witharrows-in-latex removal

git-svn-id: svn://tug.org/texlive/trunk@51791 c570f23f-e606-0410-a88d-b1316a301751

7 files changed, 0 insertions, 10959 deletions

diff --git a/Master/texmf-dist/doc/latex/witharrows/README.md b/Master/texmf-dist/doc/latex/witharrows/README.md
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index b706fd6ac2e..00000000000
--- a/Master/texmf-dist/doc/latex/witharrows/README.md
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-# Readme for the package witharrows
-
-Author : F. Pantigny (`fpantigny@wanadoo.fr`).
-
-CTAN page : `https://ctan.org/pkg/witharrows`
-
-## License
-The LaTeX extension `witharrows` is distributed under the LPPL 1.3 license.
-
-## Presentation
-
-The LaTeX package `witharrows` provides environments `{WithArrows}` and `{DispWithArrows}`
-similar to the environments `{aligned}` and `{align}` of `amsmath` but with the possibility to draw arrows on the right side of the alignment. These arrows are usually used to give explanations concerning the mathematical calculus presented.
-
-
-
-## Installation
-
-The package `witharrows` is present in the distributions MiKTeX, TeXLive and MacTeX.
-
-For a manual installation:
-
-* put the files `witharrows.ins` dans `witharrows.dtx` in the same directory; 
-* run `latex witharrows.ins`.
-
-The file `witharrows.sty` will be generated.
-
-The file `witharrows.sty` is the only file necessary to use the extension `witharrows`.
diff --git a/Master/texmf-dist/doc/latex/witharrows/witharrows-french.pdf b/Master/texmf-dist/doc/latex/witharrows/witharrows-french.pdf
deleted file mode 100644
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--- a/Master/texmf-dist/doc/latex/witharrows/witharrows-french.pdf
+++ /dev/null
diff --git a/Master/texmf-dist/doc/latex/witharrows/witharrows-french.tex b/Master/texmf-dist/doc/latex/witharrows/witharrows-french.tex
deleted file mode 100644
index 65f0355dfb7..00000000000
--- a/Master/texmf-dist/doc/latex/witharrows/witharrows-french.tex
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-% -*- coding: utf-8 ; -*-
-\documentclass[dvipsnames]{article}% dvipsnames est pour xcolor (chargé par Tikz)
-\usepackage{xltxtra}
-\usepackage[french]{babel}
-
-\usepackage[xetex]{geometry}
-\geometry{left=2.8cm,right=2.8cm,top=2.5cm,bottom=2.5cm,papersize={21cm,29.7cm}}
-
-\usepackage{amsmath}
-\usepackage{color}
-\usepackage{verbatim}
-\usepackage{mathtools}
-\usepackage[footnotehyper]{witharrows}
-\usepackage{amsfonts}
-\usepackage{amssymb}
-\usepackage{varwidth}
-\usetikzlibrary{calc}
-\usepackage[only,llbracket,rrbracket]{stmaryrd}
-
-\usepackage{fancyvrb}
-\fvset{commandchars=\~\#\@,formatcom={\color{gray}}}
-
-\usepackage{titlesec}
-\titlespacing*{\section}{0pt}{6.5ex plus 1ex minus .2ex}{4.3ex plus .2ex}
-\titlespacing*{\subsection}{0pt}{4.5ex plus 1ex minus .2ex}{2ex plus .2ex}
-
-
-\def\interitem{\vskip 7mm plus 2 mm minus 3mm}          
-\def\emphase{\bgroup\color{RoyalPurple}\let\next=}
-
-\skip \footins = 2 \bigskipamount
-
-\usepackage[hyperfootnotes = false]{hyperref}
-
-\hypersetup{
-  pdfinfo = {
-     Title = { L’extension witharrows },
-     Subject = { Une extension LaTeX } ,
-     Author = { F. Pantigny }
-  }
-}
-
-\NewDocumentEnvironment {scope} {} {} {}
-
-\NewDocumentCommand {\pkg} {m} {\textsf{#1}}
-\NewDocumentCommand {\cls} {m} {\textsf{#1}}
-
-\setlength{\parindent}{0pt}
-
-
-\begin{document}
-
-\VerbatimFootnotes
-
-\title{L'extension \pkg{witharrows}\thanks{Ce document correspond à la
-version~\myfileversion\space de \pkg{witharrows}, à la date du~\myfiledate.}} \author{F. Pantigny \\
-\texttt{fpantigny@wanadoo.fr}}  
-
-\maketitle
-
-\begin{abstract}
-L'extension LaTeX \pkg{witharrows} fournit des environments \verb|{WithArrows}| et
-\verb|{DispWithArrows}| similaires aux environnements \verb|{aligned}| et \verb|{align}| de
-l'\pkg{amsmath} mais avec la possibilité de dessiner des flèches sur le côté droit.
-Ces flèches sont habituellement utilisées pour donner des explications concernant 
-le calcul mathématique présenté. 
-\end{abstract}
-
-
-\vspace{1cm} 
-Cette extension peut être utilisée avec \verb|xelatex|, \verb|lualatex|, \verb|pdflatex|
-mais aussi avec le cheminement classique \verb|latex|-\verb|dvips|-\verb|ps2pdf| (ou Adobe
-Distiller). Plusieurs compilations peuvent être nécessaires. Cette extension nécessite les
-extensions \pkg{expl3}, \pkg{xparse} et \pkg{tikz}. Les extensions Tikz 
-\pkg{arrows.meta} et \pkg{bending} sont également requises. Toutes sont chargées par \pkg{witharrows}.
-
-\bigskip
-Cette extension fournit un environnement \verb|{WithArrows}| pour construire des alignements d'équations
-avec des flèches pour les explications sur le côté droit.
-
-\begin{Verbatim}
-$\begin{WithArrows}
-A & = (a+1)^2 ~emphase#\Arrow{on développe}@ \\
-  & = a^2 + 2a + 1  % ne pas mettre de \\ ici
-\end{WithArrows}$
-\end{Verbatim}
-
-$\begin{WithArrows}
-A & = (a+1)^2 \Arrow{on développe} \\
-  & = a^2 + 2a + 1  
-\end{WithArrows}$
-
-
-
-\medskip
-La flèche a été tracée avec la commande \verb|\Arrow| dans la rangée dont la flèche part. La commande \verb|\Arrow|
-doit être utilisée dans la seconde colonne (le mieux est de la mettre à la fin de la ligne comme dans l'exemple
-précédent).
-
-
-\medskip
-Comme on le voit, l'environnement \verb|{WithArrows}| est proche de l'environnement
-\verb|{aligned}| de l'\pkg{amsmath}. L'extension \pkg{witharrows}
-propose aussi un environnement \verb|{DispWithArrows}| qui est similaire à l'environnement \verb|{align}| de
-l'\pkg{amsmath}: cf. p. \pageref{DispWithArrows}. 
-
-
-\section{Options pour la forme des flèches}
-
-La commande \verb|\Arrow| a plusieurs options. Ces options peuvent être placées entre crochets, avant, ou après,
-l'argument obligatoire.
-
-L'option \verb|jump| indique le nombre\footnote{Il n'est pas possible de donner une valeur négative à \verb|jump|.
-Voir plus loin (p.~\pageref{Backwards}) la manière de tracer une flèche qui remonte.} de rangées que la flèche doit sauter (la valeur par défaut est, bien
-entendu,~$1$).
-
-
-\begin{Verbatim}
-$\begin{WithArrows}
-A & = \bigl((a+b)+1\bigr)^2 \Arrow[~emphase#jump=2@]{on développe} \\
-  & = (a+b)^2 +  2(a+b) +1 \\
-  & = a^2 + 2ab + b^2 + 2a + 2b +1 
-\end{WithArrows}$
-\end{Verbatim}
-
-$\begin{WithArrows}
-A & = \bigl((a+b)+1\bigr)^2 \Arrow[jump=1+1]{on développe} \\
-  & = (a+b)^2 + 2(a+b) +1 \\
-  & = a^2 + 2ab + b^2 + 2a + 2b +1 
-\end{WithArrows}$
-
-\interitem
-Il est possible de faire partir plusieurs flèches d'une même rangée.
-\begin{Verbatim}
-$\begin{WithArrows}
-A & = \bigl((a+b)+1\bigr)^2 ~emphase#\Arrow{}\Arrow{}[jump=2]@ \\
-  & = (a+b)^2 + 2(a+b) +1 \\
-  & = a^2 + 2ab + b^2 + 2a + 2b +1 
-\end{WithArrows}$
-\end{Verbatim}
-
-$\begin{WithArrows}
-A & = \bigl((a+b)+1\bigr)^2 \Arrow{}\Arrow{}[jump=2] \\
-  & = (a+b)^2 + 2(a+b) +1 \\
-  & = a^2 + 2ab + b^2 + 2a + 2b +1 
-\end{WithArrows}$
-
-\interitem
-L'option \verb|xoffset| décale la flèche vers la droite (habituellement, on ne souhaite pas que les flèches soient
-collées au texte). La valeur par défaut de \verb|xoffset| est de $3$~mm.
-\begin{Verbatim}
-$\begin{WithArrows}
-A & = \bigl((a+b)+1\bigr)^2 
-\Arrow[~emphase#xoffset=1cm@]{avec \texttt{xoffset=1cm}} \\
-  & = (a+b)^2 + 2(a+b) +1 
-\end{WithArrows}$
-\end{Verbatim}
-
-$\begin{WithArrows}
-A & = \bigl((a+b)+1\bigr)^2 
-\Arrow[xoffset=1cm]{avec \texttt{xoffset=1cm}} \\
-  & = (a+b)^2 + 2(a+b) +1 
-\end{WithArrows}$
-
-
-\interitem 
-Les flèches sont tracées avec Tikz. C'est pourquoi la commande \verb|\Arrow| a une option 
-\verb|tikz| qui peut être utilisée pour donner à la flèche (en fait, à la commande \verb|\path| de
-Tikz) les options proposées par Tikz pour une telle flèche. L'exemple suivant fournit une flèche en trait épais.
-\begin{Verbatim}
-$\begin{WithArrows}
-A & = (a+1)^2 \Arrow[~emphase#tikz=thick@]{on développe} \\
-  & = a^2 + 2a + 1 
-\end{WithArrows}$
-\end{Verbatim}
-
-$\begin{WithArrows}
-A & = (a+1)^2 \Arrow[tikz=thick]{on développe} \\
-  & = a^2 + 2a + 1 
-\end{WithArrows}$
-
-\interitem
-Il est également possible de changer les pointes de flèche. Par exemple, nous pouvons tracer une flèche
-qui remonte vers le haut avec l'option Tikz~\verb|<-|.\label{Backwards} 
-
-\begin{Verbatim}
-$\begin{WithArrows}
-A & = (a+1)^2 \Arrow~emphase#[tikz=<-]@{on factorise} \\
-  & = a^2 + 2a + 1 
-\end{WithArrows}$
-\end{Verbatim}
-
-$\begin{WithArrows}
-A & = (a+1)^2 \Arrow[tikz=<-]{on factorise} \\
-  & = a^2 + 2a + 1 
-\end{WithArrows}$
-
-\interitem
-Il est aussi possible de supprimer les deux pointes de flèche avec l'option Tikz «\verb|-|».
-\begin{Verbatim}
-$\begin{WithArrows}
-A & = (a+1)^2 \Arrow[~emphase#tikz=-@]{très classique} \\
-  & = a^2 + 2a + 1 
-\end{WithArrows}$
-\end{Verbatim}
-
-$\begin{WithArrows}
-A & = (a+1)^2 \Arrow[tikz=-]{très classique} \\
-  & = a^2 + 2a + 1 
-\end{WithArrows}$
-
-\interitem
-Pour avoir des flèches droites et non incurvées, il convient d'utiliser l'option Tikz 
-«\verb|bend left = 0|».
-\begin{Verbatim}
-$\begin{WithArrows}
-A & = (a+1)^2 \Arrow~emphase#[tikz={bend left=0}]@{on développe} \\
-  & = a^2 + 2a + 1 
-\end{WithArrows}$
-\end{Verbatim}
-
-$\begin{WithArrows}
-A & = (a+1)^2 \Arrow[tikz={bend left=0}]{on développe} \\
-  & = a^2 + 2a + 1 
-\end{WithArrows}$
-
-\smallskip 
-En fait, il est possible de modifier de manière plus drastique la forme des flèches avec l'option
-\verb|tikz-code| (présentée p.~\pageref{tikz-code}).
-
-\interitem
-Il est possible d'utiliser l'option «\verb|text width|» pour contrôler la largeur du texte associé à la
-flèche.\footnote{Il est possible d'éviter les coupures de mots dans ces étiquettes
-avec l'option «\verb|align = flush left|» de Tikz.}
-%
-\begin{Verbatim}
-$\begin{WithArrows}
-A & = \bigl((a+b)+1\bigr)^2 
-\Arrow[jump=2,~emphase#tikz={text width=5.3cm}@]{Nous avons développé...} \\
-  & = (a+b)^2 + 2(a+b) +1 \\
-  & = a^2 + 2ab + b^2 + 2a + 2b +1 
-\end{WithArrows}$
-\end{Verbatim}
-
-$\begin{WithArrows}
-A & = \bigl((a+b)+1\bigr)^2 
-\Arrow[jump=2,tikz={text width=5.3cm}]{Nous avons développé en deux étapes mais il aurait été plus habile
-  d'utiliser la formule du multinôme.} \\
-& = (a+b)^2 + 2(a+b) +1 \\
-& = a^2 + 2ab + b^2 + 2a + 2b +1
-\end{WithArrows}$
-
-
-\bigskip
-Dans les environnements \verb|{DispWithArrows}| et \verb|{DispWithArrows*}|, il y a une
-option \verb|wrap-lines|. Lorsque cette option est utilisée, les lignes des étiquettes sont
-automatiquement coupées sur la marge droite : voir p.~\pageref{wrap-lines}.
