mirror of https://github.com/hearot/notes
feat(eti): aggiunge la prima parte degli esercizi del corso
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\newcommand{\eu}{\mathrm{e}}
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\newcommand{\im}{\mathrm{i}}
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\newcommand{\degree}{\,^{\circ}}
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\newcommand{\transpose}[1]{{#1}^{\mathsf{T}}}
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\newcommand{\Int}{\int\limits_{-\infty}^{\infty}}
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\newcommand{\rint}[2]{\int{#1}\dd{#2}}
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\newcommand{\Rint}[4]{\int\limits_{#1}^{#2}{#3}\dd{#4}}
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\DeclareMathOperator{\ot}{ot}
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\DeclareMathOperator{\cof}{cof}
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\DeclareMathOperator{\TC}{TC}
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\newcommand{\ORD}{\text{ORD}}
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\makeatletter
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\newcommand*\bigcdot{\mathpalette\bigcdot@{.5}}
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\newcommand*\bigcdot@[2]{\mathbin{\vcenter{\hbox{\scalebox{#2}{$\m@th#1\bullet$}}}}}
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\makeatother
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\newcommand{\Ham}{\hat{\mathcal{H}}}
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\renewcommand{\Tr}{\mathrm{Tr}}
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\newcommand{\christoffelsecond}[4]{\dfrac{1}{2}g^{#3 #4}(\partial_{#1} g_{#2 #4} + \partial_{#2} g_{#1 #4} - \partial_{#4} g_{#1 #2})}
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\newcommand{\riemanncurvature}[5]{\partial_{#3} \Gamma_{#4 #2}^{#1} - \partial_{#4} \Gamma_{#3 #2}^{#1} + \Gamma_{#3 #5}^{#1} \Gamma_{#4 #2}^{#5} - \Gamma_{#4 #5}^{#1} \Gamma_{#3 #2}^{#5}}
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\newcommand{\covariantriemanncurvature}[5]{g_{#1 #5} R^{#5}{}_{#2 #3 #4}}
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\newcommand{\riccitensor}[5]{g_{#1 #5} R^{#5}{}_{#2 #3 #4}}
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\renewcommand{\emptyset}{\varnothing}
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\renewcommand{\iff}{\longleftrightarrow}
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\renewcommand{\implies}{\longrightarrow}
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\renewcommand{\impliedby}{\longleftarrow}
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\DeclareMathOperator{\dom}{dom}
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\DeclareMathOperator{\imm}{imm}
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\newcommand{\rel}{\mathcal{R}}
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\newcommand{\FF}{\mathcal{F}}
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\newcommand{\bigtimes}{\varprod}
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\DeclareMathOperator{\Fun}{Fun}
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\DeclareMathOperator{\id}{id}
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\newcommand{\PP}{\mathcal{P}}
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\newcommand{\NN}{\mathbb{N}}
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\newcommand{\ZZ}{\mathbb{Z}}
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\newcommand{\QQ}{\mathbb{Q}}
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\newcommand{\RR}{\mathbb{R}}
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\newcommand{\UU}{\mathbb{V}}
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\newcommand{\VV}{\mathbb{V}}
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\newcommand{\se}{\text{se }}
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\newcommand{\altrimenti}{\text{altrimenti}}
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\newcommand{\inv}{^{-1}}
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\newcommand{\AC}{$\mathsf{AC}$}
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\newcommand{\PA}{$\mathsf{PA}$}
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\newcommand{\cc}{\mathfrak{c}}
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\DeclareMathOperator{\Fin}{Fin}
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\newcommand{\PPFin}{\PP^{\mathsf{fin}}}
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\DeclareMathOperator{\FSeq}{FSeq}
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\DeclareMathOperator{\bige}{Big}
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\DeclareMathOperator{\Sym}{\mathfrak{S}}
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\newcommand{\OO}{\mathfrak{O}}
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\newcommand{\basis}{\mathcal{B}}
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\newcommand{\restr}[2]{
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#1\arrowvert_{#2}
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}
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\usepackage{titlesec}
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\usepackage[many]{tcolorbox}
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\usepackage{environ}
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\titlespacing*{\chapter}{0cm}{-2.0cm}{0.50cm}
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\titlespacing*{\section}{0cm}{0.50cm}{0.25cm}
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\setlength{\parindent}{0pt}
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\setlength{\parskip}{1ex}
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\newtcbtheorem[list inside={prob}]{problem}{Problema}%
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{enhanced,
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colback = black!5, %white,
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colbacktitle = black!5,
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coltitle = black,
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boxrule = 0pt,
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frame hidden,
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borderline west = {0.5mm}{0.0mm}{black},
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fonttitle = \bfseries\sffamily,
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breakable,
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before skip = 3ex,
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after skip = 3ex,
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boxsep = 2mm
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}{problem}
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\newenvironment{solution}
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{\let\qed\relax\begin{proof}[Soluzione]}
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{\end{proof}}
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\newenvironment{altsolution}
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{\let\qed\relax\begin{proof}[Soluzione alternativa]}
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{\end{proof}}
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\newif\ifhideproofs
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% \hideproofstrue
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\ifhideproofs
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\usepackage{environ}
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\NewEnviron{hide}{}
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\let\solution\hide
