Convert to Aviary.html and clean-up tex.
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<!DOCTYPE html>
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<html>
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<head>
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<meta charset="utf-8">
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<meta name="viewport" content="width=device-width">
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<title>Bookshelf.Combinator.Aviary</title>
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<script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script>
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<script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
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</head>
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<body>
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<h1>Bookshelf.Combinator.Aviary</h1>
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<p>
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A list of birds as defined in <i>To Mock a Mockingbird</i>.
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Refer to <a href="../Aviary.html">Bookshelf/Combinator/Aviary</a>
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for implementation examples.
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</p>
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<ul>
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<li><b>Bald Eagle:</b> \(\hat{E}xy_1y_2y_3z_1z_2z_3 = x(y_1y_2y_3)(z_1z_2z_3)\)</li>
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<li><b>Becard:</b> \(B_3xyzw = x(y(zw))\)</li>
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<li><b>Blackbird:</b> \(B_1xyzw = x(yzw)\)</li>
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<li><b>Bluebird:</b> \(Bxyz = x(yz)\)</li>
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<li><b>Bunting:</b> \(B_2xyzwv = x(yzwv)\)</li>
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<li><b>Cardinal Once Removed:</b> \(C^*xyzw = xywz\)</li>
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<li><b>Cardinal:</b> \(Cxyz = xzy\)</li>
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<li><b>Converse Warbler:</b> \(W'xy = yxx\)</li>
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<li><b>Dickcissel:</b> \(D_1xyzwv = xyz(wv)\)</li>
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<li><b>Double Mockingbird:</b> \(M_2xy = xy(xy)\)</li>
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<li><b>Dove:</b> \(Dxyzw = xy(zw)\)</li>
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<li><b>Dovekie:</b> \(D_2xyzwv = x(yz)(wv)\)</li>
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<li><b>Eagle:</b> \(Exyzwv = xy(zwv)\)</li>
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<li><b>Finch Once Removed:</b> \(F^*xyzw = xwzy\)</li>
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<li><b>Finch:</b> \(Fxyz = zyx\)</li>
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<li><b>Goldfinch:</b> \(Gxyzw = xw(yz)\)</li>
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<li><b>Hummingbird:</b> \(Hxyz = xyzy\)</li>
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<li><b>Identity Bird:</b> \(Ix = x\)</li>
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<li><b>Kestrel:</b> \(Kxy = x\)</li>
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<li><b>Lark:</b> \(Lxy = x(yy)\)</li>
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<li><b>Mockingbird:</b> \(Mx = xx\)</li>
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<li><b>Owl:</b> \(Oxy = y(xy)\)</li>
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<li><b>Phoenix:</b> \(\Phi xyzw = x(yw)(zw)\)</li>
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<li><b>Psi Bird:</b> \(\Psi xyzw = x(yz)(yw)\)</li>
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<li><b>Quacky Bird:</b> \(Q_4xyz = z(yx)\)</li>
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<li><b>Queer Bird:</b> \(Qxyz = y(xz)\)</li>
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<li><b>Quirky Bird:</b> \(Q_3xyz = z(xy)\)</li>
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<li><b>Quixotic Bird:</b> \(Q_1xyz = x(zy)\)</li>
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<li><b>Quizzical Bird:</b> \(Q_2xyz = y(zx)\)</li>
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<li><b>Robin Once Removed:</b> \(R^*xyzw = xzwy\)</li>
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<li><b>Robin:</b> \(Rxyz = yzx\)</li>
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<li><b>Sage Bird:</b> \(\Theta x = x(\Theta x)\)</li>
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<li><b>Starling:</b> \(Sxyz = xz(yz)\)</li>
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<li><b>Thrush:</b> \(Txy = yx\)</li>
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<li><b>Turing Bird:</b> \(Uxy = y(xxy)\)</li>
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<li><b>Vireo Once Removed:</b> \(V^*xyzw = xwyz\)</li>
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<li><b>Vireo:</b> \(Vxyz = zxy\)</li>
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<li><b>Warbler:</b> \(Wxy = xyy\)</li>
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</ul>
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</body>
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</html>
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\documentclass{article}
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\input{preamble}
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\begin{document}
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\newcommand{\bird}[1]{\item{\makebox[5cm][l]{\textbf{#1:}}}}
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\section*{Aviary}%
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\label{sec:aviary}
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A list of birds as defined in \textit{To Mock a Mockingbird}.