-
-\interitem
-Si on veut changer la fonte du texte associé à une flèche, on peut, bien entendu, placer une commande comme 
-\verb|\bfseries|, \verb|\large| ou \verb|\sffamily| au début du texte.
-Mais, par défaut, les étiquettes sont composées avec une combinaison
-de \verb|\small| et \verb|\itshape|. En ajoutant \verb|\bfseries| au début du texte, on ne va pas supprimer le
-\verb|\small| et le \verb|\itshape| et, par conséquent, on aura un texte en gras, italique et petite taille.
-%
-\begin{Verbatim}
-$\begin{WithArrows}
-A & = (a+1)^2 \Arrow{~emphase#\bfseries@ on développe} \\
-  & = a^2 + 2a + 1 
-\end{WithArrows}$
-\end{Verbatim}
-
-$\begin{WithArrows}
-A & = (a+1)^2 \Arrow{\bfseries on développe} \\
-  & = a^2 + 2a + 1 
-\end{WithArrows}$
-
-\interitem 
-Il est possible de placer des commandes \verb|\\| dans le texte pour forcer des retours à la ligne\footnote{Par
-défaut, ce n'est pas possible dans un nœud Tikz. Néanmoins, dans \pkg{witharrows},
-les nœuds sont construits avec l'option \verb|align=left|, et, ainsi, cela devient possible.}. Néanmoins, si on utilise des commandes \verb|\\|, une instruction de fonte placée au début
-du texte aura un effet seulement jusqu'à la première occurrence de~\verb|\\| (comme
-dans un environnement \verb|{tabular}|). C'est pourquoi Tikz fournit une option
-\verb|font| pour modifier la fonte de tout le texte de l'étiquette. Cette fois-ci, si on utilise une option
-\verb|tikz={font={\bfseries}}|, la spécification par défaut constituée par \verb|\small| et \verb|\itshape| va être
-écrasée. 
-%
-\begin{Verbatim}
-$\begin{WithArrows}
-A & = (a+1)^2 \Arrow[~emphase#tikz={font={\bfseries}}@]{on développe} \\
-  & = a^2 + 2a + 1 
-\end{WithArrows}$
-\end{Verbatim}
-
-$\begin{WithArrows}
-A & = (a+1)^2 \Arrow[tikz={font={\bfseries}}]{on développe} \\
-  & = a^2 + 2a + 1 
-\end{WithArrows}$
-
-\medskip
-Si on veut exactement le même résultat que précédemment, on doit donner à l'option \verb|font| la valeur
-\verb|\itshape\small\bfseries|.
-
-
-\interitem 
-Presque toutes les options peuvent être données entre crochets à l'environnement \verb|{WithArrows}|. Il ne doit
-pas y avoir d'espace entre le \verb|\begin{WithArrows}| et le crochet ouvrant (\verb|[|) des options de
-l'environnement. Ces options s'appliquent à toutes les flèches de l'environnement.\footnote{Elles s'appliquent
-  aussi aux environnements imbriqués dans un environnement \verb|{WithArrows}| donné (avec des exceptions attendues
-  pour les options \verb|interline|, \verb|code-before| et \verb|code-after|).}
-%
-\begin{Verbatim}
-$\begin{WithArrows}[~emphase#tikz=blue@]
-A & = \bigl((a+b)+1\bigr)^2 \Arrow{premier développement} \\
-  & = (a+b)^2 + 2(a+b) +1 \Arrow{second développement} \\
-  & = a^2 + 2ab + b^2 + 2a + 2b +1 
-\end{WithArrows}$
-\end{Verbatim}
-
-$\begin{WithArrows}[tikz=blue]
-A & = \bigl((a+b)+1\bigr)^2 \Arrow{premier développement} \\
-  & = (a+b)^2 + 2(a+b) +1 \Arrow{second développement} \\
-  & = a^2 + 2ab + b^2 + 2a + 2b +1 
-\end{WithArrows}$
-
-
-\interitem
-L'environnement \verb|{WithArrows}| a une option \verb|displaystyle|. Avec cette option,
-tous les éléments sont composés en \verb|\displaystyle| (comme dans un environnement
-\verb|{aligned}| de l'\pkg{amsmath}).
-
-\medskip
-Sans l'option \verb|displaystyle|:
-%
-\begin{Verbatim}
-$\begin{WithArrows}
-\int_0^1 (x+1)^2 dx 
-& = \int_0^1 (x^2+2x+1) dx
-\Arrow{linéarité de l'intégration}     \\
-& = \int_0^1 x^2 dx + 2 \int_0^1 x dx + \int_0^1 dx \\
-& = \frac13 + 2\frac12 + 1 \\
-& = \frac73
-\end{WithArrows}$
-\end{Verbatim}
-
-$\begin{WithArrows}
-\int_0^1 (x+1)^2 dx 
-& = \int_0^1 (x^2+2x+1) dx
-\Arrow{linéarité de l'intégration}     \\
-& = \int_0^1 x^2 dx + 2 \int_0^1 x dx + \int_0^1 dx \\
-& = \frac13 + 2\frac12 + 1 \\
-& = \frac73
-\end{WithArrows}$
-
-
-\medskip
-Le même exemple avec l'option \verb|displaystyle|:\par\nobreak
-
-$\begin{WithArrows}[displaystyle]
-\int_0^1 (x+1)^2 dx 
-& = \int_0^1 (x^2+2x+1) dx
-\Arrow{linéarité de l'intégration}     \\
-& = \int_0^1 x^2 dx + 2 \int_0^1 x dx + \int_0^1 dx \\
-& = \frac13 + 2\frac12 + 1 \\
-& = \frac73
-\end{WithArrows}$
-
-
-
-\interitem 
-Presque toutes les options peuvent aussi être fixées au niveau du document avec la commande
-\verb|\WithArrowsOptions|. Dans ce cas, la portée des déclarations est le groupe TeX courant (de telles
-déclarations sont parfois qualifiées de «semi-globales»). Par exemple, si nous voulons que tous les environnements
-\verb|{WithArrows}| soient composés en \verb|\displaystyle| avec des flèches bleues, nous pouvons écrire
-\verb|\WithArrowsOptions{displaystyle,tikz=blue}|.\footnote{Il est aussi possible de configurer \pkg{witharrows} en
-  modifiant le style Tikz \verb|WithArrows/arrow| qui est le style utilisé par \pkg{witharrows} lors du tracé d'une
-  flèche. Par exemple, pour avoir les étiquettes en bleu et en caractères droits, on peut utiliser l'instruction
-  suivante : \verb|\tikzset{WithArrows/arrow/.append style = {blue,font = {}}}|.}
-
-\begin{Verbatim}
-~emphase#\WithArrowsOptions{displaystyle,tikz=blue}@
-$\begin{WithArrows}
-\sum_{i=1}^n (x_i+1)^2 
-& = \sum_{i=1}^n (x_i^2+2x_i+1) \Arrow{par linéarité}\\
-& = \sum_{i=1}^n x_i^2 + 2\sum_{i=1}^nx_i+ n
-\end{WithArrows}$
-\end{Verbatim}
-
-\begin{scope}
-\WithArrowsOptions{displaystyle,tikz=blue}
-$\begin{WithArrows}
-\sum_{i=1}^n (x_i+1)^2 
-& = \sum_{i=1}^n (x_i^2+2x_i+1) \Arrow{par linéarité}\\
-& = \sum_{i=1}^n x_i^2 + 2\sum_{i=1}^nx_i+ n
-\end{WithArrows}$
-\end{scope}
-
-
-\interitem 
-La commande \verb|\Arrow| est reconnue seulement dans les environnements \verb|{WithArrows}|. Si on
-dispose d'une commande \verb|\Arrow| précédemment définie, il est possible de continuer à l'utiliser à
-l'extérieur des environnements \verb|{WithArrows}|.
-
-Néanmoins, une commande \verb|\Arrow| définie précédemment pourrait encore être utile dans un environnement \verb|{WithArrows}|.
-Si vous voulez l'utiliser dans un tel environnement, il est possible de changer le nom de la commande \verb|\Arrow| de
-l'extension \pkg{witharrows} grâce à une option \verb|command-name|\footnote{Pour des raisons historiques, il y a
-  un alias pour cette option : \verb|CommandeName|.} dédiée. Le nouveau nom de la commande doit être fourni à
-l'option \emph{sans} la contre-oblique.
-%
-\begin{Verbatim}
-\NewDocumentCommand {\Arrow} {} {\longmapsto}
-$\begin{WithArrows}[~emphase#command-name=Explication@]
-f & = \bigl(x \Arrow (x+1)^2\bigr)
-~emphase#\Explication{on travaille directement sur les fonctions}@\\
-& = \bigl(x \Arrow x^2+2x+1\bigr)
-\end{WithArrows}$
-\end{Verbatim}
-%
-\begin{scope}
-\NewDocumentCommand {\Arrow} {} {\longmapsto}
-$\begin{WithArrows}[command-name=Explication]
-f & = \bigl(x \Arrow (x+1)^2\bigr)
-\Explication{on travaille directement sur les fonctions}\\
-& = \bigl(x \Arrow x^2+2x+1\bigr)
-\end{WithArrows}$
-\end{scope}
-
-
-\interitem 
-L'environnement \verb|{WithArrows}| fournit aussi deux options \verb|code-before| et
-\verb|code-after|\footnote{Pour des raisons historiques, il y a aussi des alias pour ces options :
-  \verb|CodeBefore| et \verb|CodeAfter|.} pour du code LaTeX qui sera exécuté au début et à la fin de
-l'environnement. Ces options ne sont pas conçues pour être utilisées comme des \emph{hooks} (elles sont disponibles
-uniquement au niveau de l'environnement et ne s'appliquent pas aux environnements imbriqués).
-%
-\begin{Verbatim}
-$\begin{WithArrows}[~emphase#code-before = \color{blue}@]
-A & = (a+b)^2 \Arrow{on développe} \\
-  & = a^2 + 2ab + b^2 
-\end{WithArrows}$
-\end{Verbatim}
-
-$\begin{WithArrows}[code-before = \color{blue}]
-A & = (a+b)^2 \Arrow{on développe} \\
-  & = a^2 + 2ab + b^2 
-\end{WithArrows}$
-
-\medskip 
-Des commandes spéciales sont disponibles dans le \verb|code-after| : une commande \verb|\WithArrowsNbLines| qui
-indique le nombre de lignes (=rangées) de l'environnement courant (pour TeX, il s'agit d'une commande et non d'un
-compteur), une forme spéciale de la commande \verb|\Arrow| et la commande \verb|\MultiArrow| : ces commandes sont
-décrites à partir de la page~\pageref{NestedEnv}.
-
-\section{Nombre et formats des colonnes}
-
-Jusqu'à présent, nous n'avons utilisé l'environnement \verb|{WithArrows}| qu'avec deux colonnes. Néanmoins, il est
-possible de l'utiliser avec un nombre arbitraire de colonnes grâce à l'option \verb|format|. La valeur
-donnée à cette option est similaire au préambule d'un environnement \verb|{array}|: il s'agit d'une séquence de
-lettres \verb|r|, \verb|c| et \verb|l|. La valeur par défaut de cette option \verb|format| est, en fait, \verb|rl|.
-
-
-\bigskip
-Par exemple, si on veut seulement une colonne alignée à gauche, on peut utiliser l'option \verb|format=l|.
-\begin{Verbatim}
-$\begin{WithArrows}[~emphase#format = l@]
-f(x) \ge g(x) \Arrow{on élève les deux membres au carré} \\
-f(x)^2 \ge g(x)^2 \Arrow{on fait tout passer à gauche} \\
-f(x)^2 - g(x)^2 \ge 0 
-\end{WithArrows}$
-\end{Verbatim}
-
-$\begin{WithArrows}[format = l]
-f(x) \ge g(x) \Arrow{on élève les deux membres au carré} \\
-f(x)^2 \ge g(x)^2 \Arrow{on fait tout passer à gauche} \\
-f(x)^2 - g(x)^2 \ge 0 
-\end{WithArrows}$
-
-\interitem
-Dans l'exemple suivant, on utilise cinq colonnes toutes centrées (l'environnement
-\verb|{DispWithArrows*}| utilisé est présenté p.~\pageref{DispWithArrows}).
