|
Warning: this is an htmlized version!
The original is here, and the conversion rules are here. |
% (find-LATEX "2025shapes-basic-calculus.tex")
% (defun c () (interactive) (find-LATEXsh "lualatex -record 2025shapes-basic-calculus.tex" :end))
% (defun C () (interactive) (find-LATEXsh "lualatex 2025shapes-basic-calculus.tex" "Success!!!"))
% (defun D () (interactive) (find-pdf-page "~/LATEX/2025shapes-basic-calculus.pdf"))
% (defun d () (interactive) (find-pdftools-page "~/LATEX/2025shapes-basic-calculus.pdf"))
% (defun e () (interactive) (find-LATEX "2025shapes-basic-calculus.tex"))
% (defun o () (interactive) (find-LATEX "2025adapting-lean-tuts.tex"))
% (defun u () (interactive) (find-latex-upload-links "2025shapes-basic-calculus"))
% (defun v () (interactive) (find-2a '(e) '(d)))
% (defun d0 () (interactive) (find-ebuffer "2025shapes-basic-calculus.pdf"))
% (defun cv () (interactive) (C) (ee-kill-this-buffer) (v) (g))
% (defun oe () (interactive) (find-2a '(o) '(e)))
% (code-eec-LATEX "2025shapes-basic-calculus")
% (find-pdf-page "~/LATEX/2025shapes-basic-calculus.pdf")
% (find-sh0 "cp -v ~/LATEX/2025shapes-basic-calculus.pdf /tmp/")
% (find-sh0 "cp -v ~/LATEX/2025shapes-basic-calculus.pdf /tmp/pen/")
% (find-xournalpp "/tmp/2025shapes-basic-calculus.pdf")
% file:///home/edrx/LATEX/2025shapes-basic-calculus.pdf
% file:///tmp/2025shapes-basic-calculus.pdf
% file:///tmp/pen/2025shapes-basic-calculus.pdf
% http://anggtwu.net/LATEX/2025shapes-basic-calculus.pdf
% (find-LATEX "2019.mk")
% (find-Deps1-links "Caepro5 Piecewise2 Maxima2")
% (find-Deps1-cps "Caepro5 Piecewise2 Maxima2")
% (find-Deps1-anggs "Caepro5 Piecewise2 Maxima2")
% (find-MM-aula-links "2025shapes-basic-calculus" "2" "sbc" "sbc")
% «.screenshotdimens» (to "screenshotdimens")
% «.geometries» (to "geometries")
% «.screenshotgeometry» (to "screenshotgeometry")
% «.defs» (to "defs")
% «.defs-T-and-B» (to "defs-T-and-B")
% «.defs-caepro» (to "defs-caepro")
% «.defs-pict2e» (to "defs-pict2e")
% «.defs-maxima» (to "defs-maxima")
% «.defs-V» (to "defs-V")
% «.defs-S» (to "defs-S")
% «.title» (to "title")
% «.links» (to "links")
% «.CWM» (to "CWM")
% «.aqui-e-agora» (to "aqui-e-agora")
% «.example-6-defs» (to "example-6-defs")
% «.example-6-with» (to "example-6-with")
% «.example-6-just-5» (to "example-6-just-5")
