% (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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