathfrak{#2}}}}% \setlength{\temp}{0.5\Fbaselength}% \addtolength{\temp}{-0.5\Fbguqwidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\Fbaselength}{\Funitlength}% \hskip\Fspace% }% {% \setlength{\Funitlength}{\Fbaselength}% \setlength{\Fbaselength}{#1\Fbaselength}% \unskip% \setlength{\temp}{.5\Fbaselength}% \addtolength{\temp}{-0.5\Fquantwidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\unitlength}{\Fquantwidth}% \raisebox{\Fraiseheight}{% \begin{picture}(1,0)(0,0)% \linethickness{\Flinewidth}% \qbezier(0,0)(0.5,-0.6666)(1,0)% \end{picture}}% \kern-\Fquantwidth% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \raisebox{\temp}% {\makebox[\Fquantwidth]{\ensuremath{\scriptstyle\mathfrak{#2}}}}% \setlength{\temp}{.5\Fbaselength}% \addtolength{\temp}{-0.5\Fquantwidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\Fbaselength}{\Funitlength}% \hskip\Fspace% }% }% % negated universal quantifier \newcommand{\Fnquant}[2][1]% {% \ifthenelse{\boolean{bguq}}% {% \setlength{\Funitlength}{\Fbaselength}% \setlength{\Fbaselength}{#1\Fbaselength}% \unskip% \setlength{\temp}{0.25\Fbaselength}% \addtolength{\temp}{-0.25\Fbguqwidth}% \addtolength{\temp}{-0.5\Flinewidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \setlength{\temp}{.25\Fbaselength}% \addtolength{\temp}{-0.25\Fbguqwidth}% \addtolength{\temp}{-0.5\Flinewidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \raisebox{\temp}{\ensuremath{\bguq}}% \kern-\Fbguqwidth% \raisebox{\temp}% {\makebox[\Fbguqwidth]{\ensuremath{\scriptstyle\mathfrak{#2}}}}% \setlength{\temp}{.5\Fbaselength}% \addtolength{\temp}{-0.5\Fbguqwidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\Fbaselength}{\Funitlength}% \hskip\Fspace% }% {% \setlength{\Funitlength}{\Fbaselength}% \setlength{\Fbaselength}{#1\Fbaselength}% \unskip% \setlength{\temp}{0.25\Fbaselength}% \addtolength{\temp}{-0.25\Fquantwidth}% \addtolength{\temp}{-0.5\Flinewidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \setlength{\temp}{.25\Fbaselength}% \addtolength{\temp}{-0.25\Fquantwidth}% \addtolength{\temp}{-0.5\Flinewidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\unitlength}{\Fquantwidth}% \raisebox{\Fraiseheight}{% \begin{picture}(1,0)(0,0)% \linethickness{\Flinewidth}% \qbezier(0,0)(0.5,-0.6666)(1,0)% \end{picture}}% \kern-\Fquantwidth% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \raisebox{\temp}% {\makebox[\Fquantwidth]{\ensuremath{\scriptstyle\mathfrak{#2}}}}% \setlength{\temp}{.5\Fbaselength}% \addtolength{\temp}{-0.5\Fquantwidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\Fbaselength}{\Funitlength}% \hskip\Fspace% }% }% % twice negated universal quantifier \newcommand{\Fnnquant}[2][1]% {% \ifthenelse{\boolean{bguq}}% {% \setlength{\Funitlength}{\Fbaselength}% \setlength{\Fbaselength}{#1\Fbaselength}% \unskip% \setlength{\temp}{.5\Fbaselength}% \addtolength{\temp}{-0.5\Fbguqwidth}% \addtolength{\temp}{-2\Flinewidth}% \addtolength{\temp}{-\Fnegsep}% \rule[\Fraiseheight]{0.5\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \rule[\Fraiseheight]{\Fnegsep}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \setlength{\temp}{.5\Fbaselength}% \addtolength{\temp}{-0.5\Fbguqwidth}% \addtolength{\temp}{-2\Flinewidth}% \addtolength{\temp}{-\Fnegsep}% \rule[\Fraiseheight]{0.5\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \raisebox{\temp}{\ensuremath{\bguq}}% \kern-\Fbguqwidth% \raisebox{\temp}% {\makebox[\Fbguqwidth]{\ensuremath{\scriptstyle\mathfrak{#2}}}}% \setlength{\temp}{.5\Fbaselength}% \addtolength{\temp}{-0.5\Fbguqwidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\Fbaselength}{\Funitlength}% \hskip\Fspace% }% {% \setlength{\Funitlength}{\Fbaselength}% \setlength{\Fbaselength}{#1\Fbaselength}% \unskip% \setlength{\temp}{.5\Fbaselength}% \addtolength{\temp}{-0.5\Fquantwidth}% \addtolength{\temp}{-2\Flinewidth}% \addtolength{\temp}{-\Fnegsep}% \rule[\Fraiseheight]{0.5\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \rule[\Fraiseheight]{\Fnegsep}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \setlength{\temp}{.5\Fbaselength}% \addtolength{\temp}{-0.5\Fquantwidth}% \addtolength{\temp}{-2\Flinewidth}% \addtolength{\temp}{-\Fnegsep}% \rule[\Fraiseheight]{0.5\temp}{\Flinewidth}% \setlength{\unitlength}{\Fquantwidth}% \raisebox{\Fraiseheight}{% \begin{picture}(1,0)(0,0)% \linethickness{\Flinewidth}% \qbezier(0,0)(0.5,-0.6666)(1,0)% \end{picture}}% \kern-\Fquantwidth% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \raisebox{\temp}% {\makebox[\Fquantwidth]{\ensuremath{\scriptstyle\mathfrak{#2}}}}% \setlength{\temp}{.5\Fbaselength}% \addtolength{\temp}{-0.5\Fquantwidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\Fbaselength}{\Funitlength}% \hskip\Fspace% }% }% % universal quantifier with negated content: \newcommand{\Fquantn}[2][1]% {% \ifthenelse{\boolean{bguq}}% {% \setlength{\Funitlength}{\Fbaselength}% \setlength{\Fbaselength}{#1\Fbaselength}% \unskip% \setlength{\temp}{.5\Fbaselength}% \addtolength{\temp}{-0.5\Fbguqwidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \raisebox{\temp}{\ensuremath{\bguq}}% \kern-\Fbguqwidth% \raisebox{\temp}% {\makebox[\Fbguqwidth]{\ensuremath{\scriptstyle\mathfrak{#2}}}}% \setlength{\temp}{0.25\Fbaselength}% \addtolength{\temp}{-0.25\Fbguqwidth}% \addtolength{\temp}{-0.5\Flinewidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \setlength{\temp}{.25\Fbaselength}% \addtolength{\temp}{-0.25\Fbguqwidth}% \addtolength{\temp}{-0.5\Flinewidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\Fbaselength}{\Funitlength}% \hskip\Fspace% }% {% \setlength{\Funitlength}{\Fbaselength}% \setlength{\Fbaselength}{#1\Fbaselength}% \unskip% \setlength{\temp}{.5\Fbaselength}% \addtolength{\temp}{-0.5\Fquantwidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\unitlength}{\Fquantwidth}% \raisebox{\Fraiseheight}{% \begin{picture}(1,0)(0,0)% \linethickness{\Flinewidth}% \qbezier(0,0)(0.5,-0.6666)(1,0)% \end{picture}}% \kern-\Fquantwidth% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \raisebox{\temp}% {\makebox[\Fquantwidth]{\ensuremath{\scriptstyle\mathfrak{#2}}}}% \setlength{\temp}{.25\Fbaselength}% \addtolength{\temp}{-0.25\Fquantwidth}% \addtolength{\temp}{-0.5\Flinewidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \setlength{\temp}{.25\Fbaselength}% \addtolength{\temp}{-0.25\Fquantwidth}% \addtolength{\temp}{-0.5\Flinewidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\Fbaselength}{\Funitlength}% \hskip\Fspace% }% }% % universal quantifier with twice negated content: \newcommand{\Fquantnn}[2][1]% {% \ifthenelse{\boolean{bguq}}% {% \setlength{\Funitlength}{\Fbaselength}% \setlength{\Fbaselength}{#1\Fbaselength}% \unskip% \setlength{\temp}{.5\Fbaselength}% \addtolength{\temp}{-0.5\Fbguqwidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \raisebox{\temp}{\ensuremath{\bguq}}% \kern-\Fbguqwidth% \raisebox{\temp}% {\makebox[\Fbguqwidth]{\ensuremath{\scriptstyle\mathfrak{#2}}}}% \setlength{\temp}{.5\Fbaselength}% \addtolength{\temp}{-0.5\Fbguqwidth}% \addtolength{\temp}{-2\Flinewidth}% \addtolength{\temp}{-\Fnegsep}% \rule[\Fraiseheight]{0.5\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \rule[\Fraiseheight]{\Fnegsep}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \setlength{\temp}{.5\Fbaselength}% \addtolength{\temp}{-0.5\Fbguqwidth}% \addtolength{\temp}{-2\Flinewidth}% \addtolength{\temp}{-\Fnegsep}% \rule[\Fraiseheight]{0.5\temp}{\Flinewidth}% \setlength{\Fbaselength}{\Funitlength}% \hskip\Fspace% }% {% \setlength{\Funitlength}{\Fbaselength}% \setlength{\Fbaselength}{#1\Fbaselength}% \unskip% \setlength{\temp}{.5\Fbaselength}% \addtolength{\temp}{-0.5\Fquantwidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\unitlength}{\Fquantwidth}% \raisebox{\Fraiseheight}{% \begin{picture}(1,0)(0,0)% \linethickness{\Flinewidth}% \qbezier(0,0)(0.5,-0.6666)(1,0)% \end{picture}}% \kern-\Fquantwidth% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \raisebox{\temp}% {\makebox[\Fquantwidth]{\ensuremath{\scriptstyle\mathfrak{#2}}}}% \setlength{\temp}{.5\Fbaselength}% \addtolength{\temp}{-0.5\Fquantwidth}% \addtolength{\temp}{-2\Flinewidth}% \addtolength{\temp}{-\Fnegsep}% \rule[\Fraiseheight]{0.5\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \rule[\Fraiseheight]{\Fnegsep}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \setlength{\temp}{.5\Fbaselength}% \addtolength{\temp}{-0.5\Fquantwidth}% \addtolength{\temp}{-2\Flinewidth}% \addtolength{\temp}{-\Fnegsep}% \rule[\Fraiseheight]{0.5\temp}{\Flinewidth}% \setlength{\Fbaselength}{\Funitlength}% \hskip\Fspace% }% }% % negated universal quantifier with negated content \newcommand{\Fnquantn}[2][1]% {% \ifthenelse{\boolean{bguq}}% {% \setlength{\Funitlength}{\Fbaselength}% \setlength{\Fbaselength}{#1\Fbaselength}% \unskip% \setlength{\temp}{0.25\Fbaselength}% \addtolength{\temp}{-0.25\Fbguqwidth}% \addtolength{\temp}{-0.5\Flinewidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \setlength{\temp}{.25\Fbaselength}% \addtolength{\temp}{-0.25\Fbguqwidth}% \addtolength{\temp}{-0.5\Flinewidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \raisebox{\temp}{\ensuremath{\bguq}}% \kern-\Fbguqwidth% \raisebox{\temp}% {\makebox[\Fbguqwidth]{\ensuremath{\scriptstyle\mathfrak{#2}}}}% \setlength{\temp}{0.25\Fbaselength}% \addtolength{\temp}{-0.25\Fbguqwidth}% \addtolength{\temp}{-0.5\Flinewidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \setlength{\temp}{.25\Fbaselength}% \addtolength{\temp}{-0.25\Fbguqwidth}% \addtolength{\temp}{-0.5\Flinewidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\Fbaselength}{\Funitlength}% \hskip\Fspace% }% {% \setlength{\Funitlength}{\Fbaselength}% \setlength{\Fbaselength}{#1\Fbaselength}% \unskip% \setlength{\temp}{.25\Fbaselength}% \addtolength{\temp}{-0.25\Fquantwidth}% \addtolength{\temp}{-0.5\Flinewidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \setlength{\temp}{.25\Fbaselength}% \addtolength{\temp}{-0.25\Fquantwidth}% \addtolength{\temp}{-0.5\Flinewidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\unitlength}{\Fquantwidth}% \raisebox{\Fraiseheight}{% \begin{picture}(1,0)(0,0)% \linethickness{\Flinewidth}% \qbezier(0,0)(0.5,-0.6666)(1,0)% \end{picture}}% \kern-\Fquantwidth% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \raisebox{\temp}% {\makebox[\Fquantwidth]{\ensuremath{\scriptstyle\mathfrak{#2}}}}% \setlength{\temp}{.25\Fbaselength}% \addtolength{\temp}{-0.25\Fquantwidth}% \addtolength{\temp}{-0.5\Flinewidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \setlength{\temp}{.25\Fbaselength}% \addtolength{\temp}{-0.25\Fquantwidth}% \addtolength{\temp}{-0.5\Flinewidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\Fbaselength}{\Funitlength}% \hskip\Fspace% }% }% % negated