% «.example-6-just-6» (to "example-6-just-6")
% «.example-6-just-7» (to "example-6-just-7")
% «.example-6-just-9» (to "example-6-just-9")
% «.example-6-just-10» (to "example-6-just-10")
% «.eqnp» (to "eqnp")
\documentclass[oneside,12pt]{article}
\usepackage[colorlinks,citecolor=DarkRed,urlcolor=DarkRed]{hyperref} % (find-es "tex" "hyperref")
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{pict2e}
\usepackage[x11names,svgnames]{xcolor} % (find-es "tex" "xcolor")
\usepackage{colorweb} % (find-es "tex" "colorweb")
%\usepackage{tikz}
%
% (find-LATEX "dednat7-test1.tex")
%\usepackage{proof} % For derivation trees ("%:" lines)
%\input diagxy % For 2D diagrams ("%D" lines)
%\xyoption{curve} % For the ".curve=" feature in 2D diagrams
%
\usepackage{edrx21} % (find-LATEX "edrx21.sty")
\input edrxaccents.tex % (find-LATEX "edrxaccents.tex")
\input edrx21chars.tex % (find-LATEX "edrx21chars.tex")
\input edrxheadfoot.tex % (find-LATEX "edrxheadfoot.tex")
\input edrxgac2.tex % (find-LATEX "edrxgac2.tex")
%
% «screenshotdimens» (to ".screenshotdimens")
% Based on: (emacsconf2021a "screenshotdimens")
\newdimen\slidewidth
\slidewidth=15cm
\slidewidth=10.5cm
\slidewidth=16cm
\usepackage[paperwidth=\slidewidth,
paperheight=0.625\slidewidth,
top=1.5cm, bottom=.25cm, left=1cm, right=1cm, includefoot
]{geometry}
%
\begin{document}
% ____ _ _
% / ___| ___ ___ _ __ ___ ___| |_ _ __(_) ___ ___
% | | _ / _ \/ _ \| '_ ` _ \ / _ \ __| '__| |/ _ \/ __|
% | |_| | __/ (_) | | | | | | __/ |_| | | | __/\__ \
% \____|\___|\___/|_| |_| |_|\___|\__|_| |_|\___||___/
%
% «geometries» (to ".geometries")
% «screenshotgeometry» (to ".screenshotgeometry")
% (find-LATEX "2021emacsconf.tex" "geometries")
% (find-es "tex" "pagestyle")
\savegeometry{original}
\newgeometry{top=0cm, left=0cm, right=0cm, ignoreheadfoot, bottom=0cm}
\savegeometry{screenshot}
\loadgeometry{original}
%
\def\originalgeometry{
\loadgeometry{original}
\setlength{\parindent}{18pt}
\pagestyle{headings}}
\def\screenshotgeometry{
\loadgeometry{screenshot}
\setlength{\parindent}{0cm}
\pagestyle{empty}}
% «defs» (to ".defs")
% (find-LATEX "edrx21defs.tex" "colors")
% (find-LATEX "edrx21.sty")
\def\drafturl{http://anggtwu.net/LATEX/2025-1-C2.pdf}
\def\drafturl{http://anggtwu.net/2025.1-C2.html}