-
-\begin{Verbatim}
-\begin{DispWithArrows*}[~emphase#format = ccccc@,
-                        wrap-lines,
-                        tikz = {align = flush left},
-                        interline=1mm]
-k & \;\le\; & t & \;\le\; & k+1 \\
-\frac{1}{k+1} & \le & \frac{1}{t} & \le & \frac{1}{k} 
-\Arrow{nous pouvons intégrer les inégalités puisque $k \leq k+1$ } \\
-\int\limits_k^{k+1} \frac{dt}{k+1} 
-& \le & \int\limits_k^{k+1} \frac{dt}{t} 
-& \le & \int\limits_k^{k+1} \frac{dt}{k} \\
-\frac{1}{k+1} & \le & \ln(k+1)-\ln(k) & \le & \frac{1}{k} 
-\end{DispWithArrows*}
-\end{Verbatim}
-\begin{DispWithArrows*}[format = ccccc,
-                        wrap-lines,
-                        tikz = {align = flush left},
-                        interline=1mm]
-k & \;\le\; & t & \;\le\; & k+1 \\
-\frac{1}{k+1} & \le & \frac{1}{t} & \le & \frac{1}{k} 
-\Arrow{nous pouvons intégrer les inégalités puisque $k \leq k+1$} \\
-\int\limits_k^{k+1} \frac{dt}{k+1} 
-& \le & \int\limits_k^{k+1} \frac{dt}{t} 
-& \le & \int\limits_k^{k+1} \frac{dt}{k} \\
-\frac{1}{k+1} & \le & \ln(k+1)-\ln(k) & \le & \frac{1}{k} 
-\end{DispWithArrows*}
-
-
-\section{Positionnement précis des flèches}
-
-L'environnement \verb|{WithArrows}| construit, lors de la composition du tableau,
-deux séries de nœuds représentés en rouge dans l'exemple suivant.\footnote{L'option
-\verb|show-nodes| peut être utilisée pour visualiser ces nœuds. Les nœuds sont en fait des nœuds Tikz de forme
-rectangulaire et de largeur nulle. Une flèche entre deux nœuds part de l'ancre sud (\emph{south
-  anchor}) du premier nœud et arrive à l'ancre nord (\emph{north anchor}) du deuxième nœud.}
-
-
-\smallskip
-$\begin{WithArrows}[displaystyle,show-nodes]
-I
-& = \int_{\frac{\pi}4}^0 \ln\Bigl(1+\tan\left(\tfrac{\pi}4-u\right)\Bigr)(-d u) \\
-& = \int_0^{\frac{\pi}4} \ln\Bigl(1+\tan\left(\tfrac{\pi}4-u\right)\Bigr)d u \\
-& = \int_0^{\frac{\pi}4}\ln\left(1+\frac{1-\tan u}{1+\tan u}\right)\, d u \\
-& =\int_0^{\frac{\pi}4}\ln\left(\frac{1+\tan u+1-\tan u}{1+\tan u}\right) d u \\
-& =\int_0^{\frac{\pi}4} \ln\left(\frac2{1+\tan u}\right)\, d u\\
-& =\int_0^{\frac{\pi}4}\bigl(\ln2-\ln(1+\tan u)\bigr)\, d u \\
-& =\frac{\pi}4\ln2-\int_0^{\frac{\pi}4}\ln(1+\tan u)\, d u  \\
-& =\frac{\pi}4\ln2-I 
-\end{WithArrows}$
-
-\bigskip
-Les nœuds sur la gauche sont à la fin de chaque ligne de texte. Ces nœuds seront appelés \emph{nœuds de gauche}. Les
-nœuds du côté droit sont alignés verticalement sur le bord droit de l'alignement d'équations. Ces nœuds seront
-appelés \emph{nœuds de droite}.
-
-
-Par défaut, les flèches utilisent les nœuds de droite. Nous dirons que ces flèches sont dans le mode \verb|rr| (\emph{r}
-for \emph{right} en anglais). Ces flèches sont verticales (nous dirons qu'une flèche est \emph{verticale} lorsque
-ses deux extrémités sont à la même abscisse).
-
-
-
-\smallskip
-Néanmoins, il est possible d'utiliser les nœuds de gauche, ou une combinaison de nœuds de gauche et de droite avec
-l'une des options \verb|lr|, \verb|rl| et \verb|ll| (\emph{l} for \emph{left} en anglais). Ces flèches sont, la
-plupart du temps, non verticales.
-
-
-Therefore
-$\begin{WithArrows}[displaystyle]
-I
-& = \int_{\frac{\pi}4}^0 \ln\Bigl(1+\tan\left(\tfrac{\pi}4-u\right)\Bigr)(-d u) 
-\Arrow[lr]{Cette flèche utilise une option \texttt{lr}.}\\
-& = \int_0^{\frac{\pi}4} \ln\Bigl(1+\tan\left(\tfrac{\pi}4-u\right)\Bigr)d u \\
-& = \int_0^{\frac{\pi}4}\ln\left(1+\frac{1-\tan u}{1+\tan u}\right)\, d u \\
-& =\int_0^{\frac{\pi}4}\ln\left(\frac{1+\tan u+1-\tan u}{1+\tan u}\right) d u 
-\Arrow[ll,jump=2,tikz={text width = 5cm}]{Cette flèche utilise une option \texttt{ll} 
-et une option \texttt{jump} fixée à $2$}\\ 
-& =\int_0^{\frac{\pi}4} \ln\left(\frac2{1+\tan u}\right)\, d u\\
-& =\int_0^{\frac{\pi}4}\bigl(\ln2-\ln(1+\tan u)\bigr)\, d u \\
-& =\frac{\pi}4\ln2-\int_0^{\frac{\pi}4}\ln(1+\tan u)\, d u  \\
-& =\frac{\pi}4\ln2-I 
-\end{WithArrows}$
-
-
-\interitem 
-Il y a aussi une option nommée \verb|i| (\emph{i} pour \emph{intermédiaire}). Avec cette option, la flèche est
-verticale et calée à gauche.
-
-\begin{Verbatim}
-$\begin{WithArrows}
-(a+b)(a+ib)(a-b)(a-ib) 
-& = (a+b)(a-b)\cdot(a+ib)(a-ib) \\
-& = (a^2-b^2)(a^2+b^2) \Arrow~emphase#[i]@{parce que $(x-y)(x+y)=x^2-y^2$}\\
-& = a^4-b^4 
-\end{WithArrows}$
-\end{Verbatim}
-
-$\begin{WithArrows}
-(a+b)(a+ib)(a-b)(a-ib) 
-& = (a+b)(a-b)\cdot(a+ib)(a-ib) \\
-& = (a^2-b^2)(a^2+b^2) \Arrow[i]{parce que $(x-y)(x+y)=x^2-y^2$}\\
-& = a^4-b^4 
-\end{WithArrows}$
-
-
-\interitem 
-L'environnement \verb|{WithArrows}| propose aussi une option \verb|group|. Avec cette option,
-\emph{toutes} les flèches de l'environnement sont regroupées sur une même verticale calée à gauche.
-%
-\begin{Verbatim}[formatcom=\small\color{gray}]
-$\begin{WithArrows}[~emphase#displaystyle,group@]
-2xy'-3y=\sqrt x
-& \Longleftrightarrow 2x(K'y_0+Ky_0')-3Ky_0 = \sqrt x \\
-& \Longleftrightarrow 2xK'y_0 + K(2xy_0'-3y_0) = \sqrt x \\
-& \Longleftrightarrow 2x K'y_0 = \sqrt x \Arrow{...}\\
-...
-\end{WithArrows}$
-\end{Verbatim}
-
-
-$\begin{WithArrows}[displaystyle,group]
-2xy'-3y=\sqrt x
-& \Longleftrightarrow 2x(K'y_0+Ky_0')-3Ky_0 = \sqrt x \\
-& \Longleftrightarrow 2xK'y_0 + K(2xy_0'-3y_0) = \sqrt x \\
-& \Longleftrightarrow 2x K'y_0 = \sqrt x \Arrow{on remplace $y_0$ par sa valeur}\\
-& \Longleftrightarrow 2xK'x^{\frac32} = x^{\frac12} \Arrow{simplification par $x$}\\
-& \Longleftrightarrow K' = \tfrac1{2x^2} \Arrow{on primitive}\\
-& \Longleftrightarrow K = -\tfrac1{2x} 
-\end{WithArrows}$
-
-
-\bigskip
-L'environnement \verb|{WithArrows}| fournit encore une autre option, nommée \verb|groups| (avec un \emph{s} dans le
-nom). Avec cette option, les flèches sont divisées en plusieurs «groupes». Chaque groupe est un ensemble de flèches
-connectées entre elles\footnote{Plus précisément : pour chaque flèche $a$, notons $i(a)$ le numéro de sa rangée de
-  départ et
-  $f(a)$ le numéro de sa rangée d'arrivée ; pour deux flèches $a$ et $b$, nous noterons $a \sim b$ lorsque
-  $\llbracket i(a),f(a)\rrbracket \cap \llbracket i(b),f(b)\rrbracket \neq \varnothing$ ; les groupes sont les
-  classes d'équivalence de la clôture transitive de la relation $\sim$.}. Toutes les flèches d'un même groupe sont placées sur
-une même verticale qui est calée à gauche. 
-
-
-\bigskip
-$\begin{WithArrows}[groups]
-A & = B \Arrow{one} \\
-  & = C+D \Arrow{two} \\
-  & = D' \\
-  & = E+F+G+H+I \\
-  & = K + L + M \Arrow{three}\\
-  & = N \Arrow{four}\\
-  & = O
-\end{WithArrows}$
-
-\bigskip 
-Dans un environnement qui utilise l'option \verb|group| ou l'option \verb|groups|, il est encore possible de donner
-une option de position (\verb|ll|, \verb|lr|, \verb|rl|, \verb|rr| ou \verb|i|) à une flèche individuelle. Une
-telle flèche sera tracée indépendamment des groupes. Il est aussi possible de commencer un nouveau groupe avec
-l'option \verb|new-group| pour une certaine flèche.
-
-
-\bigskip
-Si on le souhaite, on peut passer l'option \verb|group| ou \verb|groups| à la commande \verb|WithArrowsOptions| de
-telle sorte qu'elle deviendra la valeur par défaut (jusqu'à la fin du groupe TeX). Dans ce cas, il est encore
-possible de revenir au comportement par défaut pour un environnement \verb|{WithArrows}| donné avec l'option
-\verb|rr|: \verb|\begin{WithArrows}[rr]|. 
-
-
-\vspace{1cm}
-Dans l'exemple suivant, nous avons utilisé l'option \verb|group| pour l'environnement
-et l'option \verb|rr| pour la dernière flèche (c'est pourquoi cette dernière flèche n'est pas alignée avec les
-premières). 
-
-$\begin{WithArrows}[interline=1mm,group]
-\sum\limits_{k=0}^n\frac{\cos kx}{\cos^k x}
-& = \sum\limits_{k=0}^n \frac{\Re (e^{ikx})}{(\cos x)^k} 
-\Arrow{$(\cos x)^k$ est réel} \\
-& = \sum\limits_{k=0}^n \Re\left(\frac{e^{ikx}}{(\cos x)^k}\right)
-\Arrow{$\Re(z+z')=\Re(z)+\Re(z')$}\\
-& = \Re \left(\sum\limits_{k=0}^n \left(\frac{e^{ix}}{\cos x}\right)^k\right)
-\Arrow{somme de termes d'une suite géométrique} \\
-& = \Re \left(\frac{1-\left(\frac{e^{ix}}{\cos x}\right)^{n+1}}{1-\frac{e^{ix}}{\cos x}} \right)
-\Arrow{calcul algébrique} \\
-& = \Re \left(\frac{1-\frac{e^{i(n+1)x}}{\cos^{n+1}x}}{1-\frac{e^{ix}}{\cos x}}\right)
-\Arrow{réduction au même dénominateur} \\
-& = \Re \left(\frac{\frac{\cos^{n+1}x-e^{i(n+1)x}}{\cos^{n+1}x}}{\frac{\cos x-e^{ix}}{\cos x}}\right)
-\Arrow{$\Re(kz) = k\cdot\Re(z)$ lorsque $k$ est réel} \\
-& = \frac1{\cos^n x}\Re \left(\frac{\cos^{n+1}x-e^{i(n+1)x}}{\cos x-e^{ix}}\right)
-\Arrow[rr]{forme algébrique des nombres complexes} \\
-& =\frac1{\cos^n x}\Re\left(\frac{\cos^{n+1}x-(\cos(n+1)x+i\sin(n+1)x)}{\cos x-(\cos x+i\sin x)}\right) \\
-& =\frac1{\cos^n x}\Re\left(\frac{(\cos^{n+1}x-\cos(n+1)x)-i\sin(n+1)x}{-i\sin x}\right) \\
-& = \frac1{\cos^nx}\cdot\frac{\sin(n+1)x}{\sin x}
-\end{WithArrows}$
-
-\interitem
-
-\section{Les options «up» et «down» pour des flèches individuelles} 
-
-\label{up-and-down}
-Au niveau local, il y a deux options pour les flèches individuelles, nommée «\verb|up|» et «\verb|down|». L'exemple
-suivant illustre ces types de flèches: 
-
-
-\begin{Verbatim}
-\(\begin{WithArrows}
-A & = B 
-\Arrow~emphase#[up]@{une flèche de type \texttt{up}} \\
-  & = C + C + C + C + C + C + C + C  \\
-  & = C + C + C + C + C + C + C + C  
-\Arrow~emphase#[down]@{une flèche de type \texttt{down}} \\
-  & = E + E 
-\end{WithArrows}\)
-\end{Verbatim}
-
-\vspace{1cm}
-\(\begin{WithArrows}
-A & = B 
-\Arrow[up]{une flèche de type \texttt{up}} \\
-  & = C + C + C + C + C + C + C + C  \\
-  & = C + C + C + C + C + C + C + C  
-\Arrow[down]{une flèche de type \texttt{down}} \\
-  & = E + E 
-\end{WithArrows}\)
-
-
-\vspace{1cm}
-Les options \verb|up| et \verb|down| nécessitent l'extension \pkg{varwidth} et l'extension Tikz
-\pkg{calc}. Si elles ne sont pas chargées, une erreur sera levée.