universal quantifier with twice negated content \newcommand{\Fnquantnn}[2][1]% {% \ifthenelse{\boolean{bguq}}% {% \setlength{\Funitlength}{\Fbaselength}% \setlength{\Fbaselength}{#1\Fbaselength}% \unskip% \setlength{\temp}{0.25\Fbaselength}% \addtolength{\temp}{-0.25\Fbguqwidth}% \addtolength{\temp}{-0.5\Flinewidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \setlength{\temp}{.25\Fbaselength}% \addtolength{\temp}{-0.25\Fbguqwidth}% \addtolength{\temp}{-0.5\Flinewidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \raisebox{\temp}{\ensuremath{\bguq}}% \kern-\Fbguqwidth% \raisebox{\temp}% {\makebox[\Fbguqwidth]{\ensuremath{\scriptstyle\mathfrak{#2}}}}% \setlength{\temp}{.5\Fbaselength}% \addtolength{\temp}{-0.5\Fbguqwidth}% \addtolength{\temp}{-2\Flinewidth}% \addtolength{\temp}{-\Fnegsep}% \rule[\Fraiseheight]{0.5\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \rule[\Fraiseheight]{\Fnegsep}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \setlength{\temp}{.5\Fbaselength}% \addtolength{\temp}{-0.5\Fbguqwidth}% \addtolength{\temp}{-2\Flinewidth}% \addtolength{\temp}{-\Fnegsep}% \rule[\Fraiseheight]{0.5\temp}{\Flinewidth}% \setlength{\Fbaselength}{\Funitlength}% \hskip\Fspace% }% {% \setlength{\Funitlength}{\Fbaselength}% \setlength{\Fbaselength}{#1\Fbaselength}% \unskip% \setlength{\temp}{.25\Fbaselength}% \addtolength{\temp}{-0.25\Fquantwidth}% \addtolength{\temp}{-0.5\Flinewidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \setlength{\temp}{.25\Fbaselength}% \addtolength{\temp}{-0.25\Fquantwidth}% \addtolength{\temp}{-0.5\Flinewidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\unitlength}{\Fquantwidth}% \raisebox{\Fraiseheight}{% \begin{picture}(1,0)(0,0)% \linethickness{\Flinewidth}% \qbezier(0,0)(0.5,-0.6666)(1,0)% \end{picture}}% \kern-\Fquantwidth% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \raisebox{\temp}% {\makebox[\Fquantwidth]{\ensuremath{\scriptstyle\mathfrak{#2}}}}% \setlength{\temp}{.5\Fbaselength}% \addtolength{\temp}{-0.5\Fquantwidth}% \addtolength{\temp}{-2\Flinewidth}% \addtolength{\temp}{-\Fnegsep}% \rule[\Fraiseheight]{0.5\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \rule[\Fraiseheight]{\Fnegsep}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \setlength{\temp}{.5\Fbaselength}% \addtolength{\temp}{-0.5\Fquantwidth}% \addtolength{\temp}{-2\Flinewidth}% \addtolength{\temp}{-\Fnegsep}% \rule[\Fraiseheight]{0.5\temp}{\Flinewidth}% \setlength{\Fbaselength}{\Funitlength}% \hskip\Fspace% }% }% % twice negated universal quantifier with negated content \newcommand{\Fnnquantn}[2][1]% {% \ifthenelse{\boolean{bguq}}% {% \setlength{\Funitlength}{\Fbaselength}% \setlength{\Fbaselength}{#1\Fbaselength}% \unskip% \setlength{\temp}{.5\Fbaselength}% \addtolength{\temp}{-0.5\Fbguqwidth}% \addtolength{\temp}{-2\Flinewidth}% \addtolength{\temp}{-\Fnegsep}% \rule[\Fraiseheight]{0.5\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \rule[\Fraiseheight]{\Fnegsep}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \setlength{\temp}{.5\Fbaselength}% \addtolength{\temp}{-0.5\Fbguqwidth}% \addtolength{\temp}{-2\Flinewidth}% \addtolength{\temp}{-\Fnegsep}% \rule[\Fraiseheight]{0.5\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \raisebox{\temp}{\ensuremath{\bguq}}% \kern-\Fbguqwidth% \raisebox{\temp}% {\makebox[\Fbguqwidth]{\ensuremath{\scriptstyle\mathfrak{#2}}}}% \setlength{\temp}{0.25\Fbaselength}% \addtolength{\temp}{-0.25\Fbguqwidth}% \addtolength{\temp}{-0.5\Flinewidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \setlength{\temp}{.25\Fbaselength}% \addtolength{\temp}{-0.25\Fbguqwidth}% \addtolength{\temp}{-0.5\Flinewidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\Fbaselength}{\Funitlength}% \hskip\Fspace% }% {% \setlength{\Funitlength}{\Fbaselength}% \setlength{\Fbaselength}{#1\Fbaselength}% \unskip% \setlength{\temp}{.5\Fbaselength}% \addtolength{\temp}{-0.5\Fquantwidth}% \addtolength{\temp}{-2\Flinewidth}% \addtolength{\temp}{-\Fnegsep}% \rule[\Fraiseheight]{0.5\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \rule[\Fraiseheight]{\Fnegsep}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \setlength{\temp}{.5\Fbaselength}% \addtolength{\temp}{-0.5\Fquantwidth}% \addtolength{\temp}{-2\Flinewidth}% \addtolength{\temp}{-\Fnegsep}% \rule[\Fraiseheight]{0.5\temp}{\Flinewidth}% \setlength{\unitlength}{\Fquantwidth}% \raisebox{\Fraiseheight}{% \begin{picture}(1,0)(0,0)% \linethickness{\Flinewidth}% \qbezier(0,0)(0.5,-0.6666)(1,0)% \end{picture}}% \kern-\Fquantwidth% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \raisebox{\temp}% {\makebox[\Fquantwidth]{\ensuremath{\scriptstyle\mathfrak{#2}}}}% \setlength{\temp}{.25\Fbaselength}% \addtolength{\temp}{-0.25\Fquantwidth}% \addtolength{\temp}{-0.5\Flinewidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \setlength{\temp}{.25\Fbaselength}% \addtolength{\temp}{-0.25\Fquantwidth}% \addtolength{\temp}{-0.5\Flinewidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\Fbaselength}{\Funitlength}% \hskip\Fspace% }% }% % twice