\def\draftfooter{\tiny \href{\drafturl}{\jobname{}} \ColorBrown{\shorttoday{} \hours}}
% (find-LATEX "2024-1-C2-carro.tex" "defs-caepro")
% (find-LATEX "2024-1-C2-carro.tex" "defs-pict2e")
\catcode`\^^J=10
\directlua{dofile "dednat7load.lua"} % (find-LATEX "dednat7load.lua")
\directlua{dednat7preamble()} % (find-angg "LUA/DednatPreamble1.lua")
\directlua{dednat7oldheads()} % (find-angg "LUA/Dednat7oldheads.lua")
% «defs-T-and-B» (to ".defs-T-and-B")
\long\def\ColorDarkOrange#1{{\color{orange!90!black}#1}}
\def\T(Total: #1 pts){{\bf(Total: #1)}}
\def\T(Total: #1 pts){{\bf(Total: #1 pts)}}
\def\T(Total: #1 pts){\ColorRed{\bf(Total: #1 pts)}}
\def\B (#1 pts){\ColorDarkOrange{\bf(#1 pts)}}
% «defs-caepro» (to ".defs-caepro")
%L dofile "Caepro5.lua" -- (find-angg "LUA/Caepro5.lua" "LaTeX")
\def\Caurl #1{\expr{Caurl("#1")}}
\def\Cahref#1#2{\href{\Caurl{#1}}{#2}}
\def\Ca #1{\Cahref{#1}{#1}}
% «defs-pict2e» (to ".defs-pict2e")
%L dofile "Piecewise2.lua" -- (find-LATEX "Piecewise2.lua")
%L --dofile "Escadas1.lua" -- (find-LATEX "Escadas1.lua")
\def\pictgridstyle{\color{GrayPale}\linethickness{0.3pt}}
\def\pictaxesstyle{\linethickness{0.5pt}}
\def\pictnaxesstyle{\color{GrayPale}\linethickness{0.5pt}}
\celllower=2.5pt
% «defs-maxima» (to ".defs-maxima")
%L dofile "Maxima2.lua" -- (find-angg "LUA/Maxima2.lua")
\pu
% «defs-V» (to ".defs-V")
%L --- See: (find-angg "LUA/MiniV1.lua" "problem-with-V")
%L V = MiniV
%L v = V.fromab
\pu
% «defs-S» (to ".defs-S")
\input 2025-1-C2-S-defs.tex % (find-LATEX "2025-1-C2-S-defs.tex")
% _____ _ _ _
% |_ _(_) |_| | ___ _ __ __ _ __ _ ___
% | | | | __| |/ _ \ | '_ \ / _` |/ _` |/ _ \
% | | | | |_| | __/ | |_) | (_| | (_| | __/
% |_| |_|\__|_|\___| | .__/ \__,_|\__, |\___|
% |_| |___/
%
% «title» (to ".title")
% (sbcp 1 "title")
% (sbca "title")
\thispagestyle{empty}
\begin{center}
\vspace*{0.5cm}
\begin{tabular}{c}
\phantom{a}\\[-15pt]
{\Large {\bf On the Shapes of Proofs}} \\[1.25pt]
{\Large {\bf in Basic Calculus}} \\[1pt]
\\[-9pt]
\ColorGray{(Preliminary version)}\\[-5pt]
\\[-9pt]
{\tiny\url{http://anggtwu.net/math-b.html\#2025-sbc}}\\[8pt]
Eduardo Ochs \\
%Serra Negra, 2022may13 \\
\end{tabular}
\end{center}
\newpage
% «links» (to ".links")
% (sbcp 2 "links")
% (sbca "links")
%
% {\bf Links}
%
% \scalebox{0.6}{\def\colwidth{16cm}\firstcol{