-
-
-\interitem
-
-\section{Comparaison avec l'environnement \{aligned\}}
-
-L'environnement \verb|{WithArrows}| présente des similitudes avec l'environnement \verb|{aligned}| de l'extension
-\pkg{amsmath}. Ce sont seulement des similitudes car \verb|{WithArrows}| n'a pas été écrit en s'appuyant sur
-\verb|{aligned}|.\footnote{En fait, il est 
-possible d'utiliser l'extension \pkg{witharrows} sans l'extension \pkg{amsmath}.}
-
-\interitem 
-Comme dans les environnements de l'\pkg{amsmath}, il est possible de changer l'espacement entre deux rangées avec
-l'option de la commande \verb|\\| de fin de ligne (il est aussi possible d'utiliser \verb|\\*| mais cela a
-exactement le même effet que \verb|\\| puisqu'un environnement \verb|{WithArrows}| est toujours insécable). Cette
-option est conçu pour être utilisée avec des valeurs positives uniquement.
-%
-\begin{Verbatim}
-$\begin{WithArrows}
-A & = (a+1)^2 \Arrow{on développe} ~emphase#\\[2ex]@
-  & = a^2 + 2a + 1 
-\end{WithArrows}$
-\end{Verbatim}
-
-$\begin{WithArrows}
-A & = (a+1)^2 \Arrow{on développe} \\*[2ex]
-\noalign{\vspace{3mm}}
-  & = a^2 + 2a + 1 
-\end{WithArrows}$
-
-
-\interitem 
-Dans les environnements de l'\pkg{amsmath} (ou de \pkg{mathtools}), l'espace entre deux rangées
-est fixé par un paramètre appelé \verb|\jot| (il s'agit d'une dimension et non d'un ressort). C'est aussi le cas
-pour l'environnement \verb|{WithArrows}|. Une option \verb|jot| a été ajoutée à l'environnement \verb|{WithArrows}|
-dans le but de changer ce paramètre \verb|\jot| pour un environnement donné.\footnote{Il est aussi possible de
-changer \verb|\jot| avec l'environnement \verb|{spreadlines}| de \pkg{mathtools}.}
-%
-\begin{Verbatim}
-$\begin{WithArrows}[displaystyle,~emphase#jot=2ex@]
-F & = \frac12G     \Arrow{on développe}\\
-  & = H + \frac12K \Arrow{on continue}\\
-  & = K 
-\end{WithArrows}$
-\end{Verbatim}
-
-
-$\begin{WithArrows}[displaystyle,jot=2ex]
-F & = \frac12G     \Arrow{on développe}\\
-  & = H + \frac12K \Arrow{on continue}\\
-  & = K 
-\end{WithArrows}$
-
-
-\bigskip
-Néanmoins, cette nouvelle valeur de \verb|\jot| sera aussi utilisée dans les nouveaux alignements
-inclus dans l'environnement~\verb|{WithArrows}|:
-%
-\begin{Verbatim}
-$\begin{WithArrows}[jot=2ex]
-\varphi(x,y) = 0  & \Leftrightarrow (x+y)^2 + (x+2y)^2 = 0 
-\Arrow{$x$ et $y$ sont réels}\\
-& \Leftrightarrow \left\{
-\begin{aligned}
-x+y & = 0 \\
-x+2y & = 0 
-\end{aligned}
-\right.
-\end{WithArrows}$
-\end{Verbatim}
-
-
-$\begin{WithArrows}[jot=2ex]
-\varphi(x,y) = 0  & \Leftrightarrow (x+y)^2 + (x+2y)^2 = 0 
-\Arrow{$x$ et $y$ sont réels}\\
-& \Leftrightarrow \left\{
-\begin{aligned}
-x+y & = 0 \\
-x+2y & = 0 
-\end{aligned}
-\right.
-\end{WithArrows}$
-
-\bigskip
-Peut-être que cela ne correspond pas au résultat souhaité. C'est pourquoi une option
-\verb|interline| est fournie. Il est possible d'utiliser un ressort (\emph{skip}) pour cette option. 
-%
-\begin{Verbatim}
-$\begin{WithArrows}[~emphase#interline=2ex@]
-\varphi(x,y) = 0  & \Leftrightarrow (x+y)^2 + (x+2y)^2 = 0 
-\Arrow{$x$ et $y$ sont réels}\\
-& \Leftrightarrow \left\{
-\begin{aligned}
-x+y & = 0 \\
-x+2y & = 0 \\
-\end{aligned}
-\right.
-\end{WithArrows}$
-\end{Verbatim}
-
-
-$\begin{WithArrows}[interline=2ex]
-\varphi(x,y) = 0  & \Leftrightarrow (x+y)^2 + (x+2y)^2 = 0 
-\Arrow{$x$ et $y$ sont réels}\\
-& \Leftrightarrow \left\{
-\begin{aligned}
-x+y & = 0 \\
-x+2y & = 0 \\
-\end{aligned}
-\right.
-\end{WithArrows}$
-
-
-\interitem
-De même que l'environnement \verb|{aligned}|, \verb|{WithArrows}| a une option de placement qui peut prendre les valeurs
-\verb|t|, \verb|c| ou \verb|b|. Néanmoins, la valeur par défaut n'est pas \verb|c| mais \verb|t|. 
-Si on le souhaite, il est possible d'avoir la valeur \verb|c| comme valeur par défaut
-en utilisant l'instruction \verb|\WithArrowsOptions{c}| au début du document.
-%
-\begin{Verbatim}
-Ainsi\enskip
-$\begin{WithArrows}
-A & = (a+1)^2 \Arrow{on développe} \\
-  & = a^2 + 2a + 1 
-\end{WithArrows}$
-\end{Verbatim}
-
-Ainsi\enskip 
-$\begin{WithArrows}
-A & = (a+1)^2 \Arrow{on développe} \\
-  & = a^2 + 2a + 1 
-\end{WithArrows}$
-
-\bigskip
-La valeur \verb|c| peut être utile, par exemple, si on souhaite mettre une accolade :
-
-\smallskip
-\begin{Verbatim}
-On pose\enskip $~emphase#\left\{@
-\begin{WithArrows}[~emphase#c@]
-f(x) & = 3x^3+2x^2-x+4 
-\Arrow[tikz=-]{les deux sont des polynômes}\\
-g(x) & = 5x^2-5x+6
-\end{WithArrows}
-~emphase#\right.@$
-\end{Verbatim}
-
-
-On pose\enskip $\left\{
-\begin{WithArrows}[c]
-f(x) & = 3x^3+2x^2-x+4 
-\Arrow[tikz=-]{les deux sont des polynômes}\\
-g(x) & = 5x^2-5x+6
-\end{WithArrows}
-\right.$
-
-
-\interitem
-Contrairement à \verb|{aligned}|, l'environnement \verb|{WithArrows}| utilise \verb|\textstyle| par
-défaut.
-
-Là aussi, il est possible de changer ce comportement avec \verb|\WithArrowsOptions|:
-
-\quad \verb|\WithArrowsOptions{displaystyle}|.
-
-
-\smallskip
-L'exemple suivant est composé avec \verb|{aligned}|:\par\nobreak
-
-\smallskip
-$\left\{
-\begin{aligned}
-\sum_{i=1}^n (x_i+1)^2  
-& = \sum_{i=1}^n (x_i^2 + 2x_i+1) \\
-& = \sum_{i=1}^n x_i^2 + 2 \sum_{i=1}^nx_i + n 
-\end{aligned}
-\right.$
-
-
-\medskip 
-L'exemple suivant est composé avec \verb|{WithArrows}[c,displaystyle]|. Les résultats 
-sont parfaitement identiques.\footnote{Dans les versions de l'\pkg{amsmath} antérieures au
-5~novembre~2016, un espace fin était ajouté sur la gauche de l'environnement \verb|{aligned}|.
-Les versions plus récentes n'ajoutent pas d'espace et \verb|{WithArrows}| non plus.}\par\nobreak
-
-\smallskip
-$\left\{
-\begin{WithArrows}[c,displaystyle]
-\sum_{i=1}^n (x_i+1)^2 
-& = \sum_{i=1}^n (x_i^2 + 2x_i+1) \\
-& = \sum_{i=1}^n x_i^2 + 2 \sum_{i=1}^nx_i + n 
-\end{WithArrows}
-\right.$
-
-
-\section{Les flèches dans les environnements imbriqués}
-
-\label{NestedEnv}
-
-Les environnements \verb|{WithArrows}| peuvent être imbriqués. Dans ce cas, les options fournies
-à l'environnement englobant s'appliquent aussi aux environnements imbriqués (avec des
-exceptions tout à fait attendues pour \verb|interline|, \verb|code-before| et \verb|code-after|). La commande
-\verb|Arrow| peut être utilisée dans chaque environnement \verb|{WithArrows}|.
-
-\begin{Verbatim}[formatcom=\small\color{gray}]
-$~emphase#\begin{WithArrows}@
-\varphi(x,y)=0
-  & \Leftrightarrow (x+2y)^2+(2x+4y)^2 = 0 \Arrow{les nombres sont réels}\\
-  & \Leftrightarrow
-  \left\{~emphase#\begin{WithArrows}@[c]
-  x+2y & = 0 \\
-  2x+4y & = 0 
-  ~emphase#\end{WithArrows}@\right. \\
-  & \Leftrightarrow
-  \left\{~emphase#\begin{WithArrows}@[c]
-  x+2y & = 0 \Arrow[tikz=-]{la même équation}\\
-  x+2y & = 0 
-  ~emphase#\end{WithArrows}@\right. \\
-  & \Leftrightarrow x+2y=0 
-~emphase#\end{WithArrows}@$
-\end{Verbatim}
-
-$\begin{WithArrows}
-\varphi(x,y)=0
-  & \Leftrightarrow (x+2y)^2+(2x+4y)^2 = 0 \Arrow{les nombres sont réels}\\
-  & \Leftrightarrow
-  \left\{\begin{WithArrows}[c]
-  x+2y & = 0 \\
-  2x+4y & = 0 
-  \end{WithArrows}\right. \\
-  & \Leftrightarrow
-  \left\{\begin{WithArrows}[c]
-  x+2y & = 0 \Arrow[tikz=-]{la même équation}\\
-  x+2y & = 0 
-  \end{WithArrows}\right. \\
-  & \Leftrightarrow x+2y=0 
-\end{WithArrows}$
-
-\bigskip
-Néanmoins, on peut souhaiter tracer une flèche entre des rangées qui ne sont pas dans le même 
-environnement. Par exemple, on pourrait souhaiter tracer la flèche suivante :
-
-\bigskip
-$\begin{WithArrows}[code-after = \Arrow[v]{1-2}{2-2}{division par $2$} ]
-\varphi(x,y)=0
-  & \Leftrightarrow (x+2y)^2+(2x+4y)^2 = 0 \\
-  & \Leftrightarrow
-  \left\{\begin{WithArrows}[c]
-  x+2y & = 0 \\
-  2x+4y & = 0 
-  \end{WithArrows}\right. \\
-  & \Leftrightarrow
-  \left\{\begin{WithArrows}[c]
-  x+2y & = 0 \\
-  x+2y & = 0 
-  \end{WithArrows}\right. \\
-  & \Leftrightarrow x+2y=0 
-\end{WithArrows}$
-
-
-\bigskip
-Une telle construction est possible en utilisant \verb|\Arrow| dans le \verb|code-after| :
-dans le \verb|code-after|, une version spéciale de la commande \verb|\Arrow| est disponible 
-(nous l'appellerons  «\verb|\Arrow| dans le \verb|code-after|»).
-
-\smallskip
-Une commande \verb|\Arrow| dans le \verb|code-after| prend trois arguments :
-\begin{itemize}
-\item une spécification pour la rangée de départ de la flèche ;
-\item une spécification pour la rangée d'arrivée ;
-\item une étiquette pour la flèche.
-\end{itemize}
-Comme d'habitude, il est possible de donner des options entre crochets avant ou après les trois arguments
-obligatoires. Néanmoins, ces options sont limitées (voir plus bas).
-
-\interitem
-La spécification de rangée est construite avec la position de l'environnement conidéré dans l'arbre des
-imbrications, suivie, après un trait d'union, par le numéro de la rangée.
-
-\bigskip
-Dans l'exemple précédent, il y a deux environnements \verb|{WithArrows}| imbriqués dans l'environnement
-\verb|{WithArrows}| principal.
-
-\medskip
-$\begin{WithArrows}[tikz-code = {\path (#1) to node {#3} (#2) ; }]
-\varphi(x,y)=0
-  & \Leftrightarrow (x+2y)^2+(2x+4y)^2 = 0 \\
-  & \Leftrightarrow \color{blue}
-  \left\{\begin{WithArrows}[c]
-  x+2y & = 0 \Arrow{environnement \no 1}\\
-  2x+4y & = 0 
-  \end{WithArrows}\right. \\
-  & \Leftrightarrow \color{red}
-  \left\{\begin{WithArrows}[c]
-  x+2y & = 0 \Arrow{environnement \no 2}\\
-  x+2y & = 0 
-  \end{WithArrows}\right. \\
-  & \Leftrightarrow x+2y=0 
-\end{WithArrows}$
-
-\bigskip
-La flèche que nous voulons tracer part de la rangée~$2$ du sous-environnement
-\no $1$ (et, par conséquent, la spécification est \verb|1-2|) et arrive à la rangée~$2$
-du sous-environnement \no $2$ (et, par conséquent, la spécification est \verb|2-2|).
-Nous pouvons tracer la flèche avec une commande \verb|\Arrow| dans le \verb|code-after| de la manière suivante : 
-\begin{Verbatim}
-$\begin{WithArrows}[~emphase#code-after = \Arrow{1-2}{2-2}{division par $2$}@ ]
-\varphi(x,y)=0
-  & \Leftrightarrow (x+2y)^2+(2x+4y)^2 = 0 \\
-.........