negated universal quantifier with twice negated content \newcommand{\Fnnquantnn}[2][1]% {% \ifthenelse{\boolean{bguq}}% {% \setlength{\Funitlength}{\Fbaselength}% \setlength{\Fbaselength}{#1\Fbaselength}% \unskip% \setlength{\temp}{.5\Fbaselength}% \addtolength{\temp}{-0.5\Fbguqwidth}% \addtolength{\temp}{-2\Flinewidth}% \addtolength{\temp}{-\Fnegsep}% \rule[\Fraiseheight]{0.5\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \rule[\Fraiseheight]{\Fnegsep}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \setlength{\temp}{.5\Fbaselength}% \addtolength{\temp}{-0.5\Fbguqwidth}% \addtolength{\temp}{-2\Flinewidth}% \addtolength{\temp}{-\Fnegsep}% \rule[\Fraiseheight]{0.5\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \raisebox{\temp}{\ensuremath{\bguq}}% \kern-\Fbguqwidth% \raisebox{\temp}% {\makebox[\Fbguqwidth]{\ensuremath{\scriptstyle\mathfrak{#2}}}}% \setlength{\temp}{.5\Fbaselength}% \addtolength{\temp}{-0.5\Fbguqwidth}% \addtolength{\temp}{-2\Flinewidth}% \addtolength{\temp}{-\Fnegsep}% \rule[\Fraiseheight]{0.5\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \rule[\Fraiseheight]{\Fnegsep}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \setlength{\temp}{.5\Fbaselength}% \addtolength{\temp}{-0.5\Fbguqwidth}% \addtolength{\temp}{-2\Flinewidth}% \addtolength{\temp}{-\Fnegsep}% \rule[\Fraiseheight]{0.5\temp}{\Flinewidth}% \setlength{\Fbaselength}{\Funitlength}% \hskip\Fspace% }% {% \setlength{\Funitlength}{\Fbaselength}% \setlength{\Fbaselength}{#1\Fbaselength}% \unskip% \setlength{\temp}{.5\Fbaselength}% \addtolength{\temp}{-0.5\Fquantwidth}% \addtolength{\temp}{-2\Flinewidth}% \addtolength{\temp}{-\Fnegsep}% \rule[\Fraiseheight]{0.5\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \rule[\Fraiseheight]{\Fnegsep}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \setlength{\temp}{.5\Fbaselength}% \addtolength{\temp}{-0.5\Fquantwidth}% \addtolength{\temp}{-2\Flinewidth}% \addtolength{\temp}{-\Fnegsep}% \rule[\Fraiseheight]{0.5\temp}{\Flinewidth}% \setlength{\unitlength}{\Fquantwidth}% \raisebox{\Fraiseheight}{% \begin{picture}(1,0)(0,0)% \linethickness{\Flinewidth}% \qbezier(0,0)(0.5,-0.6666)(1,0)% \end{picture}}% \kern-\Fquantwidth% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \raisebox{\temp}% {\makebox[\Fquantwidth]{\ensuremath{\scriptstyle\mathfrak{#2}}}}% \setlength{\temp}{.5\Fbaselength}% \addtolength{\temp}{-0.5\Fquantwidth}% \addtolength{\temp}{-2\Flinewidth}% \addtolength{\temp}{-\Fnegsep}% \rule[\Fraiseheight]{0.5\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \rule[\Fraiseheight]{\Fnegsep}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \setlength{\temp}{.5\Fbaselength}% \addtolength{\temp}{-0.5\Fquantwidth}% \addtolength{\temp}{-2\Flinewidth}% \addtolength{\temp}{-\Fnegsep}% \rule[\Fraiseheight]{0.5\temp}{\Flinewidth}% \setlength{\Fbaselength}{\Funitlength}% \hskip\Fspace% }% }% % asserted universal quantifier: \newcommand{\Faquant}[2][1]% {% \ifthenelse{\boolean{bguq}}% {% \setlength{\Funitlength}{\Fbaselength}% \setlength{\Fbaselength}{#1\Fbaselength}% \unskip% \setlength{\temp}{2\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \rule{\Fassertwidth}{\temp}% \setlength{\temp}{.5\Fbaselength}% \addtolength{\temp}{-0.5\Fbguqwidth}% \addtolength{\temp}{-\Fassertwidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \raisebox{\temp}{\ensuremath{\bguq}}% \kern-\Fbguqwidth% \raisebox{\temp}% {\makebox[\Fbguqwidth]{\ensuremath{\scriptstyle\mathfrak{#2}}}}% \setlength{\temp}{.5\Fbaselength}% \addtolength{\temp}{-0.5\Fbguqwidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\Fbaselength}{\Funitlength}% \hskip\Fspace% }% {% \setlength{\Funitlength}{\Fbaselength}% \setlength{\Fbaselength}{#1\Fbaselength}% \unskip% \setlength{\temp}{2\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \rule{\Fassertwidth}{\temp}% \setlength{\temp}{.5\Fbaselength}% \addtolength{\temp}{-0.5\Fquantwidth}% \addtolength{\temp}{-\Fassertwidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\unitlength}{\Fquantwidth}% \raisebox{\Fraiseheight}{% \begin{picture}(1,0)(0,0)% \linethickness{\Flinewidth}% \qbezier(0,0)(0.5,-0.6666)(1,0)% \end{picture}}% \kern-\Fquantwidth% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \raisebox{\temp}% {\makebox[\Fquantwidth]{\ensuremath{\scriptstyle\mathfrak{#2}}}}% \setlength{\temp}{.5\Fbaselength}% \addtolength{\temp}{-0.5\Fquantwidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\Fbaselength}{\Funitlength}% \hskip\Fspace% }% }% % asserted