% }\anothercol{
% }}
\newpage
% «CWM» (to ".CWM")
% (sbcp 2 "CWM")
% (sbca "CWM")
{\bf CWM}
\scalebox{0.9}{\def\colwidth{9cm}\firstcol{
% (find-books "__cats/__cats.el" "maclane" "84" "Then since G is a functor and")
From CWM, p.84:
$$\begin{array}{rcll}
φθg &=& Gε_a ∘ GFg ∘ η_x \\
&=& Gε_a ∘ η_{Ga} ∘ g \\
&=& g \\
\end{array}
$$
$$\begin{array}{rcll}
φθg &=& φ(ε_a ∘ Fg) & \text{by $def_θ$} \\
&=& G(ε_a ∘ Fg) ∘ η_x & \text{by $def_φ.$} \\
&=& Gε_a ∘ GFg ∘ η_x & \text{by $respcomp_G$} \\
&=& Gε_a ∘ η_{Ga} ∘ g & \text{by $sqcond_η$} \\
&=& \id_{Ga} ∘ g & \text{by $Gε∘ηG=1$} \\
&=& g \\
\end{array}
$$
}\anothercol{
}}
\newpage
% «aqui-e-agora» (to ".aqui-e-agora")
% (sbcp 3 "aqui-e-agora")
% (sbca "aqui-e-agora")
{\bf O aqui e agora não existe mais}
% (find-fline "~/LATEX/2025shapes-basic-calculus/")
% (find-THfile "2025-antidoto-para-zumbis.blogme" "goffman__capa_e_zumbis.jpg")
% (find-fline "~/IMAGES/" "goffman__capa_e_zumbis.jpg")
% (find-fline "~/IMAGES/goffman__capa_e_zumbis.jpg")
% (find-books "__politics/__politics.el" "graeber" "122" "please pass the salt")
\newpage
% «eqnp» (to ".eqnp")
% (sbcp 4 "eqnp")
% (sbca "eqnp")
% 2jT77: (c2m242justp 5 "por-com-1")
% (c2m242justa "por-com-1")
% (find-LATEX "edrx21.sty" "more-than-9-args")
% «example-6-defs» (to ".example-6-defs")
% (sbcp 4 "example-6-defs")
% (sbca "example-6-defs")
% (c2m251justp 4 "example-6")
% (c2m251justa "example-6")
% (c2m251sda "eq-if")
% (c2m251sda "eq-p")
\def\veja#1{\text{Veja \Ca{#1}}}
\def\porcom#1#2{\text{Por \ga{#1} com $#2$}}
\sa{example 6: body}{
F(x) &\ga{=}{1}& (6x^3)(7x^4) \\
\ga{p}{2L}{F'(x)}
&\ga{=}{2}& \ga{p}{2R}{(\ga{p}{3L}{F(x)})'} \\
&\ga{=}{3}& \ga{p}{4L}{(\ga{p}{3R}{(6x^3)(7x^4)})'} \\
&\ga{=}{4}& \ga{p}{4}{\ddx((6x^3)(7x^4))} \\
&\ga{=}{5}& \ga{p}{5R}{(6x^3)\ddx(7x^4) + (7x^4)\ga{p}{6L}{\ddx(6x^3)}} & \ga{just 5} \\
&\ga{=}{6}& (6x^3)\ddx(7x^4) + (7x^4)·\ga{p}{6R}{6\ga{p}{7L}{\ddx x^3}} & \ga{just 6} \\
&\ga{=}{7}& (6x^3)\ddx(7x^4) + (7x^4)·\ga{p}{8L}{6·\ga{p}{7R}{3 x^2}} & \ga{just 7} \\
&\ga{=}{8}& (6x^3)\ga{p}{9L}{\ddx(7x^4)} + (7x^4)\ga{p}{8R}{(18x^2)} \\
&\ga{=}{9}& (6x^3)·\ga{p}{9R}{7\ga{p}{10L}{\ddx x^4}} + (7x^4)(18x^2) & \ga{just 9} \\
&\ga{=}{10}& (6x^3)·\ga{p}{11L}{7·\ga{p}{10R}{4x^3}} + (7x^4)(18x^2) & \ga{just 10} \\
&\ga{=}{11}& (6x^3)\ga{p}{11R}{(28x^3)} + \ga{p}{12L}{(7x^4)(18x^2)} \\