-\end{WithArrows}$
-\end{Verbatim}
-
-$\begin{WithArrows}[code-after = \Arrow{1-2}{2-2}{division par $2$} ]
-\varphi(x,y)=0
-  & \Leftrightarrow (x+2y)^2+(2x+4y)^2 = 0 \\
-  & \Leftrightarrow
-  \left\{\begin{WithArrows}[c]
-  x+2y & = 0 \\
-  2x+4y & = 0 
-  \end{WithArrows}\right. \\
-  & \Leftrightarrow
-  \left\{\begin{WithArrows}[c]
-  x+2y & = 0 \\
-  x+2y & = 0 
-  \end{WithArrows}\right. \\
-  & \Leftrightarrow x+2y=0 
-\end{WithArrows}$
-
-\bigskip
-Les options autorisées pour une commande \verb|\Arrow| dans le \verb|code-after| sont : \verb|ll|, \verb|lr|,
-\verb|rl|, \verb|rr|, \verb|v|, \verb|xoffset|, \verb|tikz| et \verb|tikz-code|. Exceptée \verb|v|, qui est 
-spécifique à \verb|\Arrow| dans le \verb|code-after|, toutes ces options ont leur signification habituelle.
-
-
-Avec l'option \verb|v|, la flèche tracée est verticale à une abscisse calculée avec
-la rangée de départ et la rangée d'arrivée uniquement : les lignes intermédiaires ne sont pas prises en compte
-contrairement à ce qui se passe avec l'option \verb|i|. Pour le moment, l'option \verb|i| n'est pas disponible
-pour la commande~\verb|\Arrow| dans le \verb|code-after|. Néanmoins, il est toujours possible
-de déplacer une flèche avec \verb|xoffset| (ou \verb|xshift| de Tikz).
-\begin{Verbatim}
-$\begin{WithArrows}[code-after=\Arrow~emphase#[v]@{1-2}{2-2}{division by $2$}]
-\varphi(x,y)=0
-  & \Leftrightarrow (x+2y)^2+(2x+4y)^2 = 0 \\
-.........
-\end{WithArrows}$
-\end{Verbatim}
-
-$\begin{WithArrows}[code-after = \Arrow[v]{1-2}{2-2}{division par $2$} ]
-\varphi(x,y)=0
-  & \Leftrightarrow (x+2y)^2+(2x+4y)^2 = 0 \\
-  & \Leftrightarrow
-  \left\{\begin{WithArrows}[c]
-  x+2y & = 0 \\
-  2x+4y & = 0 
-  \end{WithArrows}\right. \\
-  & \Leftrightarrow
-  \left\{\begin{WithArrows}[c]
-  x+2y & = 0 \\
-  x+2y & = 0 
-  \end{WithArrows}\right. \\
-  & \Leftrightarrow x+2y=0 
-\end{WithArrows}$
-
- 
-\interitem
-L'extension \pkg{witharrows} fournit une autre commande disponible dans le \verb|code-after| : la commande
-\verb|\MultiArrow|. Cette commande dessine un «rateau». La liste des rangées concernées par ce rateau
-est donnée dans le premier argument de la commande \verb|\MultiArrow|. La syntaxe utilisée pour décrire cette liste
-est celle de la commande \verb|\foreach| de \pkg{pgffor}.
-
-\begin{Verbatim}
-$\begin{WithArrows}[tikz = rounded corners,
-                    code-after = {~emphase#\MultiArrow{1,...,4}{text}@} ]
-A & = B \\
-  & = C \\
-  & = D \\
-  & = E \\
-  & = F
-\end{WithArrows}$
-\end{Verbatim}
-
-
-$\begin{WithArrows}[tikz = rounded corners,
-                    code-after = {\MultiArrow{1,...,4}{text}}]
-A & = B \\
-  & = C \\
-  & = D \\
-  & = E \\
-  & = F
-\end{WithArrows}$
-
-\medskip
-Pour le moment, aucune option n'est disponible pour cette commande \verb|\MultiArrow|.
-
-
-\medskip
-\section{Dessiner des flèches depuis l'extérieur des  environnements \{WithArrows\}}
-
-Si on désire dessiner des flèches depuis l'extérieur des environnements \verb|{WithArrows}|, il est possible de le
-faire en utilisant les nœuds Tikz créés par ces environnements.
-
-Le nom d'un nœud Tikz crée par \pkg{witharrows} est préfixé par \verb|wa-|. Ensuite, on trouve une liste de nombres
-qui indique quelle est la position de l'environnement dans l'arbre d'imbrication des environnements. À la fin, on a
-le suffixe \verb|l| pour un nœud de gauche et le suffixe \verb|r| pour un nœud de droite.
-
-\smallskip
-À titre d'illustration, nous donnons un exemple d'environnements \verb|{WithArrows}| imbriqués et, pour chaque nœud
-de droite, le nom de ce nœud.\footnote{Il existe une option \verb|show-node-names| pour faire afficher les noms de
-  ces nœuds.}
-
-
-\medskip
-\[\begin{WithArrows}[show-nodes,show-node-names]
-A & \vartriangleleft B+B+B+B+B+B+B+B+B+B+B+B+B \\
-& \vartriangleleft \left\{
-\begin{WithArrows}[c]
-C & \vartriangleleft D \\
-E & \vartriangleleft F 
-\end{WithArrows}
-\right. \\
- & \vartriangleleft 
-\left\{
-\begin{WithArrows}[c]
-G & \vartriangleleft H+H+H+H+H+H+H \\
-I & \vartriangleleft 
-\left\{
-\begin{WithArrows}
-J &\vartriangleleft K \\
-L &\vartriangleleft M 
-\end{WithArrows}
-\right.
-\end{WithArrows}
-\right. \\
- & \vartriangleleft 
-\left\{
-\begin{WithArrows}[c]
-N & \vartriangleleft O \\
-P & \vartriangleleft Q 
-\end{WithArrows}
-\right.
-\end{WithArrows}\]
-
-\medskip
-The package \pkg{witharrows} fournit quelques outils pour faciliter l'utilisation de ces nœuds :
-\begin{itemize}
-\item la commande \verb|\WithArrowsLastEnv| donne le numéro du dernier environnement de niveau~$0$ (c'est-à-dire
-non imbriqué dans un autre environnement de \pkg{witharrows}) ;
-
-\item un nom peut être donné à un environnement avec l'option \verb|name| et, dans ce cas, les nœuds créés dans
-l'environnement auront des alias construits en utilisant ce nom ;
-
-\item le style Tikz \verb|WithArrows/arrow| est le style utilisé par \pkg{witharrows} pour dessiner une
-flèche\footnote{Plus précisément, ce style est passé à Tikz via l'option «\verb|every path|» avant le dessin de la
-  flèche (qui se fait avec l'instruction Tikz stockée dans \verb|tikz-code|). Ce style est modifié par l'option
-  \verb|tikz| de \pkg{witharrows} (avec une portée correspondant au groupe TeX courant).} ;
-
-\item le style Tikz \verb|WithArrows/arrow/tips| est le style utilisé pour la pointe de flèche (ce style est
-lui-même chargé par le style \verb|WithArrows/arrow|).
-\end{itemize}
-
-Par exemple, nous pouvons tracer une flèche allant de  \texttt{wa-\WithArrowsLastEnv-2-1-2-r.south}
-à \texttt{wa-\WithArrowsLastEnv-3-2-r.north} avec l'instruction Tikz suivante :
-
-\begin{Verbatim}
-\begin{tikzpicture}[remember picture,overlay]
-\draw [WithArrows/arrow] 
-      ([xshift=3mm]wa-\WithArrowsLastEnv-2-1-2-r.south)
-   to ([xshift=3mm]wa-\WithArrowsLastEnv-3-2-r.north) ;
-\end{tikzpicture}
-\end{Verbatim}
-
-\[\begin{WithArrows}
-A & \vartriangleleft B+B+B+B+B+B+B+B+B+B+B+B+B \\
-& \vartriangleleft \left\{
-\begin{WithArrows}[c]
-C & \vartriangleleft D \\
-E & \vartriangleleft F 
-\end{WithArrows}
-\right. \\
- & \vartriangleleft 
-\left\{
-\begin{WithArrows}[c]
-G & \vartriangleleft H+H+H+H+H+H+H \\
-I & \vartriangleleft 
-\left\{
-\begin{WithArrows}
-J &\vartriangleleft K \\
-L &\vartriangleleft M 
-\end{WithArrows}
-\right.
-\end{WithArrows}
-\right. \\
- & \vartriangleleft 
-\left\{
-\begin{WithArrows}[c]
-N & \vartriangleleft O \\
-P & \vartriangleleft Q 
-\end{WithArrows}
-\right.
-\end{WithArrows}\]
-
-\begin{tikzpicture}[remember picture,overlay]
-\draw [WithArrows/arrow] 
-      ([xshift=3mm]wa-\WithArrowsLastEnv-2-1-2-r.south)
-   to ([xshift=3mm]wa-\WithArrowsLastEnv-3-2-r.north) ;
-\end{tikzpicture}
-
-\medskip
-Dans le cas présent, il aurait été plus facile d'utiliser une commande \verb|\Arrow| dans le \verb|code-after| mais
-c'était seulement un exemple pour expliquer comment les nœuds Tikz créés par \pkg{witharrows} peuvent être utilisés.
-
-\bigskip
-Dans l'exemple suivant, on crée deux environnements \verb|{WithArrows}| nommés
-«\verb|premier|» et «\verb|second|» et on dessine une flèche entre un nœud du premier et un nœud du second.
-
-\begin{Verbatim}
-$\begin{WithArrows}[~emphase#name=premier@]
-A & = B \\
-  & = C 
-\end{WithArrows}$
-
-\bigskip
-$\begin{WithArrows}[~emphase#name=second@]
-A' & = B' \\
-   & = C'
-\end{WithArrows}$
-
-\begin{tikzpicture}[remember picture,overlay]
-\draw [WithArrows/arrow] 
-      ([xshift=3mm]~emphase#premier@-1-r.south)
-   to ([xshift=3mm]~emphase#second@-1-r.north) ;
-\end{tikzpicture}
-\end{Verbatim}
-
-
-\begin{center}
-$\begin{WithArrows}[name=premier]
-A & = B \\
-  & = C 
-\end{WithArrows}$
-
-\bigskip
-$\begin{WithArrows}[name=second]
-A' & = B' \\
-   & = C' 
-\end{WithArrows}$
-\end{center}
-
-\begin{tikzpicture}[remember picture,overlay]
-\draw [WithArrows/arrow] 
-      ([xshift=3mm]premier-1-r.south)
-   to ([xshift=3mm]second-1-r.north) ;
-\end{tikzpicture}
-
-\section{L'environnement \{DispWithArrows\}}
-\label{DispWithArrows}
-
-Comme dit précédemment, l'environnement \verb|{WithArrows}| présente des similitudes avec l'environnement
-\verb|{aligned}| de l'\pkg{amsmath} (et de \verb|mathtools|). L'extension \pkg{witharrows}
-fournit aussi un environnement \verb|{DispWithArrows}| qui est similaire aux 
-environnements \verb|{align}| et \verb|{flalign}| de l'\pkg{amsmath}.
-
-\medskip
-L'environnement \verb|{DispWithArrows}| doit être utilisé \emph{hors} du mode mathématique. Comme
-\verb|{align}|, il doit être utilisé en mode horizontal.
-\begin{Verbatim}
-\begin{~emphase#DispWithArrows@}
-A & = (a+1)^2 \Arrow{on développe} \\
-  & = a^2 + 2a + 1 
-\end{~emphase#DispWithArrows@}
-\end{Verbatim}
-\begin{DispWithArrows}
-A & = (a+1)^2 \Arrow{on développe} \\
-  & = a^2 + 2a + 1 
-\end{DispWithArrows}
-
-\medskip
-Il est possible d'utiliser la commande \verb|\notag| (ou \verb|\nonumber|) pour supprimer un numéro d'équation. 
-
-Il est possible d'utiliser la commande \verb|\tag| pour placer une étiquette spéciale (par ex. $\star$).
-
-Il est aussi possible de placer un label pour une ligne de l'environnement avec la commande 
-\verb|\label|.
-
-Ces commandes doivent être utilisées dans la dernière colonne de l'environnement.
-\begin{Verbatim}
-\begin{DispWithArrows}
-A & = (a+1)^2 \Arrow{on développe} ~emphase#\notag@ \\
-  & = a^2 + 2a + 1 ~emphase#\tag{$\star$} \label{mon-équation}@
-\end{DispWithArrows}
-\end{Verbatim}
-\begin{DispWithArrows}
-A & = (a+1)^2 \Arrow{on développe} \notag \\
-  & = a^2 + 2a + 1 \tag{$\star$} \label{mon-équation}
-\end{DispWithArrows}
-Un lien vers l'équation \eqref{mon-équation}. On a obtenu ce lien avec la commande
-\verb|\eqref{mon-équation}| (la commande \verb|\eqref| est une commande de l'extension \pkg{amsmath}).
-
-\medskip
-Si \pkg{amsmath} (ou \pkg{mathtools}) est chargée, il est toujours possible d'utiliser
-\verb|\tag*| qui, comme dans l'extension\pkg{amsmath}, compose le label sans les parenthèses.
