Further normalize links to Lean from TeX.
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\documentclass{article}
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\input{preamble}
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\newcommand{\ns}{Real}
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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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\section*{Sum of Arithmetic Series}%
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\label{sec:sum-arithmetic-series}
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Let $(a_i)_{i \geq 0}$ be an arithmetic sequence with common difference $d$.
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Then for some $n \in \mathbb{N}$,
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$$\sum_{i=0}^n a_i = \frac{(n + 1)(a_0 + a_n)}{2}.$$
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\begin{proof}
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\linkA{Arithmetic.sum\_recursive\_closed}
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\end{proof}
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\section*{Sum of Geometric Series}%
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\label{sec:sum-geometric-series}
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Let $(a_i)_{i \geq 0}$ be a geometric sequence with common ratio $r \neq 1$.
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Then for some $n \in \mathbb{N}$,
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$$\sum_{i=0}^n a_i = \frac{a_0(1 - r^{n+1})}{1 - r}.$$
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\begin{proof}
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\linkG{Geometric.sum\_recursive\_closed}
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\end{proof}
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\end{document}
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@ -0,0 +1,23 @@
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\documentclass{article}
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\input{preamble}
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\newcommand{\link}[1]{\lean{../../..}{Bookshelf/Real/Sequence/Arithmetic}
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{Real.Arithmetic.#1}}
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\begin{document}
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\section*{Sum of Arithmetic Series}%
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\label{sec:sum-arithmetic-series}
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Let $(a_i)_{i \geq 0}$ be an arithmetic sequence with common difference $d$.
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Then for some $n \in \mathbb{N}$,
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$$\sum_{i=0}^n a_i = \frac{(n + 1)(a_0 + a_n)}{2}.$$
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\begin{proof}
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\link{sum_recursive_closed}
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\end{proof}
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\end{document}
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@ -0,0 +1,23 @@
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\documentclass{article}
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\input{preamble}
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\newcommand{\link}[1]{\lean{../../..}{Bookshelf/Real/Sequence/Geometric}
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{Real.Geometric.#1}}
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\begin{document}
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\section*{Sum of Geometric Series}%
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\label{sec:sum-geometric-series}
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Let $(a_i)_{i \geq 0}$ be a geometric sequence with common ratio $r \neq 1$.
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Then for some $n \in \mathbb{N}$,
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$$\sum_{i=0}^n a_i = \frac{a_0(1 - r^{n+1})}{1 - r}.$$
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\begin{proof}
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\link{sum_recursive_closed}
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\end{proof}
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\end{document}
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@ -3,8 +3,8 @@
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\input{preamble}
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\input{preamble}
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\newcommand{\ns}{Exercises.Apostol.Chapter\_I\_3.Real}
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\newcommand{\link}[1]{\lean{../..}{Exercises/Apostol/Chapter_I_3}
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\newcommand{\link}[1]{\href{../Chapter_I_3.html\#\ns.#1}{\ns.#1}}
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{Exercises.Apostol.Chapter\_I\_3.Real.#1}}
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\begin{document}
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\begin{document}
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@ -16,7 +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{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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@ -27,7 +27,7 @@ For every real $x$ there exists a positive integer $n$ such that $n > x$.
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\begin{proof}
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\begin{proof}
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\link{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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@ -39,7 +39,7 @@ integer $n$ such that $nx > y$.
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\begin{proof}
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\begin{proof}
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\link{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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@ -52,7 +52,7 @@ for every integer $n \geq 1$, then $x = a$.
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\begin{proof}
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\begin{proof}
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\link{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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@ -70,8 +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{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{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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@ -92,8 +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{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{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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@ -109,7 +109,7 @@ $$\sup{S} \leq \inf{T}.$$
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\begin{proof}
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\begin{proof}
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\link{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{\ns}{Exercises.Enderton.Chapter0}
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\newcommand{\link}[1]{\lean{../..}{Exercises/Enderton/Chapter0}
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\newcommand{\link}[1]{\href{../Chapter0.html\#\ns.#1}{\ns.#1}}
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{Exercises.Enderton.Chapter0.#1}}
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\begin{document}
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\begin{document}
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@ -15,7 +15,7 @@ Then $x_1 = \langle y_1, \ldots, y_{k+1} \rangle$.
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\begin{proof}
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\begin{proof}
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\link{lemma\_0a}
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\link{lemma_0a}
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\end{proof}
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\end{proof}
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13
preamble.tex
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preamble.tex
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\usepackage{amsfonts, amsthm}
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\usepackage{amsfonts, amsthm}
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\usepackage[T1]{fontenc}
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\usepackage{hyperref}
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\usepackage{hyperref}
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\usepackage{underscore}
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\newtheorem{theorem}{Theorem}
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\newtheorem{theorem}{Theorem}
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\newtheorem{xtheoreminner}{Theorem}
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\newtheorem{xtheoreminner}{Theorem}
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}{\endxtheoreminner}
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}{\endxtheoreminner}
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\hypersetup{colorlinks=true, urlcolor=blue}
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\hypersetup{colorlinks=true, urlcolor=blue}
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% https://tex.stackexchange.com/a/232188
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\newcommand{\startunderscoreletter}{\catcode`_ 12\relax}
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\newcommand{\stopunderscoreletter}{\catcode`_ 8\relax}
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% The first argument refers to a relative path upward from a current file to
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% the root of the workspace (i.e. where this `preamble.tex` file is located).
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% We include an additional nesting of `..` to account for the generated `LaTeX`
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% directory automatically included when generating documentation.
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\newcommand{\lean}[3]{\href{#1/../#2.html\##3}{
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\startunderscoreletter #3 \stopunderscoreletter}}
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