&\ga{=}{12}& \ga{p}{13L}{(6x^3)(28x^3)} + \ga{p}{12R}{126x^6} \\
&\ga{=}{13}& \ga{p}{14L}{\ga{p}{13R}{168x^6} + 126x^6} \\
&\ga{=}{14}& \ga{p}{14R}{294x^6} \\
}
\sa{example 6}{
\begin{array}{rcll}
\ga{example 6: body}
\end{array}
}
% (c2m251sda "eq-if")
% (c2m251sda "eq-p")
\def\He#1{\sa{=.#1.}{foo}} % highlight an `='
\def\Hp#1{\sa{p.#1.}{foo}} % highlight a `p'
\sa{Highlight all ps}{\sa{p after 2}{\standout{$\ga{2}$}_{\ga{1}}}}
\sa{Number all =s}{\sa{eq after 1}{=_{\ga{1}}}}
\sa{Highlight 2}{\Hp {2L}\He {2}\Hp{2R}}
\sa{Highlight 3}{\Hp {3L}\He {3}\Hp{3R}}
\sa{Highlight 4}{\Hp {4L}\He {4}\Hp{4}}
\sa{Highlight 5}{\Hp {4} \He {5}\Hp{5R} \sa{just 5}{RProd}}
\sa{Highlight 6}{\Hp {6L}\He {6}\Hp{6R} \sa{just 6}{RMC}}
\sa{Highlight 7}{\Hp {7L}\He {7}\Hp{7R} \sa{just 7}{RPowx}}
\sa{Highlight 8}{\Hp {8L}\He {8}\Hp{8R}}
\sa{Highlight 9}{\Hp {9L}\He {9}\Hp{9R} \sa{just 9}{RMC}}
\sa{Highlight 10}{\Hp{10L}\He{10}\Hp{10R} \sa{just 10}{RPowx}}
\sa{Highlight 11}{\Hp{11L}\He{11}\Hp{11R}}
\sa{Highlight 12}{\Hp{12L}\He{12}\Hp{12R}}
\sa{Highlight 13}{\Hp{13L}\He{13}\Hp{13R}}
\sa{Highlight 14}{\Hp{14L}\He{14}\Hp{14R}}
%%% A low-level test:
% $$\sa{=.1.}{foo}
% \sa{=.12.}{foo}
% \sa{p.5b.}{foo}
% \sa{p.6.}{foo}
% \sa{eq after 1}{=_{\ga{1}}}
% \ga{example 6}
% $$
\scalebox{0.7}{\def\colwidth{7cm}\firstcol{
\vspace*{-1cm}
$$%\ga{Highlight 2}
%\ga{Highlight 3}
%\ga{Highlight 4}
%\ga{Highlight 5}
%\ga{Highlight 6}
%\ga{Highlight 7}
%\ga{Highlight 8}
%\ga{Highlight 9}
\ga{Highlight 10}
%\ga{Highlight 11}
%\ga{Highlight 12}
%\ga{Highlight 13}
%\ga{Highlight 14}
\ga{example 6}
$$
}\anothercol{
\vspace*{-1cm}
$$\ga{Number all =s}
\ga{Highlight all ps}
\ga{example 6}
$$
}}
\newpage
% «example-6-with» (to ".example-6-with")
% (sbcp 7 "example-6-with")
% (sbca "example-6-with")
\Sa{Example 6 with}#1{\sa{1}{#1}\ga{Example 6 with after 1}}
\Sa{Example 6 with after 1}{
\newpage
\scalebox{0.7}{\def\colwidth{7cm}\firstcol{
\vspace*{-1cm}
\ga{1}
$$\ga{example 6}$$
}\anothercol{
}}}
\def\und#1#2{\underbrace{#1}_{\textstyle #2}}
\def\undph#1#2#3{\underbrace{\phantom{#1}#2\phantom{#1}}_{\textstyle #3}}
\sa {(RProd v)} {\pmat{\ddx(f(x)g(x))
\;=\; \ph{mmm} \\
f(x) \ddx g(x) + g(x) \ddx f(x)}}
\sa {(RProd 5 v)} {\pmat{\ddx((6x^3)(7x^4))
\;=\; \ph{mmm} \\