-Par exemple, il est possible de l'utiliser pour mettre le symbole \verb|\square| de
-\pkg{amssymb}. Ce symbole est souvent utilisé pour marquer la fin d'une démonstration.\footnote{Signalons que l'environnement \verb|{DispWithArrows}| est compatible
-avec la commande \verb|\qedhere| de \pkg{amsthm}.}
-\begin{Verbatim}
-\begin{DispWithArrows}
-A & = (a+1)^2 \Arrow{on développe} \notag \\
-  & = a^2 + 2a + 1 ~emphase#\tag*{$\square$}@
-\end{DispWithArrows}
-\end{Verbatim}
-\begin{DispWithArrows}
-A & = (a+1)^2 \Arrow{on développe} \notag \\
-  & = a^2 + 2a + 1 \tag*{$\square$} 
-\end{DispWithArrows}
-
-\medskip
-Il est également possible de supprimer tous les numéros d'équations avec l'option booléenne \verb|notag| (ou
-\verb|nonumber|), au niveau global ou bien au niveau d'un environnement.
-
-Enfin, il existe aussi 
-un environnement \verb|{DispWithArrows*}| qui supprime tous les numéros.\footnote{Même dans ce cas, il est possible
-de mettre une étiquette manuellement avec la commande \verb|\tag|.}
-\begin{Verbatim}
-\begin{~emphase#DispWithArrows*@}
-A & = (a+1)^2 \Arrow{on développe} \\
-  & = a^2 + 2a + 1 
-\end{~emphase#DispWithArrows*@}
-\end{Verbatim}
-\begin{DispWithArrows*}
-A & = (a+1)^2 \Arrow{on développe} \\
-  & = a^2 + 2a + 1 
-\end{DispWithArrows*}
-
-\medskip
-En fait, il y a une autre option, nommée \verb|tagged-lines|, qui peut être utilisée pour contrôler quelles lignes
-seront numérotées. La valeur de cette option est la liste des numéros de lignes (dans l'environnement) qui seront
-numérotées (par le système de numérotage des équations). Par exemple, avec l'option
-\verb|tagged-lines = {first,3,last}|, seulement la première, la troisième et la dernière lignes seront numérotées.
-Il y a aussi une valeur spéciale \verb|all| qui signifie que toutes les lignes doivent être numérotées.
-\begin{Verbatim}
-\begin{DispWithArrows}[~emphase#tagged-lines = last@]
-A & = A_1 \Arrow{première étape} \\
-  & = A_2 \Arrow{deuxième étape} \\
-  & = A_3 
-\end{DispWithArrows}
-\end{Verbatim}
-\begin{DispWithArrows}[tagged-lines = last]
-A & = A_1 \Arrow{première étape} \\
-  & = A_2 \Arrow{deuxième étape} \\
-  & = A_3 
-\end{DispWithArrows}
-
-\bigskip
-Avec l'option \verb|fleqn|, l'environnement est composé calé à gauche (d'une manière similaire
-à l'option \verb|fleqn| des classes standard de LaTeX). Dans ce cas, la marge gauche peut être réglée avec
-l'option \verb|mathindent| (qui a un nom inspiré du paramètre \verb|\mathindent| de LaTeX). La valeur par défaut
-pour cette option est de 25~pt.
-
-\begin{Verbatim}
-\begin{DispWithArrows}[~emphase#fleqn,mathindent = 1cm@]
-A & = (a+1)^2 \Arrow{on développe} \\
-  & = a^2 + 2a + 1 
-\end{DispWithArrows}
-\end{Verbatim}
-\begin{DispWithArrows}[fleqn,mathindent = 1cm]
-A & = (a+1)^2 \Arrow{on développe} \\
-  & = a^2 + 2a + 1 
-\end{DispWithArrows}
-
-\medskip
-\emph{Remarque} : Par conception, l'option \verb|fleqn| de \pkg{witharrows} est 
-indépendante de l'option de classe \verb|fleqn| de LaTeX. En effet, puisque les environnement de
-\pkg{witharrows} sont conçus pour être utilisés avec des flèches sur le côté droit, l'utilisateur
-peut souhaiter utiliser \pkg{witharrows} avec l'option \verb|fleqn| (de manière à avoir plus de place sur la droite
-des équations pour les flèches) tout en continuant à centrer les équations classiques.
-
-\medskip
-Si l'option \verb|leqno| est utilisée comme option de classe, les labels seront composés
-à gauche également pour les environnements \verb|{DispWithArrows}|.\footnote{L'extension \pkg{amsmath} a une option \verb|leqno|
-mais \pkg{witharrows}, bien entendu, ne tient pas compte de cette option : \pkg{witharrows}
-vérifie seulement l'option \verb|leqno| de la classe du document.}
-
-
-\medskip
-Si l'extension \pkg{amsmath} est chargée, il est possible d'utiliser la commande \verb|\intertext| dans les
-environnements \verb|{DispWithArrows}|. Il est également possible d'utiliser l'environnement \verb|{subequations}|.
-Néanmoins, il existe pour les environnements \verb|{DispWithArrows}| une option \verb|subequations| qui demande
-d'encapsuler l'environnement dans un environnement \verb|{subequations}|. 
-
-
-\medskip
-Dans l'exemple suivant, l'option \verb|subequations| est fixée via la commande \verb|\WithArrowsOptions|. Chacun
-des environnements suivants sera alors sous-numéroté (dans la portée de la commande \verb|WithArrowsOptions|).
-
-\begin{Verbatim}
-~emphase#\WithArrowsOptions{subequations}@
-Premier environnement.
-\begin{DispWithArrows}
-A & = B \\
-  & = C 
-\end{DispWithArrows}
-Deuxième environnement.
-\begin{DispWithArrows}
-D & = E \\
-  & = F 
-\end{DispWithArrows}
-\end{Verbatim}
-%
-\begin{scope}
-\WithArrowsOptions{subequations}
-Premier environnement.
-\begin{DispWithArrows}
-A & = B \\
-  & = C 
-\end{DispWithArrows}
-Deuxième environnement.
-\begin{DispWithArrows}
-D & = E \\
-  & = F 
-\end{DispWithArrows}
-\end{scope}
-
-\bigskip
-S'il n'y a pas suffisamment de place pour faire appraraître le numéro d'équation à la fin de la ligne, il n'y a pas
-de positionnement automatique de ce numéro sur la ligne suivante (comme dans les environnements de
-l'\pkg{amsmath}) : il y aura surimpression de texte. Néanmoins, dans \verb|{DispWithArrows}|, l'utilisateur peut
-utiliser la commande \verb|\tagnextline| pour demander manuellement la composition du numéro sur la ligne suivante.
-\begin{Verbatim}
-\begin{DispWithArrows}[displaystyle]
-S_{2(p+1)}
-& =\sum_{k=1}^{2(p+1)} (-1)^k k^2 \\
-& \smash[b]{=\sum_{k=1}^{2p}(-1)^kk²
-   +(-1)^{2p+1}(2p+1)^2+(-1)^{2p+2}(2p+2)^2} ~emphase#\tagnextline@ \\
-&= S_{2p}-(2p+1)^2+(2p+2)^2\\
-&=p(2p+1)-(2p+1)^2+(2p+2)^2\\
-&= 2p^2+5p+3 
-\end{DispWithArrows}
-\end{Verbatim}
-\begin{center}
-\color{gray}\vrule%
-\begin{minipage}{275pt}\color{black}
-\begin{DispWithArrows}[displaystyle]
-S_{2(p+1)}
-& =\sum_{k=1}^{2(p+1)} (-1)^k k^2 \\
-& \smash[b]{=\sum_{k=1}^{2p}(-1)^kk^2+(-1)^{2p+1}(2p+1)^2+(-1)^{2p+2}(2p+2)^2}
-\tagnextline \\ 
-&= S_{2p}-(2p+1)^2+(2p+2)^2\\
-&= 2p^2+p-4p^2-4p-1+4p^2+8p+4\\
-&= 2p^2+5p+3 
-\end{DispWithArrows}
-\end{minipage}%
-\color{gray}\vrule
-\end{center}
-
-
-
-\bigskip
-Les environnements \verb|{DispWithArrows}| et \verb|{DispWithArrows*}| fournissent également une option
-\verb|wrap-lines|. Avec cette option, les lignes de l'étiquette sont automatiquement coupées à droite.\footnote{Il
-  est possible d'éviter la coupure des mots avec l'option «\verb|align = flush left|» de Tikz.}\label{wrap-lines}
-
-\begin{Verbatim}
-\begin{DispWithArrows*}[displaystyle,~emphase#wrap-lines@]
-S_n
-& = \frac1n \Re \left(\sum_{k=0}^{n-1}\bigl(e^{i\frac{\pi}{2n}}\bigr)^k\right)
-\Arrow{somme des termes d'une suite géométrique de raison $e^{i\frac{2\pi}n}$}\\
-& = \frac1n \Re \left( \frac{1-\bigl(e^{i\frac{\pi}{2n}}\bigr)^n}
-                            {1-e^{i\frac{\pi}{2n}}}\right)
-\Arrow{cette ligne de texte a été coupée automatiquement} \\
-& = \frac1n \Re \left(\frac{1-i}{1-e^{i\frac{\pi}{2n}}}\right) 
-\end{DispWithArrows*}
-\end{Verbatim}
-\begin{DispWithArrows*}[displaystyle,wrap-lines]
-S_n
-& = \frac1n \Re \left(\sum_{k=0}^{n-1}\bigl(e^{i\frac{\pi}{2n}}\bigr)^k\right)
-\Arrow{somme des termes d'une suite géométrique de raison $e^{i\frac{2\pi}n}$}\\
-& = \frac1n \Re \left(
-\frac{1-\bigl(e^{i\frac{\pi}{2n}}\bigr)^n}{1-e^{i\frac{\pi}{2n}}} \right) 
-\Arrow{cette ligne de texte a été coupée automatiquement} \\
-& = \frac1n \Re \left(\frac{1-i}{1-e^{i\frac{\pi}{2n}}}\right) 
-\end{DispWithArrows*}
-
-\bigskip
-L'option \verb|wrap-lines| ne s'applique pas aux environnements \verb|{WithArrows}|
-imbriqués dans un environnement \verb|{DispWithArrows}| ou \verb|{DispWithArrows*}|. Néanmoins,
-elle s'applique aux instructions \verb|\Arrow| et \verb|\MultiArrow| du \verb|code-after|
-de l'environnement englobant.
-
-\vspace{1cm}
-Nous avons dit que les environnements \verb|{DispWithArrows}| et \verb|{DispWithArrows*}|
-devaient être utilisés en mode horizontal et non en mode vertical. Il y a néanmoins
-une exception. Ces environnements peuvent être utilisés directement après un \verb|\item| d'une liste
-LaTeX. Dans ce cas, aucun espace vertical n'est ajouté avant l'environnement.\footnote{Il est possible de désactiver
-  cette fonctionnalité avec l'option \verb|standard-behaviour-with-items|.}
-
-\medskip
-Voici un exemple où, avec \verb|{DispWithArrows}|, on peut insérer l'équation dans un environnement 
-\verb|{enumerate}| tout en utilisant l'option \verb|wrap-lines|.
-
-\begin{Verbatim}
-~emphase#\begin{enumerate}@
-~emphase#\item @
-\begin{DispWithArrows}%
-  [displaystyle, wrap-lines, tagged-lines = last, fleqn, mathindent = 0 pt]
-S_n
-& = \frac1n \Re \left(\sum_{k=0}^{n-1}\bigl(e^{i\frac{\pi}{2n}}\bigr)^k\right)
-\Arrow{on utilise la formule pour la somme de termes d'une suite géométrique de raison
-$e^{i\frac{2\pi}n}$} \\ 
-& = \frac1n \Re \left( \frac{1-\bigl(e^{i\frac{\pi}{2n}}\bigr)^n}
-                            {1-e^{i\frac{\pi}{2n}}}\right)
-\Arrow{$\bigl(e^{i\frac{\pi}{2n}}\bigr)^n = e^{i\frac{\pi}2}=i$} \\
-& = \frac1n \Re \left(\frac{1-i}{1-e^{i\frac{\pi}{2n}}}\right) 
-\end{DispWithArrows}
-~emphase#\end{enumerate}@
-\end{Verbatim}
-\begin{enumerate}
-\item 
-\begin{DispWithArrows}[displaystyle, wrap-lines, tagged-lines = last, fleqn, mathindent = 0 pt]
-S_n
-& = \frac1n \Re \left(\sum_{k=0}^{n-1}\bigl(e^{i\frac{\pi}{2n}}\bigr)^k\right)
-\Arrow{on utilise la formule pour la somme de termes d'une suite géométrique de raison
-$e^{i\frac{2\pi}n}$}\\ 
-& = \frac1n \Re \left(
-\frac{1-\bigl(e^{i\frac{\pi}{2n}}\bigr)^n}{1-e^{i\frac{\pi}{2n}}} \right) 
-\Arrow{$\bigl(e^{i\frac{\pi}{2n}}\bigr)^n = e^{i\frac{\pi}2}=i$} \\
-& = \frac1n \Re \left(\frac{1-i}{1-e^{i\frac{\pi}{2n}}}\right) 
-\end{DispWithArrows}
-\end{enumerate}
-
-\vspace{1cm}
-L'environnement \verb|{DispWithArrows}| est similaire à l'environnement \verb|{align}| de
-l'\pkg{amsmath}. Néanmoins, \verb|{DispWithArrows}| n'est pas construit en utilisant \verb|{align}|
-(en fait, il est possible d'utiliser \pkg{witharrows} sans \pkg{amsmath}).
-
-Il y a quelques différences entre \verb|{DispWithArrows}| et \verb|{align}|. 
-\begin{itemize}
-\item L'environnement \verb|{DispWithArrows}| ne peut pas être inséré dans un environment
-\verb|{gather}| de l'\pkg{amsmath}.
-\item Un environment \verb|{DispWithArrows}| est toujours insécable (même avec
-\verb|\allowdisplaybreaks| de l'\pkg{amsmath}).