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Refer to \href{../../../../Bookshelf/Combinator/Aviary.html}{Bookshelf/Combinator/Aviary}
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for implementation examples.
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\begin{itemize}
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\bird{Bald Eagle} $\hat{E}xy_1y_2y_3z_1z_2z_3 = x(y_1y_2y_3)(z_1z_2z_3)$
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\bird{Becard} $B_3xyzw = x(y(zw))$
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\bird{Blackbird} $B_1xyzw = x(yzw)$
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\bird{Bluebird} $Bxyz = x(yz)$
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\bird{Bunting} $B_2xyzwv = x(yzwv)$
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\bird{Cardinal Once Removed} $C^*xyzw = xywz$
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\bird{Cardinal} $Cxyz = xzy$
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\bird{Converse Warbler} $W'xy = yxx$
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\bird{Dickcissel} $D_1xyzwv = xyz(wv)$
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\bird{Double Mockingbird} $M_2xy = xy(xy)$
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\bird{Dove} $Dxyzw = xy(zw)$
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\bird{Dovekie} $D_2xyzwv = x(yz)(wv)$
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\bird{Eagle} $Exyzwv = xy(zwv)$
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\bird{Finch Once Removed} $F^*xyzw = xwzy$
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\bird{Finch} $Fxyz = zyx$
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\bird{Goldfinch} $Gxyzw = xw(yz)$
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\bird{Hummingbird} $Hxyz = xyzy$
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\bird{Identity Bird} $Ix = x$
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\bird{Kestrel} $Kxy = x$
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\bird{Lark} $Lxy = x(yy)$
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\bird{Mockingbird} $Mx = xx$
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\bird{Owl} $Oxy = y(xy)$
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\bird{Phoenix} $\Phi xyzw = x(yw)(zw)$
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\bird{Psi Bird} $\Psi xyzw = x(yz)(yw)$
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\bird{Quacky Bird} $Q_4xyz = z(yx)$
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\bird{Queer Bird} $Qxyz = y(xz)$
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\bird{Quirky Bird} $Q_3xyz = z(xy)$
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\bird{Quixotic Bird} $Q_1xyz = x(zy)$
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\bird{Quizzical Bird} $Q_2xyz = y(zx)$
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\bird{Robin Once Removed} $R^*xyzw = xzwy$
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\bird{Robin} $Rxyz = yzx$
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\bird{Sage Bird} $\Theta x = x(\Theta x)$
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\bird{Starling} $Sxyz = xz(yz)$
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\bird{Thrush} $Txy = yx$
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\bird{Turing Bird} $Uxy = y(xxy)$
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\bird{Vireo Once Removed} $V^*xyzw = xwyz$
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\bird{Vireo} $Vxyz = zxy$
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\bird{Warbler} $Wxy = xyy$
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\end{itemize}
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\end{document}
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\input{preamble}
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\input{preamble}
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\newcommand{\linkA}[1]{\href{../../../Bookshelf/Real/Sequence/Arithmetic.html\##1}{#1}}
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\newcommand{\ns}{Real}
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\newcommand{\linkG}[1]{\href{../../../Bookshelf/Real/Sequence/Geometric.html\##1}{#1}}
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\newcommand{\linkA}[1]{\href{../Sequence/Arithmetic.html\#\ns.#1}{\ns.#1}}
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\newcommand{\linkG}[1]{\href{../Sequence/Geometric.html\#\ns.#1}{\ns.#1}}
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\begin{document}
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\begin{document}
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@ -16,7 +17,7 @@ $$\sum_{i=0}^n a_i = \frac{(n + 1)(a_0 + a_n)}{2}.$$
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\begin{proof}
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\begin{proof}
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\linkA{Real.Arithmetic.sum\_recursive\_closed}
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\linkA{Arithmetic.sum\_recursive\_closed}
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\end{proof}
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\end{proof}
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\begin{proof}
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\begin{proof}
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\linkG{Real.Geometric.sum\_recursive\_closed}
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\linkG{Geometric.sum\_recursive\_closed}
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\end{proof}
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\end{proof}
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\input{preamble}
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\input{preamble}
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\newcommand{\link}[1]{\href{../../../../Exercises/Apostol/Chapter_I_3.html\##1}{#1}}
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\newcommand{\ns}{Exercises.Apostol.Chapter\_I\_3.Real}
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\newcommand{\link}[1]{\href{../Chapter_I_3.html\#\ns.#1}{\ns.#1}}
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\begin{document}
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\begin{document}
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@ -15,7 +16,7 @@ is, there is a real number $L$ such that $L = \inf{S}$.