(6x^3) \ddx (7x^4) + (7x^4) \ddx (6x^3)}}
\newpage
% «example-6-just-5» (to ".example-6-just-5")
% (sbcp 5 "example-6-just-5")
% (sbca "example-6-just-5")
\sa{Just 5 [RProd].1} {\ga{[RProd]}}
\sa{Just 5 [RProd].2} {\ga{(RProd v)}}
\sa{Just 5 [RProd]} {\undph{mmmmm}
{\ga{Just 5 [RProd].1}}
{\ga{Just 5 [RProd].2}}}
\sa{Just 5 [S]} {\bmat{f(x):= 6x^3 \\ g(x):=7x^4}}
\sa{Just 5 [RProd][S].1}{\ga{Just 5 [RProd]}
\ga{Just 5 [S]}}
\sa{Just 5 [RProd][S].2}{\pmat{\ddx((6x^3)(7x^4))
\;=\; \ph{mmm} \\
(6x^3) \ddx (7x^4) + (7x^4) \ddx (6x^3)}}
\sa{Just 5 [RProd][S]} {\und{\ga{Just 5 [RProd][S].1}}
{\ga{Just 5 [RProd][S].2}}}
\sa{Just 5} {Por \ga{Just 5 [RProd][S]}}
\sa{Just 5} {Por \setdepthto{0pt}{\ga{Just 5 [RProd][S]}}}
\ga{Example 6 with}{
\ga{Highlight 5}
\sa{just 5}{\ga{Just 5}}
}
\newpage
% «example-6-just-6» (to ".example-6-just-6")
% (sbcp 6 "example-6-just-6")
% (sbca "example-6-just-6")
\sa{Just 6 [RMC].1} {\ga{[RMC]}}
\sa{Just 6 [RMC].2} {\ga{(RMC)}}
\sa{Just 6 [RMC]} {\undph{mmmm}
{\ga{Just 6 [RMC].1}}
{\ga{Just 6 [RMC].2}}}
\sa{Just 6 [S]} {\bmat{c:=6 \\ f(x):= x^3}}
\sa{Just 6 [RMC][S].1}{\ga{Just 6 [RMC]}
\ga{Just 6 [S]}}
\sa{Just 6 [RMC][S].2}{\pmat{\ddx(6x^3) \;=\; 6\ddx x^3}}
\sa{Just 6 [RMC][S]} {\und{\ga{Just 6 [RMC][S].1}}
{\ga{Just 6 [RMC][S].2}}}
\sa{Just 6} {Por \ga{Just 6 [RMC][S]}}
\sa{Just 6} {Por \setdepthto{0pt}{\ga{Just 6 [RMC][S]}}}
\ga{Example 6 with}{
\ga{Highlight 6}
\sa{just 6}{\ga{Just 6}}
}
\newpage
% «example-6-just-7» (to ".example-6-just-7")
% (sbcp 7 "example-6-just-7")
% (sbca "example-6-just-7")
\sa{Just 7 [RPot].1} {\ga{[RPot]}}
\sa{Just 7 [RPot].2} {\ga{(RPot)}}
\sa{Just 7 [RPot]} {\undph{mmmm}
{\ga{Just 7 [RPot].1}}
{\ga{Just 7 [RPot].2}}}
\sa{Just 7 [S]} {\bmat{n:=3}}
\sa{Just 7 [RPot][S].1}{\ga{Just 7 [RPot]}
\ga{Just 7 [S]}}
\sa{Just 7 [RPot][S].2}{\pmat{\ddx x^3 \;=\; nx^{3-1}}}
\sa{Just 7 [RPot][S]} {\und{\ga{Just 7 [RPot][S].1}}
{\ga{Just 7 [RPot][S].2}}}
\sa{Just 7} {Por \ga{Just 7 [RPot][S]}}
\sa{Just 7} {Por \setdepthto{0pt}{\ga{Just 7 [RPot][S]}}}
\ga{Example 6 with}{
\ga{Highlight 7}
\sa{just 7}{\ga{Just 7}}
}
\newpage
% «example-6-just-9» (to ".example-6-just-9")
% (sbcp 8 "example-6-just-9")
% (sbca "example-6-just-9")
\sa{Just 9 [RMC].1} {\ga{[RMC]}}
\sa{Just 9 [RMC].2} {\ga{(RMC)}}
\sa{Just 9 [RMC]} {\undph{mmmm}{\ga{Just 9 [RMC].1}}