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\let\endsolution\endhide
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\let\altsolution\hide
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\let\endaltsolution\endhide
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\fi
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\tcbuselibrary{skins, breakable}
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% \usepackage{fontspec}
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% ==================================================
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\usepackage[italian]{babel}
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\usepackage[margin = 1in]{geometry}
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% ==================================================
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\usepackage{mathrsfs}
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\usepackage{amsfonts}
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\usepackage{amsmath}
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\usepackage{amsthm}
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\usepackage{amssymb}
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\usepackage{physics}
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\usepackage{dsfont}
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\usepackage{esint}
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\usepackage{marvosym}
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\usepackage{kpfonts}
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\usepackage{quiver}
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% ==================================================
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\usepackage{enumerate}
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\usepackage[shortlabels, inline]{enumitem}
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\usepackage{framed}
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\usepackage{csquotes}
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% ==================================================
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\usepackage{float}
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\usepackage{tabularx}
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\usepackage{xcolor}
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\usepackage{multicol}
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\usepackage{subcaption}
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\usepackage{caption}
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\captionsetup{format = hang, margin = 10pt, font = small, labelfont = bf}
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\usepackage[round, authoryear]{natbib}
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\usepackage{hyperref}
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\definecolor{links}{rgb}{0.36,0.54,0.66}
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\hypersetup{
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colorlinks = true,
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linkcolor = black,
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urlcolor = blue,
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citecolor = blue,
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filecolor = blue,
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pdfauthor = {Author},
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pdftitle = {Title},
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pdfsubject = {subject},
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pdfkeywords = {one, two},
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pdfproducer = {LaTeX},
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pdfcreator = {pdfLaTeX},
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}
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\usepackage{lmodern}
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\renewcommand{\familydefault}{\sfdefault}
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\usepackage{sfmath}
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\usepackage{hyperref}
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% *** quiver ***
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% A package for drawing commutative diagrams exported from https://q.uiver.app.
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%
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% This package is currently a wrapper around the `tikz-cd` package, importing necessary TikZ
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% libraries, and defining a new TikZ style for curves of a fixed height.
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%
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% Version: 1.5.2
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% Authors:
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% - varkor (https://github.com/varkor)
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% - AndréC (https://tex.stackexchange.com/users/138900/andr%C3%A9c)
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\NeedsTeXFormat{LaTeX2e}
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\ProvidesPackage{quiver}[2021/01/11 quiver]
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% `tikz-cd` is necessary to draw commutative diagrams.
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\RequirePackage{tikz-cd}
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% `amssymb` is necessary for `\lrcorner` and `\ulcorner`.
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\RequirePackage{amssymb}
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% `calc` is necessary to draw curved arrows.
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\usetikzlibrary{calc}
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% `pathmorphing` is necessary to draw squiggly arrows.
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\usetikzlibrary{decorations.pathmorphing}
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% A TikZ style for curved arrows of a fixed height, due to AndréC.
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\tikzset{curve/.style={settings={#1},to path={(\tikztostart)
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.. controls ($(\tikztostart)!\pv{pos}!(\tikztotarget)!\pv{height}!270:(\tikztotarget)$)
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and ($(\tikztostart)!1-\pv{pos}!(\tikztotarget)!\pv{height}!270:(\tikztotarget)$)
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.. (\tikztotarget)\tikztonodes}},
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settings/.code={\tikzset{quiver/.cd,#1}
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\def\pv##1{\pgfkeysvalueof{/tikz/quiver/##1}}},
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quiver/.cd,pos/.initial=0.35,height/.initial=0}
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% TikZ arrowhead/tail styles.
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\tikzset{tail reversed/.code={\pgfsetarrowsstart{tikzcd to}}}
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\tikzset{2tail/.code={\pgfsetarrowsstart{Implies[reversed]}}}
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\tikzset{2tail reversed/.code={\pgfsetarrowsstart{Implies}}}
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% TikZ arrow styles.
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\tikzset{no body/.style={/tikz/dash pattern=on 0 off 1mm}}
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\endinput
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