negated universal quantifier \newcommand{\Fanquant}[2][1]% {% \ifthenelse{\boolean{bguq}}% {% \setlength{\Funitlength}{\Fbaselength}% \setlength{\Fbaselength}{#1\Fbaselength}% \unskip% \setlength{\temp}{2\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \rule{\Fassertwidth}{\temp}% \setlength{\temp}{.25\Fbaselength}% \addtolength{\temp}{-0.25\Fbguqwidth}% \addtolength{\temp}{-0.5\Flinewidth}% \addtolength{\temp}{-\Fassertwidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \setlength{\temp}{.25\Fbaselength}% \addtolength{\temp}{-0.25\Fbguqwidth}% \addtolength{\temp}{-0.5\Flinewidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \raisebox{\temp}{\ensuremath{\bguq}}% \kern-\Fbguqwidth% \raisebox{\temp}% {\makebox[\Fbguqwidth]{\ensuremath{\scriptstyle\mathfrak{#2}}}}% \setlength{\temp}{.5\Fbaselength}% \addtolength{\temp}{-0.5\Fbguqwidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\Fbaselength}{\Funitlength}% \hskip\Fspace% }% {% \setlength{\Funitlength}{\Fbaselength}% \setlength{\Fbaselength}{#1\Fbaselength}% \unskip% \setlength{\temp}{2\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \rule{\Fassertwidth}{\temp}% \setlength{\temp}{.25\Fbaselength}% \addtolength{\temp}{-0.25\Fquantwidth}% \addtolength{\temp}{-0.5\Flinewidth}% \addtolength{\temp}{-\Fassertwidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \setlength{\temp}{.25\Fbaselength}% \addtolength{\temp}{-0.25\Fquantwidth}% \addtolength{\temp}{-0.5\Flinewidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\unitlength}{\Fquantwidth}% \raisebox{\Fraiseheight}{% \begin{picture}(1,0)(0,0)% \linethickness{\Flinewidth}% \qbezier(0,0)(0.5,-0.6666)(1,0)% \end{picture}}% \kern-\Fquantwidth% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \raisebox{\temp}% {\makebox[\Fquantwidth]{\ensuremath{\scriptstyle\mathfrak{#2}}}}% \setlength{\temp}{.5\Fbaselength}% \addtolength{\temp}{-0.5\Fquantwidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\Fbaselength}{\Funitlength}% \hskip\Fspace% }% }% % asserted twice negated universal quantifier \newcommand{\Fannquant}[2][1]% {% \ifthenelse{\boolean{bguq}}% {% \setlength{\Funitlength}{\Fbaselength}% \setlength{\Fbaselength}{#1\Fbaselength}% \unskip% \setlength{\temp}{2\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \rule{\Fassertwidth}{\temp}% \setlength{\temp}{.25\Fbaselength}% \addtolength{\temp}{-0.25\Fbguqwidth}% \addtolength{\temp}{-\Flinewidth}% \addtolength{\temp}{-0.5\Fnegsep}% \addtolength{\temp}{-\Fassertwidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \rule[\Fraiseheight]{\Fnegsep}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \setlength{\temp}{.25\Fbaselength}% \addtolength{\temp}{-0.25\Fbguqwidth}% \addtolength{\temp}{-\Flinewidth}% \addtolength{\temp}{-0.5\Fnegsep}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \raisebox{\temp}{\ensuremath{\bguq}}% \kern-\Fbguqwidth% \raisebox{\temp}% {\makebox[\Fbguqwidth]{\ensuremath{\scriptstyle\mathfrak{#2}}}}% \setlength{\temp}{.5\Fbaselength}% \addtolength{\temp}{-0.5\Fbguqwidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\Fbaselength}{\Funitlength}% \hskip\Fspace% }% {% \setlength{\Funitlength}{\Fbaselength}% \setlength{\Fbaselength}{#1\Fbaselength}% \unskip% \setlength{\temp}{2\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \rule{\Fassertwidth}{\temp}% \setlength{\temp}{.25\Fbaselength}% \addtolength{\temp}{-0.25\Fquantwidth}% \addtolength{\temp}{-\Flinewidth}% \addtolength{\temp}{-0.5\Fnegsep}% \addtolength{\temp}{-\Fassertwidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \rule[\Fraiseheight]{\Fnegsep}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \setlength{\temp}{.25\Fbaselength}% \addtolength{\temp}{-0.25\Fquantwidth}% \addtolength{\temp}{-\Flinewidth}% \addtolength{\temp}{-0.5\Fnegsep}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\unitlength}{\Fquantwidth}% \raisebox{\Fraiseheight}{% \begin{picture}(1,0)(0,0)% \linethickness{\Flinewidth}% \qbezier(0,0)(0.5,-0.6666)(1,0)% \end{picture}}% \kern-\Fquantwidth% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \raisebox{\temp}% {\makebox[\Fquantwidth]{\ensuremath{\scriptstyle\mathfrak{#2}}}}% \setlength{\temp}{.5\Fbaselength}% \addtolength{\temp}{-0.5\Fquantwidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\Fbaselength}{\Funitlength}% \hskip\Fspace% }% }% % asserted universal quantifier with negated content: \newcommand{\Faquantn}[2][1]% {% \ifthenelse{\boolean{bguq}}% {% \setlength{\Funitlength}{\Fbaselength}% \setlength{\Fbaselength}{#1\Fbaselength}% \unskip% \setlength{\temp}{2\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \rule{\Fassertwidth}{\temp}% \setlength{\temp}{.5\Fbaselength}% \addtolength{\temp}{-0.5\Fbguqwidth}% \addtolength{\temp}{-\Fassertwidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \raisebox{\temp}{\ensuremath{\bguq}}% \kern-\Fbguqwidth% \raisebox{\temp}% {\makebox[\Fbguqwidth]{\ensuremath{\scriptstyle\mathfrak{#2}}}}% \setlength{\temp}{0.25\Fbaselength}% \addtolength{\temp}{-0.25\Fbguqwidth}% \addtolength{\temp}{-0.5\Flinewidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \setlength{\temp}{.25\Fbaselength}% \addtolength{\temp}{-0.25\Fbguqwidth}% \addtolength{\temp}{-0.5\Flinewidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\Fbaselength}{\Funitlength}% \hskip\Fspace% }% {% \setlength{\Funitlength}{\Fbaselength}% \setlength{\Fbaselength}{#1\Fbaselength}% \unskip% \setlength{\temp}{2\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \rule{\Fassertwidth}{\temp}% \setlength{\temp}{.5\Fbaselength}% \addtolength{\temp}{-0.5\Fquantwidth}% \addtolength{\temp}{-\Fassertwidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\unitlength}{\Fquantwidth}% \raisebox{\Fraiseheight}{% \begin{picture}(1,0)(0,0)% \linethickness{\Flinewidth}% \qbezier(0,0)(0.5,-0.6666)(1,0)% \end{picture}}% \kern-\Fquantwidth% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \raisebox{\temp}% {\makebox[\Fquantwidth]{\ensuremath{\scriptstyle\mathfrak{#2}}}}% \setlength{\temp}{.25\Fbaselength}% \addtolength{\temp}{-0.25\Fquantwidth}% \addtolength{\temp}{-0.5\Flinewidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \setlength{\temp}{.25\Fbaselength}% \addtolength{\temp}{-0.25\Fquantwidth}% \addtolength{\temp}{-0.5\Flinewidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\Fbaselength}{\Funitlength}% \hskip\Fspace% }% }% % asserted universal quantifier with twice negated content: \newcommand{\Faquantnn}[2][1]% {% \ifthenelse{\boolean{bguq}}% {% \setlength{\Funitlength}{\Fbaselength}% \setlength{\Fbaselength}{#1\Fbaselength}% \unskip% \setlength{\temp}{2\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \rule{\Fassertwidth}{\temp}% \setlength{\temp}{.5\Fbaselength}% \addtolength{\temp}{-0.5\Fbguqwidth}% \addtolength{\temp}{-\Fassertwidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \raisebox{\temp}{\ensuremath{\bguq}}% \kern-\Fbguqwidth% \raisebox{\temp}% {\makebox[\Fbguqwidth]{\ensuremath{\scriptstyle\mathfrak{#2}}}}% \setlength{\temp}{.5\Fbaselength}% \addtolength{\temp}{-0.5\Fbguqwidth}% \addtolength{\temp}{-2\Flinewidth}% \addtolength{\temp}{-\Fnegsep}% \rule[\Fraiseheight]{0.5\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \rule[\Fraiseheight]{\Fnegsep}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \setlength{\temp}{.5\Fbaselength}% \addtolength{\temp}{-0.5\Fbguqwidth}% \addtolength{\temp}{-2\Flinewidth}% \addtolength{\temp}{-\Fnegsep}% \rule[\Fraiseheight]{0.5\temp}{\Flinewidth}% \setlength{\Fbaselength}{\Funitlength}% \hskip\Fspace% }% {% \setlength{\Funitlength}{\Fbaselength}% \setlength{\Fbaselength}{#1\Fbaselength}% \unskip% \setlength{\temp}{2\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \rule{\Fassertwidth}{\temp}% \setlength{\temp}{.5\Fbaselength}% \addtolength{\temp}{-0.5\Fquantwidth}% \addtolength{\temp}{-\Fassertwidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\unitlength}{\Fquantwidth}% \raisebox{\Fraiseheight}{% \begin{picture}(1,0)(0,0)% \linethickness{\Flinewidth}% \qbezier(0,0)(0.5,-0.6666)(1,0)% \end{picture}}% \kern-\Fquantwidth% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \raisebox{\temp}% {\makebox[\Fquantwidth]{\ensuremath{\scriptstyle\mathfrak{#2}}}}% \setlength{\temp}{.5\Fbaselength}% \addtolength{\temp}{-0.5\Fquantwidth}% \addtolength{\temp}{-2\Flinewidth}% \addtolength{\temp}{-\Fnegsep}% \rule[\Fraiseheight]{0.5\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \rule[\Fraiseheight]{\Fnegsep}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \setlength{\temp}{.5\Fbaselength}% \addtolength{\temp}{-0.5\Fquantwidth}% \addtolength{\temp}{-2\Flinewidth}% \addtolength{\temp}{-\Fnegsep}% \rule[\Fraiseheight]{0.5\temp}{\Flinewidth}% \setlength{\Fbaselength}{\Funitlength}% \hskip\Fspace% }% }% % asserted negated universal quantifier with negated content: \newcommand{\Fanquantn}[2][1]% {% \ifthenelse{\boolean{bguq}}% {% \setlength{\Funitlength}{\Fbaselength}% \setlength{\Fbaselength}{#1\Fbaselength}% \unskip% \setlength{\temp}{2\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \rule{\Fassertwidth}{\temp}% \setlength{\temp}{.25\Fbaselength}% \addtolength{\temp}{-0.25\Fbguqwidth}% \addtolength{\temp}{-0.5\Flinewidth}% \addtolength{\temp}{-\Fassertwidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \setlength{\temp}{.25\Fbaselength}% \addtolength{\temp}{-0.25\Fbguqwidth}% \addtolength{\temp}{-0.5\Flinewidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \raisebox{\temp}{\ensuremath{\bguq}}% \kern-\Fbguqwidth% \raisebox{\temp}% {\makebox[\Fbguqwidth]{\ensuremath{\scriptstyle\mathfrak{#2}}}}% \setlength{\temp}{0.25\Fbaselength}% \addtolength{\temp}{-0.25\Fbguqwidth}% \addtolength{\temp}{-0.5\Flinewidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \setlength{\temp}{.25\Fbaselength}% \addtolength{\temp}{-0.25\Fbguqwidth}% \addtolength{\temp}{-0.5\Flinewidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\Fbaselength