{\ga{Just 9 [RMC].2}}}
\sa{Just 9 [S]} {\bmat{c:=7 \\ f(x):= x^4}}
\sa{Just 9 [RMC][S].1}{\ga{Just 9 [RMC]}
\ga{Just 9 [S]}}
\sa{Just 9 [RMC][S].2}{\PBig{\ddx(7x^4) \;=\; 7\ddx x^4}}
\sa{Just 9 [RMC][S]} {\und{\ga{Just 9 [RMC][S].1}}
{\ga{Just 9 [RMC][S].2}}}
\sa{Just 9} {Por \setdepthto{0pt}{\ga{Just 9 [RMC][S]}}}
\ga{Example 6 with}{
\ga{Highlight 9}
\sa{just 9}{\ga{Just 9}}
}
\newpage
% «example-6-just-10» (to ".example-6-just-10")
% (sbcp 9 "example-6-just-10")
% (sbca "example-6-just-10")
\sa{Just 10 [RPot].1} {\ga{[RPot]}}
\sa{Just 10 [RPot].2} {\ga{(RPot)}}
\sa{Just 10 [RPot]} {\undph{mmm}{\ga{Just 10 [RPot].1}}
{\ga{Just 10 [RPot].2}}}
\sa{Just 10 [S]} {\bmat{n:=4}}
\sa{Just 10 [RPot][S].1}{\ga{Just 10 [RPot]}
\ga{Just 10 [S]}}
\sa{Just 10 [RPot][S].2}{\PBig{\ddx x^4 \;=\; nx^{4-1}}}
\sa{Just 10 [RPot][S]} {\und{\ga{Just 10 [RPot][S].1}}
{\ga{Just 10 [RPot][S].2}}}
\sa{Just 10} {Por \setdepthto{0pt}{\ga{Just 10 [RPot][S]}}}
\ga{Example 6 with}{
\ga{Highlight 10}
\sa{just 10}{\ga{Just 10}}
}
\sa {(RDC)} {\pmat{\ddx c \;=\; 0}}
\sa {(RMC)} {\pmat{\ddx(cf(x)) \;=\; c\ddx f(x)}}
\sa {(RPot)} {\pmat{\ddx x^n \;=\; nx^{n-1}}}
\sa {(RSoma)} {\pmat{\ddx(f(x)+g(x)) \;=\; \ddx f(x) + \ddx g(x)}}
\sa {[RC]} {\CFname{RC}{}}
\sa {(RC)} {\PBig{\ddx f(g(x)) \;=\; f'(g(x))g'(x)}}
%\ga{Example 6 with}{foo}
%\sa {[RPot]}{\CFname{RPot}{}}
%\sa{[RProd]}{\CFname{RProd}{}}
%\sa {[RC]}{\CFname{RC}{}}
%\sa {[RMC]}{\CFname{RMC}{}}
%\sa{[RSoma]}{\CFname{RSoma}{}}
%\sa {[TFC2]}{\CFname{TFC2}{}}
%\sa{[TFC2?]}{\CFname{TFC2?}{}}
%\sa{[TFC2L]}{\CFname{TFC2L}{}}
\sa{Highlight 5}{\Hp {4} \He {5}\Hp{5R} \sa{just 5}{RProd}}
\sa{Highlight 6}{\Hp {6L}\He {6}\Hp{6R} \sa{just 6}{RMC}}
\sa{Highlight 7}{\Hp {7L}\He {7}\Hp{7R} \sa{just 7}{RPowx}}
\sa{Highlight 8}{\Hp {8L}\He {8}\Hp{8R}}
\sa{Highlight 9}{\Hp {9L}\He {9}\Hp{9R} \sa{just 9}{RMC}}
\sa{Highlight 10}{\Hp{10L}\He{10}\Hp{10R} \sa{just 10}{RPowx}}
\def\HH#1{
\newpage
\scalebox{0.7}{\def\colwidth{7cm}\firstcol{
\vspace*{-1cm}
\ga{Highlight #1}
$$\ga{example 6}$$
}\anothercol{
}}
}
\HH{ none }
\HH{2}
\HH{3}
\HH{4}
\HH{5}
\HH{6}
\HH{7}
\HH{8}
\HH{9}
\HH{10}
\HH{11}
\HH{12}
\HH{13}
\HH{14}
\GenericWarning{Success:}{Success!!!} % Used by `M-x cv'
\end{document}
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