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\begin{proof}
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\begin{proof}
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\link{Real.exists\_isGLB}
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\link{exists\_isGLB}
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\end{proof}
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\end{proof}
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\begin{proof}
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\begin{proof}
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\link{Real.exists\_pnat\_geq\_self}
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\link{exists\_pnat\_geq\_self}
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\end{proof}
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\end{proof}
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\begin{proof}
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\begin{proof}
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\link{Real.exists\_pnat\_mul\_self\_geq\_of\_pos}
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\link{exists\_pnat\_mul\_self\_geq\_of\_pos}
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\end{proof}
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\end{proof}
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\begin{proof}
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\begin{proof}
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\link{Real.forall\_pnat\_leq\_self\_leq\_frac\_imp\_eq}
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\link{forall\_pnat\_leq\_self\_leq\_frac\_imp\_eq}
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\end{proof}
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\end{proof}
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@ -69,8 +70,8 @@ Let $h$ be a given positive number and let $S$ be a set of real numbers.
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\begin{proof}
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\begin{proof}
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\begin{enumerate}[(a)]
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\begin{enumerate}[(a)]
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\item \link{Real.sup\_imp\_exists\_gt\_sup\_sub\_delta}
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\item \link{sup\_imp\_exists\_gt\_sup\_sub\_delta}
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\item \link{Real.inf\_imp\_exists\_lt\_inf\_add\_delta}
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\item \link{inf\_imp\_exists\_lt\_inf\_add\_delta}
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\end{enumerate}
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\end{enumerate}
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\end{proof}
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\end{proof}
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@ -91,8 +92,8 @@ $$C = \{a + b : a \in A, b \in B\}.$$
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\begin{proof}
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\begin{proof}
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\begin{enumerate}[(a)]
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\begin{enumerate}[(a)]
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\item \link{Real.sup\_minkowski\_sum\_eq\_sup\_add\_sup}
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\item \link{sup\_minkowski\_sum\_eq\_sup\_add\_sup}
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\item \link{Real.inf\_minkowski\_sum\_eq\_inf\_add\_inf}
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\item \link{inf\_minkowski\_sum\_eq\_inf\_add\_inf}
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\end{enumerate}
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\end{enumerate}
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\end{proof}
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\end{proof}
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@ -108,7 +109,7 @@ $$\sup{S} \leq \inf{T}.$$
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\begin{proof}
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\begin{proof}
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\link{Real.forall\_mem\_le\_forall\_mem\_imp\_sup\_le\_inf}
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\link{forall\_mem\_le\_forall\_mem\_imp\_sup\_le\_inf}
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\end{proof}
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\end{proof}
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\input{preamble}
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\input{preamble}
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\newcommand{\link}[1]{\href{../../../../Exercises/Enderton/Chapter0.html\##1}{#1}}
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\newcommand{\ns}{Exercises.Enderton.Chapter0}
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\newcommand{\link}[1]{\href{../Chapter0.html\#\ns.#1}{\ns.#1}}
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\begin{document}
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\begin{document}
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