-\item Les commandes \verb|\label|, \verb|\tag|, \verb|\notag| et \verb|\nonumber| ne sont autorisées
-que dans la dernière colonne.
-\item Après un \verb|\item| d'une liste LaTeX, aucun espace vertical n'est ajouté (cela peut être 
-modifié avec l'option \verb|standard-behaviour-with-items|).
-\item 
-\begin{bfseries}
-Enfin, par défaut, les éléments d'un environnement \verb|\{DispWithArrows\}|
-sont composés en \verb|textstyle| et non en \verb|displaystyle| (il est possible de modifier
-ce point avec l'option \verb|displaystyle|). 
-\end{bfseries}
-\end{itemize}
-
-\bigskip 
-En ce qui concerne les références, l'extension \pkg{witharrows} est compatible avec les
-extensions \pkg{autonum}, \pkg{cleveref}, \pkg{fancyref}, \pkg{fncylab},
-\pkg{hyperref}, \pkg{listlbls}, \pkg{prettyref}, \pkg{refcheck},
-\pkg{refstyle}, \pkg{showlabels}, \pkg{smartref}, \pkg{typedref} et
-\pkg{varioref} et avec les options \verb|showonlyrefs| et \verb|showmanualtags| de
-\pkg{mathtools}.\footnote{Rappelons que \pkg{varioref}, \pkg{hyperref},
-\pkg{cleveref} et \pkg{autonum} doivent être chargés dans cet ordre. L'extension
-\pkg{witharrows} peut être chargée n'importe où.}
-
-Elle n'est pas compatible avec \pkg{showkeys} (certains labels ne sont pas affichés).
-
-
-
-
-\subsection*{L'option <...> de DispWithArrows}
-
-L'environnement \verb|{DispWithArrows}| propose une option \verb|left-brace|. Si cette option est présente, son
-contenu est composé à gauche, suivi d'une accolade (d'où le nom) puis du corps de
-l'environnement.\footnote{L'option \verb|left-brace| peut aussi être utilisée sans valeur: dans ce cas, seule
-  l'accolade est tracée.}
-
-Pour la lisibilité, cette option \verb|left-brace| est aussi disponible avec une syntaxe spéciale : on peut la
-rentrer en la mettant entre chevrons (\verb|<| et \verb|>|) juste après le \verb|{DispWithArrows}| (et donc avant
-les éventuels arguments optionnels entre crochets).
-
-\bigskip
-On peut alors faire des constructions avec distinctions de cas, comme dans l'exemple
-suivant.\footnote{L'environnement \verb|{cases}| de l'\pkg{amsmath} permet de réaliser de telles distinctions de
-  cas mais on ne peut pas utiliser la numérotation automatique des équations. L'environnement \verb|{numcases}| de
-  l'extension \pkg{cases} (de Donald Arseneau) permet d'utiliser ces numéros d'équations, mais, bien entendu, il
-  n'y a pas de composition de flèches.}
-
-
-
-\medskip
-
-\begin{BVerbatim}
-\begin{DispWithArrows}~emphase#< \binom{n}{p} = >@[format = ll,fleqn,displaystyle]
-0 & \quad \text{si } p > n  
-\Arrow{ce cas peut en fait rentrer\\ dans le suivant} \\
-\frac{n(n-1)\cdots(n-p+1)}{p!} & \quad \text{si } 0 \leq p \leq n  \\
-0 & \quad \text{si } p < 0 
-\end{DispWithArrows}
-\end{BVerbatim}
-%
-\begin{DispWithArrows}< \binom{n}{p} = >[format = ll,fleqn,displaystyle]
-0 & \quad \text{si } p > n  
-\Arrow{ce cas peut en fait rentrer\\ dans le suivant} \\
-\frac{n(n-1)\cdots(n-p+1)}{p!} & \quad \text{si } 0 \leq p \leq n  \\
-0 & \quad \text{si } p < 0 
-\end{DispWithArrows}
-
-\interitem
-Dans l'exemple suivant, on sous-numérote les équations d'un système avec l'option \verb|subnumerate| (disponible
-quand l'\verb|amsmath| est chargé).
-
-\begin{Verbatim}
-\begin{DispWithArrows}~emphase#< \label{système} (\ref*{système}) \Leftrightarrow >@%
-    [format = l, subequations]
-x+y+z = -3 \Arrow[tikz=-,jump=2]{3 equations} \\
-xy+xz+yz=-2 \\
-xyz = -15 \label{dernière-équation}
-\end{DispWithArrows}
-\end{Verbatim}
-%
-\begin{DispWithArrows}< \label{système} (\ref*{système}) \Leftrightarrow >%
-    [format = l, subequations]
-x+y+z = -3 \Arrow[tikz=-,jump=2]{3 équations} \\
-xy+xz+yz=-2 \\
-xyz = -15 \label{dernière-équation} 
-\end{DispWithArrows}
-
-\bigskip
-Le système complet est l'équation \eqref{système} (cette référence a été obtenue avec
-\verb|\eqref{système}|) et la dernière équation est l'équation \eqref{dernière-équation} (référence obtenue
-avec \verb|\eqref{dernière-équation}|). Notons que \verb|\ref*|, utilisé dans le code ci-dessus, est une variante
-de \verb|ref| proposée par \pkg{hyperref} pour composer une référence sans créer de lien.
-
-\bigskip
-On peut souhaiter remplacer l'accolade gauche par un autre délimiteur extensible (gauche). On peut le faire 
-avec l'option \verb|replace-curly-brace-by|. 
-
-\bigskip
-\section{Fonctionnalités avancées}
-
-\subsection{L'option tikz-code : comment changer la forme des flèches}
-
-\label{tikz-code}
-
-L'option \verb|tikz-code|\footnote{Pour des raisons historiques, l'option \verb|tikz-code| a un alias :
-  \verb|TikzCode|.} permet à l'utilisateur de changer la forme des flèches.\footnote{Si l'option \verb|wrap-lines|
-  est utilisée dans un environnement \verb|{DispWithArrows}| ou \verb|{DispWithArrows*}|, l'option \verb|tikz-code|
-  n'aura pas d'effet sur les flèches de cet environnement mais uniquement sur les flèches des environnements
-  \verb|{WithArrows}| imbriqués.}
-
-\smallskip
-Par exemple, les options «\verb|up|» et «\verb|down|» décrites précédemment (cf.
-p.~\pageref{up-and-down}) sont programmées en interne avec \verb|tikz-code|.
-
-\smallskip
-La valeur de cette option doit être une instruction de tracé Tikz valide (avec le point-virgule final) où les trois
-marqueurs \verb|#1|, \verb|#2| et \verb|#3| représentent le point de départ, le point d'arrivée et l'étiquette de
-la flèche.
-
-
-\bigskip
-Par défaut, la valeur de \verb|tikz-code| est la suivante :
-
-\smallskip
-\qquad \verb|\draw (#1) to node {#3} (#2) ;|
-
-
-\bigskip
-Dans l'exemple suivant, nous remplaçons le chemin par défaut par un chemin avec trois segments (et un 
-nœud recouvrant le deuxième segment).
-\begin{Verbatim}
-\begin{WithArrows}[format=c,ygap=5pt,interline=4mm,
-      ~emphase#tikz-code = {\draw[rounded corners]@
-      ~emphase#                  (~#1) -- ([xshift=5mm]~#1)@
-      ~emphase#                  -- node[circle,@
-      ~emphase#                          draw,@
-      ~emphase#                          auto = false,@
-      ~emphase#                          fill = gray!50,@
-      ~emphase#                          inner sep = 1pt] {\tiny ~#3}@ 
-      ~emphase#                  ([xshift=5mm]~#2)@
-      ~emphase#                  -- (~#2) ; }@]
-3 (2x+4) = 6   \Arrow{$\div 3$} \\
-2x+4 = 2       \Arrow{$-4$}     \\
-2x = -2        \Arrow{$\div 2$} \\
- x = -1
-\end{WithArrows}
-\end{Verbatim}
-
-
-\[\begin{WithArrows}[format=c,
-      ygap=5pt,
-      interline=4mm,
-      tikz-code = {\draw[rounded corners]
-                        (#1) 
-                        --
-                        ([xshift=5mm]#1)
-                        -- node[circle,
-                                draw,
-                                auto=false,
-                                fill=gray!50,
-                                inner sep = 1pt] {\tiny #3} 
-                        ([xshift=5mm]#2)
-                        --
-                        (#2) ; }]
-3 (2x+4) = 6   \Arrow{$\div 3$} \\
-2x+4 = 2       \Arrow{$-4$}     \\
-2x = -2        \Arrow{$\div 2$} \\
- x = -1
-\end{WithArrows}\]
-
-\bigskip
-L'environnement \verb|{DispWithArrows}| et sa version étoilée \verb|{DispWithArrows*}| fournissent une commande
-\verb|\WithArrowsRightX| qui peut être utilisée dans l'option \verb|tikz-code|. Cette commande fournit
-l'abscisse de la marge droite de la boîte de composition courante (en prenant en compte les éventuels numéros des
-équations). Pour un exemple d'utilisation, voir p.~\pageref{example-WithArrowsRightX}.
-
-
-\bigskip
-\subsection{La commande \textbackslash WithArrowsNewStyle}
-
-L'extension \pkg{witharrows} fournit une commande \verb|\WithArrowsNewStyle| pour définir
-des styles d'une manière similaire aux «styles» de Tikz.
-
-La commande \verb|\WithArrowsNewStyle| prend deux arguments obligatoires. Le premier est 
-le nom du style et le second est une liste de couples clé-valeur. La portée
-de la definition ainsi faite par \verb|\WithArrowsNewStyle| est le groupe TeX courant.
-
-Le style peut être utilisé comme une clé au niveau du document (avec \verb|\WithArrowsOptions|), au niveau d'un
-environnement (via les arguments optionnels) ou bien encore dans une autre commande \verb|\WithArrowsNewStyle|.
-
-Pour un exemple d'utilisation, voir p.~\pageref{example-WithArrowsRightX}.
-
-
-\bigskip
-\subsection{Postionnement vertical des flèches}
-
-Il y a quatre paramètres pour ajuster finement la position verticale des flèches :
-\verb|ygap|, \verb|ystart|, \verb|start-adjust| et \verb|end-adjust|.
-
-\medskip
-Nous expliquons d'abord le comportement quand les paramètres \verb|start-adjust| et \verb|end-adjust| sont égaux à
-zéro:
-\begin{itemize}
-\item l'option \verb|ystart| représente la distance verticale entre la ligne de base du
-texte et le début de la flèche (valeur par défaut : $0.4$~ex);
-\item l'option \verb|ygap| représente la distance verticale entre deux flèches consécutives
-(valeur par défaut : $0.4$~ex).
-\end{itemize}
-
-
-\bigskip
-$\begin{WithArrows}[interline=1mm, adjust = 0pt]
- (\cos x + \sin x)^2 & = \cos^2 x +2 \cos x \sin x + \sin^2 x\Arrow{}\tikz[remember picture] \coordinate (A) ; \\
-   & = \cos^2x + \sin^2x + 2\sin x\cos x \Arrow{} \\
-   & = 1 + \sin(2x) 
-\end{WithArrows}$
-
-\begin{tikzpicture}[remember picture,overlay,blue]
-\draw (wa-\WithArrowsLastEnv-1-r.south) to ++(1,0) coordinate (B) to ++(0.1,0) ;;
-\draw (A) to ++(1,0) coordinate (C) to ++(0.1,0) ;;
-\draw (B) -- (C) ;
-\draw[<-] (B) to ++(0,0.2) ;
-\draw[<-] (C) to ++(0,-0.2) ;
-\path (C) node[right=1mm] {\texttt{ystart}} ;
-\draw (wa-\WithArrowsLastEnv-2-r.north) to ++(3,0) coordinate (E) to ++(0.1,0);
-\draw (wa-\WithArrowsLastEnv-2-r.south) to ++(3,0) coordinate (F) to ++(0.1,0);
-\draw (E) -- (F) ;
-\draw[<-] (E) to ++(0,0.2) ;
-\draw[<-] (F) to ++(0,-0.2) ;
-\path (F) node[right=1mm] {\texttt{ygap}} ;
-\end{tikzpicture}
-
-\interitem 
-Néanmoins, pour des raisons esthétiques, quand il est possible, \pkg{witharrows} commence
-la flèche un peu plus haut (d'une quantité \verb|start-adjust|) et termine la flèche un peu plus
-bas (par une quantité \verb|end-adjust|). Par défaut, ces deux paramètres \verb|start-adjust|
-est \verb|end-adjust| sont égaux à $0.4$~ex.
-
-\bigskip
-Voici par exemple le comportement sans le mécanisme de \verb|start-adjust| et
-\verb|end-adjust| (c'était le comportement par défaut dans les version antérieures à la version 1.13). 
-\begin{Verbatim}
-$\begin{WithArrows}~emphase#[start-adjust=0pt, end-adjust=0pt]@
-A & = (a+1)^2 \Arrow{on développe} \\
-  & = a^2 + 2a + 1  
-\end{WithArrows}$
-\end{Verbatim}
-
-$\begin{WithArrows}[start-adjust=0pt, end-adjust=0pt]
-A & = (a+1)^2 \Arrow{on développe} \\
-  & = a^2 + 2a + 1  
-\end{WithArrows}$
-
-
-\bigskip
-Voici le comportement par défaut depuis la version 1.13 (les paramètres
-\verb|start-adjust| et \verb|end-ajust| sont utilisés avec la valeur par défaut $0.4$~ex). La flèche
-est plus longue et le résultat est plus esthétique.