}{\Funitlength}% \hskip\Fspace% }% {% \setlength{\Funitlength}{\Fbaselength}% \setlength{\Fbaselength}{#1\Fbaselength}% \unskip% \setlength{\temp}{2\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \rule{\Fassertwidth}{\temp}% \setlength{\temp}{.25\Fbaselength}% \addtolength{\temp}{-0.25\Fquantwidth}% \addtolength{\temp}{-0.5\Flinewidth}% \addtolength{\temp}{-\Fassertwidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \setlength{\temp}{.25\Fbaselength}% \addtolength{\temp}{-0.25\Fquantwidth}% \addtolength{\temp}{-0.5\Flinewidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\unitlength}{\Fquantwidth}% \raisebox{\Fraiseheight}{% \begin{picture}(1,0)(0,0)% \linethickness{\Flinewidth}% \qbezier(0,0)(0.5,-0.6666)(1,0)% \end{picture}}% \kern-\Fquantwidth% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \raisebox{\temp}% {\makebox[\Fquantwidth]{\ensuremath{\scriptstyle\mathfrak{#2}}}}% \setlength{\temp}{.25\Fbaselength}% \addtolength{\temp}{-0.25\Fquantwidth}% \addtolength{\temp}{-0.5\Flinewidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \setlength{\temp}{.25\Fbaselength}% \addtolength{\temp}{-0.25\Fquantwidth}% \addtolength{\temp}{-0.5\Flinewidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\Fbaselength}{\Funitlength}% \hskip\Fspace% }% }% % asserted negated universal quantifier with twice negated content: \newcommand{\Fanquantnn}[2][1]% {% \ifthenelse{\boolean{bguq}}% {% \setlength{\Funitlength}{\Fbaselength}% \setlength{\Fbaselength}{#1\Fbaselength}% \unskip% \setlength{\temp}{2\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \rule{\Fassertwidth}{\temp}% \setlength{\temp}{.25\Fbaselength}% \addtolength{\temp}{-0.25\Fbguqwidth}% \addtolength{\temp}{-0.5\Flinewidth}% \addtolength{\temp}{-\Fassertwidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \setlength{\temp}{.25\Fbaselength}% \addtolength{\temp}{-0.25\Fbguqwidth}% \addtolength{\temp}{-0.5\Flinewidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \raisebox{\temp}{\ensuremath{\bguq}}% \kern-\Fbguqwidth% \raisebox{\temp}% {\makebox[\Fbguqwidth]{\ensuremath{\scriptstyle\mathfrak{#2}}}}% \setlength{\temp}{.5\Fbaselength}% \addtolength{\temp}{-0.5\Fbguqwidth}% \addtolength{\temp}{-2\Flinewidth}% \addtolength{\temp}{-\Fnegsep}% \rule[\Fraiseheight]{0.5\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \rule[\Fraiseheight]{\Fnegsep}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \setlength{\temp}{.5\Fbaselength}% \addtolength{\temp}{-0.5\Fbguqwidth}% \addtolength{\temp}{-2\Flinewidth}% \addtolength{\temp}{-\Fnegsep}% \rule[\Fraiseheight]{0.5\temp}{\Flinewidth}% \setlength{\Fbaselength}{\Funitlength}% \hskip\Fspace% }% {% \setlength{\Funitlength}{\Fbaselength}% \setlength{\Fbaselength}{#1\Fbaselength}% \unskip% \setlength{\temp}{2\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \rule{\Fassertwidth}{\temp}% \setlength{\temp}{.25\Fbaselength}% \addtolength{\temp}{-0.25\Fquantwidth}% \addtolength{\temp}{-0.5\Flinewidth}% \addtolength{\temp}{-\Fassertwidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \setlength{\temp}{.25\Fbaselength}% \addtolength{\temp}{-0.25\Fquantwidth}% \addtolength{\temp}{-0.5\Flinewidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\unitlength}{\Fquantwidth}% \raisebox{\Fraiseheight}{% \begin{picture}(1,0)(0,0)% \linethickness{\Flinewidth}% \qbezier(0,0)(0.5,-0.6666)(1,0)% \end{picture}}% \kern-\Fquantwidth% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \raisebox{\temp}% {\makebox[\Fquantwidth]{\ensuremath{\scriptstyle\mathfrak{#2}}}}% \setlength{\temp}{.5\Fbaselength}% \addtolength{\temp}{-0.5\Fquantwidth}% \addtolength{\temp}{-2\Flinewidth}% \addtolength{\temp}{-\Fnegsep}% \rule[\Fraiseheight]{0.5\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \rule[\Fraiseheight]{\Fnegsep}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \setlength{\temp}{.5\Fbaselength}% \addtolength{\temp}{-0.5\Fquantwidth}% \addtolength{\temp}{-2\Flinewidth}% \addtolength{\temp}{-\Fnegsep}% \rule[\Fraiseheight]{0.5\temp}{\Flinewidth}% \setlength{\Fbaselength}{\Funitlength}% \hskip\Fspace% }% }% % asserted twice negated universal quantifier with negated content: \newcommand{\Fannquantn}[2][1]% {% \ifthenelse{\boolean{bguq}}% {% \setlength{\Funitlength}{\Fbaselength}% \setlength{\Fbaselength}{#1\Fbaselength}% \unskip% \setlength{\temp}{2\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \rule{\Fassertwidth}{\temp}% \setlength{\temp}{.25\Fbaselength}% \addtolength{\temp}{-0.25\Fbguqwidth}% \addtolength{\temp}{-\Flinewidth}% \addtolength{\temp}{-0.5\Fnegsep}% \addtolength{\temp}{-\Fassertwidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \rule[\Fraiseheight]{\Fnegsep}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \setlength{\temp}{.25\Fbaselength}% \addtolength{\temp}{-0.25\Fbguqwidth}% \addtolength{\temp}{-\Flinewidth}% \addtolength{\temp}{-0.5\Fnegsep}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \raisebox{\temp}{\ensuremath{\bguq}}% \kern-\Fbguqwidth% \raisebox{\temp}% {\makebox[\Fbguqwidth]{\ensuremath{\scriptstyle\mathfrak{#2}}}}% \setlength{\temp}{0.25\Fbaselength}% \addtolength{\temp}{-0.25\Fbguqwidth}% \addtolength{\temp}{-0.5\Flinewidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \setlength{\temp}{.25\Fbaselength}% \addtolength{\temp}{-0.25\Fbguqwidth}% \addtolength{\temp}{-0.5\Flinewidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\Fbaselength}{\Funitlength}% \hskip\Fspace% }% {% \setlength{\Funitlength}{\Fbaselength}% \setlength{\Fbaselength}{#1\Fbaselength}% \unskip% \setlength{\temp}{2\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \rule{\Fassertwidth}{\temp}% \setlength{\temp}{.25\Fbaselength}% \addtolength{\temp}{-0.25\Fquantwidth}% \addtolength{\temp}{-\Flinewidth}% \addtolength{\temp}{-0.5\Fnegsep}% \addtolength{\temp}{-\Fassertwidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \rule[\Fraiseheight]{\Fnegsep}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \setlength{\temp}{.25\Fbaselength}% \addtolength{\temp}{-0.25\Fquantwidth}% \addtolength{\temp}{-\Flinewidth}% \addtolength{\temp}{-0.5\Fnegsep}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\unitlength}{\Fquantwidth}% \raisebox{\Fraiseheight}{% \begin{picture}(1,0)(0,0)% \linethickness{\Flinewidth}% \qbezier(0,0)(0.5,-0.6666)(1,0)% \end{picture}}% \kern-\Fquantwidth% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \raisebox{\temp}% {\makebox[\Fquantwidth]{\ensuremath{\scriptstyle\mathfrak{#2}}}}% \setlength{\temp}{.25\Fbaselength}% \addtolength{\temp}{-0.25\Fquantwidth}% \addtolength{\temp}{-0.5\Flinewidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \setlength{\temp}{.25\Fbaselength}% \addtolength{\temp}{-0.25\Fquantwidth}% \addtolength{\temp}{-0.5\Flinewidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\Fbaselength}{\Funitlength}% \hskip\Fspace% }% }% % asserted twice negated universal quantifier with twice negated content: \newcommand{\Fannquantnn}[2][1]% {% \ifthenelse{\boolean{bguq}}% {% \setlength{\Funitlength}{\Fbaselength}% \setlength{\Fbaselength}{#1\Fbaselength}% \unskip% \setlength{\temp}{2\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \rule{\Fassertwidth}{\temp}% \setlength{\temp}{.25\Fbaselength}% \addtolength{\temp}{-0.25\Fbguqwidth}% \addtolength{\temp}{-\Flinewidth}% \addtolength{\temp}{-0.5\Fnegsep}% \addtolength{\temp}{-\Fassertwidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \rule[\Fraiseheight]{\Fnegsep}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \setlength{\temp}{.25\Fbaselength}% \addtolength{\temp}{-0.25\Fbguqwidth}% \addtolength{\temp}{-\Flinewidth}% \addtolength{\temp}{-0.5\Fnegsep}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \raisebox{\temp}{\ensuremath{\bguq}}% \kern-\Fbguqwidth% \raisebox{\temp}% {\makebox[\Fbguqwidth]{\ensuremath{\scriptstyle\mathfrak{#2}}}}% \setlength{\temp}{.5\Fbaselength}% \addtolength{\temp}{-0.5\Fbguqwidth}% \addtolength{\temp}{-2\Flinewidth}% \addtolength{\temp}{-\Fnegsep}% \rule[\Fraiseheight]{0.5\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \rule[\Fraiseheight]{\Fnegsep}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \setlength{\temp}{.5\Fbaselength}% \addtolength{\temp}{-0.5\Fbguqwidth}% \addtolength{\temp}{-2\Flinewidth}% \addtolength{\temp}{-\Fnegsep}% \rule[\Fraiseheight]{0.5\temp}{\Flinewidth}% \setlength{\Fbaselength}{\Funitlength}% \hskip\Fspace% }% {% \setlength{\Funitlength}{\Fbaselength}% \setlength{\Fbaselength}{#1\Fbaselength}% \unskip% \setlength{\temp}{2\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \rule{\Fassertwidth}{\temp}% \setlength{\temp}{.25\Fbaselength}% \addtolength{\temp}{-0.25\Fquantwidth}% \addtolength{\temp}{-\Flinewidth}% \addtolength{\temp}{-0.5\Fnegsep}% \addtolength{\temp}{-\Fassertwidth}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \rule[\Fraiseheight]{\Fnegsep}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \setlength{\temp}{.25\Fbaselength}% \addtolength{\temp}{-0.25\Fquantwidth}% \addtolength{\temp}{-\Flinewidth}% \addtolength{\temp}{-0.5\Fnegsep}% \rule[\Fraiseheight]{\temp}{\Flinewidth}% \setlength{\unitlength}{\Fquantwidth}% \raisebox{\Fraiseheight}{% \begin{picture}(1,0)(0,0)% \linethickness{\Flinewidth}% \qbezier(0,0)(0.5,-0.6666)(1,0)% \end{picture}}% \kern-\Fquantwidth% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \raisebox{\temp}% {\makebox[\Fquantwidth]{\ensuremath{\scriptstyle\mathfrak{#2}}}}% \setlength{\temp}{.5\Fbaselength}% \addtolength{\temp}{-0.5\Fquantwidth}% \addtolength{\temp}{-2\Flinewidth}% \addtolength{\temp}{-\Fnegsep}% \rule[\Fraiseheight]{0.5\temp}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \rule[\Fraiseheight]{\Fnegsep}{\Flinewidth}% \setlength{\temp}{\Fraiseheight}% \addtolength{\temp}{\Flinewidth}% \addtolength{\temp}{-\Fnegshort}% \rule[\Fnegshort]{\Flinewidth}{\temp}% \setlength{\temp}{.5\Fbaselength}% \addtolength{\temp}{-0.5\Fquantwidth}% \addtolength{\temp}{-2\Flinewidth}% \addtolength{\temp}{-\Fnegsep}% \rule[\Fraiseheight]{0.5\temp}{\Flinewidth}% \setlength{\Fbaselength}{\Funitlength}% \hskip\Fspace% }% }%