-
-\medskip
-$\begin{WithArrows}
-A & = (a+1)^2 \Arrow{on développe} \\
-  & = a^2 + 2a + 1  
-\end{WithArrows}$
-
-
-\bigskip
-Il est possible d'utiliser l'option \verb|adjust| qui fixe à la fois \verb|start-adjust| et \verb|end-ajust|.
-
-\bigskip
-Puisque le mécanisme de \verb|start-adjust| et \verb|end-ajust| a été ajouté dans la 
-version 1.13 of \pkg{witharrows}, cette version n'est pas strictement compatible avec
-les versions précédentes. Néanmoins, il est possible de retrouver le comportement précédent
-en fixant simplement \verb|start-adjust| et \verb|end-adjust| à $0$~pt:
-\begin{Verbatim}
-\WithArrowsOptions{adjust = 0pt}
-\end{Verbatim}
-
-\bigskip
-\subsection{Notes de pied de page dans les environnements de witharrows}
-
-Si vous voulez mettre des notes de pied de page dans un environnement de \pkg{witharrows},
-vous pouvez utiliser une paire \verb|\footnotemark|--\verb|\footnotetext|.
-
-\smallskip
-Il est aussi possible d'extraire les notes de pieds de page avec l'extension \pkg{footnote} ou bien l'extension
-\pkg{footnotehyper}.
-
-\smallskip
-Si \pkg{witharrows} est chargée avec l'option \verb|footnote| (avec \verb|\usepackage[footnote]{witharrows}| ou
-avec \verb|\PassOptionsToPackage|), l'extension \pkg{footnote} est chargée (si elle ne l'est pas déjà) et elle est
-utilisée pour extraire les notes de pied de page.
-
-\smallskip
-Si \pkg{witharrows} est chargée avec l'option \verb|footnotehyper|, l'extension \pkg{footnotehyper} est chargée (si
-elle ne l'est pas déjà) et elle est utilisée pour extraire les notes de pied de page.
-
-\smallskip
-Attention : Les extensions \pkg{footnote} et \pkg{footnotehyper} sont incompatibles.
-L'extension \pkg{footnotehyper} est le successeur de l'extension \pkg{footnote}
-et devrait être utilisée préférentiellement. L'extension \pkg{footnote} a quelques défauts ;
-en particulier, elle doit être chargée après l'extension \pkg{xcolor} et elle n'est pas parfaitement
-compatible avec \pkg{hyperref}.
-
-\medskip
-Dans ce document, l'extension \pkg{witharrows} a été chargée avec l'option \verb|footnotehyper| et nous donnons un
-exemple avec une note de pied de page dans l'étiquette d'une flèche :
-
-
-\smallskip
-$\begin{WithArrows}
-A & = (a+b)^2 
-\Arrow{on développe\,\footnote{Une note de pied de page.}} \\
-   & = a^2+b^2+2ab
-\end{WithArrows}$
-
-\bigskip
-\subsection{L'option no-arrows}
-
-L'option \verb|no-arrows| est une facilité donnée à l'utilisateur. Avec cette option,
-les flèches ne sont pas tracées. Néanmoins, une analyse des flèches est effectuée et certains erreurs sont
-détectées (par exemple, si une flèche arrive après la dernière ligne de l'environnement).
-
-
-\bigskip
-\subsection{Note pour les développeurs}
-
-Si vous définissez un environnement s'appuyant sur un environnement de 
-\pkg{witharrows}, nous recommandons de faire appel à l'environnement de \pkg{witharrows} avec 
-\verb|\WithArrows|--\verb|\endWithArrows| ou \verb|\DispWithArrows|--\verb|\endDispWithArrows| (et
-non \verb|\begin{WithArrows}|--\verb|\end{WithArrows}|, etc.).
-
-\smallskip
-En faisant ainsi, les messages d'erreur affichés par \pkg{witharrows} mentionneront (le cas échéant) le nom de
-votre environnement et seront plus faciles à comprendre pour l'utilisateur final.
-
-\smallskip
-Par exemple, vous pouvez définir un environnement \verb|{DWA}| qui va être un alias de \verb|{DispWithArrows}|:
-\begin{BVerbatim}
-\NewDocumentEnvironment {DWA} {} {\DispWithArrows}{\endDispWithArrows}
-\end{BVerbatim}
-
-\smallskip
-Si vous utilisez cet environnement \verb|{DWA}| en mode mathématique, vous aurez le message d'erreur suivant :
-
-\begin{BVerbatim}
-L'environnement {DWA} should be used only outside math mode.
-\end{BVerbatim}
-
-\interitem
-Une autre exemple est donné en interne par la définition de l'environnement \verb|{DispWithArrows*}|
-dans l'extension \pkg{witharrows} avec le code suivant:
-\begin{Verbatim}
-\NewDocumentEnvironment {DispWithArrows*} {}
-    {\WithArrowsOptions{notag}%
-     \DispWithArrows}
-    {\endDispWithArrows}
-\end{Verbatim}
-
-
-
-\section{Examples}
-
-\subsection{\textbackslash MoveEqLeft}
-
-Il est possible d'utiliser \verb|\MoveEqLeft| de \pkg{mathtools}. Dans ce cas, on doit se souvenir que la commande
-\verb|\MoveEqLeft| a aussi la valeur d'une esperluette (\verb|&|). Il faut en tenir compte pour le positionnement
-d'une éventuelle commande \verb|\Arrow|.
-
-
-%
-\begin{Verbatim}[formatcom=\small\color{gray}]
-$\begin{WithArrows}[interline=0.5ex]
-~emphase#\MoveEqLeft@ \arccos(x) = \arcsin \frac45 + \arcsin \frac5{13} 
-\Arrow{parce que les deux sont dans $[-\frac{\pi}2,\frac{\pi}2]$} \\
-& \Leftrightarrow x = \sin\left(\arcsin\frac45 + \arcsin\frac5{13}\right) \\
-& \Leftrightarrow x = \frac45\cos\arcsin\frac5{13} + \frac5{13} \cos\arcsin\frac45 
-\Arrow{$\forall x \in [-1,1], \cos(\arcsin x) = \sqrt{1-x^2}$} \\
-& \Leftrightarrow x = \frac45\sqrt{1-\bigl(\frac5{13}\bigr)^2}
-+ \frac5{13}\sqrt{1-\bigl(\frac45\bigr)^2} 
-\end{WithArrows}$
-\end{Verbatim}
-
-
-\medskip
-$\begin{WithArrows}[interline=0.5ex]
-\MoveEqLeft \arccos(x) = \arcsin \frac45 + \arcsin \frac5{13} 
-\Arrow{parce que les deux sont dans $[-\frac{\pi}2,\frac{\pi}2]$} \\
-& \Leftrightarrow x = \sin\left(\arcsin\frac45 + \arcsin\frac5{13}\right) \\
-& \Leftrightarrow x = \frac45\cos\arcsin\frac5{13} + \frac5{13} \cos\arcsin\frac45 
-\Arrow{$\forall x \in [-1,1], \cos(\arcsin x) = \sqrt{1-x^2}$} \\
-& \Leftrightarrow x = \frac45\sqrt{1-\bigl(\frac5{13}\bigr)^2}
-+ \frac5{13}\sqrt{1-\bigl(\frac45\bigr)^2} 
-\end{WithArrows}$
-
-
-\bigskip
-\subsection{Modifier la forme des nœuds}
-
-Il est possible de changer la forme des étiquettes, qui sont des nœuds Tikz, en
-modifiant la clé «\verb|every node|» de Tikz.
-
-\begin{Verbatim}
-\begin{WithArrows}%
-     [format = c,    
-      interline = 4mm,
-      tikz = {~emphase#every node/.style = {circle,@
-              ~emphase#                     draw,@
-              ~emphase#                     auto = false,@
-              ~emphase#                     fill = gray!50,@
-              ~emphase#                     inner sep = 1pt,@
-              ~emphase#                     font = \tiny}@}]
- 3 (2x+4) = 6 \Arrow{$\div 3$} \\
- 2x+4 = 2     \Arrow{$-4$} \\
- 2x = -2      \Arrow{$\div 2$} \\
- 2x = -1
-\end{WithArrows}
-\end{Verbatim}
-
-\[\begin{WithArrows}[%
-      format = c,
-      interline = 4mm,
-      tikz = {every node/.style = {circle,
-                                   draw,
-                                   auto = false,
-                                   fill = gray!50,
-                                   inner sep = 1pt,
-                                   font = \tiny}}]
- 3 (2x+4) = 6 \Arrow{$\div 3$} \\
- 2x+4 = 2     \Arrow{$-4$}     \\
- 2x = -2      \Arrow{$\div 2$} \\
- 2x = -1
-\end{WithArrows}\]
-
-
-\bigskip
-\subsection{Exemples avec l'option tikz-code}
-
-Rappelons que l'option \verb|tikz-code| est le code Tikz utilisé par \pkg{witharrows}
-pour tracer les flèches.\footnote{Si un environnement \verb|{DispWithArrows}| ou
-\verb|{DispWithArrows*}| est utilisé avec l'option \verb|wrap-lines|, la valeur de l'option
-\verb|tikz-code| n'est pas utilisée pour cet environnement (mais est utilisée pour les 
-environnements imbriqués à l'intérieur).}
-
-\smallskip
-La valeur par défaut de \verb|tikz-code| est \verb|\draw (#1) to node {#3} (#2) ;|
-où les trois marqueurs \verb|#1|, \verb|#2| et \verb|#3| représentent le point de départ, le point d'arrivée 
-et l'étiquette de la flèche.
-
-
-\bigskip
-\subsubsection{Exemple 1}
-Dans l'exemple suivant, nous définissons la valeur de \verb|tikz-code| avec deux
-instructions \verb|\path| : la première instruction trace la flèche elle-même et la seconde
-place l'étiquette dans un nœud Tikz dans le rectangle délimité par la flèche.
-
-\begin{Verbatim}
-\begin{DispWithArrows*}%
-      [displaystyle,
-       ygap = 2mm,
-       ystart = 0mm,
-       ~emphase#tikz-code = {\draw (~#1) -- ++(4.5cm,0) \verb|- (~#2) ;@
-       ~emphase#             \path (~#1) -- (~#2) @
-       ~emphase#                    node[text width = 4.2cm, right, midway] {~#3} ;}@]
-S_n
-& = \frac1n \sum_{k=0}^{n-1}\cos\bigl(\tfrac{\pi}2\cdot\tfrac kn\bigr)
-...........
-\end{Verbatim}
-
-
-\bigskip
-\begin{DispWithArrows*}[
-       displaystyle,
-       ygap = 2mm,
-       ystart = 0mm,
-       tikz-code = {\draw (#1) -- ++(4.5cm,0) |- (#2) ;
-                    \path (#1) -- (#2) 
-                           node[text width = 4.2cm, right, midway] {#3} ;}]
-S_n
-& = \frac1n \sum_{k=0}^{n-1}\cos\bigl(\tfrac{\pi}2\cdot\tfrac kn\bigr)
-\Arrow{$\cos x = \Re(e^{ix})$}\\
-& = \frac1n\sum_{k=0}^{n-1} \Re\left(e^{i\frac{k\pi}{2n}}\right)
-\Arrow{$\Re(z+z')=\Re(z)+\Re(z')$}\\
-& = \frac1n \Re\left(\sum_{k=0}^{n-1} e^{i\frac{k\pi}{2n}}\right)
-\Arrow{$\exp$ est un morphisme pour $\times$ et $+$} \\
-& = \frac1n \Re \left(\sum_{k=0}^{n-1}\bigl(e^{i\frac{\pi}{2n}}\bigr)^k\right)
-\Arrow{somme de termes d'une suite géométrique de raison $e^{i\frac{2\pi}n}$}\\
-& = \frac1n \Re \left( \frac{1-\bigl(e^{i\frac{\pi}{2n}}\bigr)^n}{1-e^{i\frac{\pi}{2n}}}\right)\\
-& = \frac1n \Re \left(\frac{1-i}{1-e^{i\frac{\pi}{2n}}}\right) 
-\end{DispWithArrows*}
-
-\bigskip
-\subsubsection{Exemple 2}
-
-\label{example-WithArrowsRightX}
-Il est possible de modifier l'exemple précédent pour avoir «\verb|text width|» calculé automatiquement en fonction 
-de la marge droite (d'une manière similaire à l'option \verb|wrap-lines|) dans les environnements
-\verb|{DispWithArrows}| et \verb|{DispWithArrows*}|. Dans la définition de \verb|tikz-code|, nous utilisons la commande 
-\verb|\WithArrowsRightX| qui donne l'abscisse de la marge droite de la boîte de composition (pour TeX, il s'agit d'une commande
-et non d'une dimension). Pour la lisibilité, nous avons utilisé un style de \pkg{witharrows}. Cet exemple nécessite
-l'extension Tikz \pkg{calc}. 
-
-\begin{Verbatim}
-\WithArrowsNewStyle{MonStyle}       
-  {displaystyle,
-   ygap = 2mm, 
-   xoffset = 0pt,
-   ystart = 0mm,
-   tikz-code = {\path let \p1 = (~#~#1)
-                      in (~#~#1)
-                          -- node [anchor = west, 
-                                   text width = {~emphase#\WithArrowsRightX@ - \x1 - 0.5 em}] 
-                                  {~#~#3} 
-                         (~#~#2) ;
-                \draw let \p1 = (~#~#1) 
-                      in (~#~#1) -- ++(~emphase#\WithArrowsRightX@ - \x1,0) |- (~#~#2) ; }}
-\end{Verbatim}
-
-\begin{Verbatim}
-\begin{DispWithArrows}[MonStyle]
-  S_n
-  & = \frac1n \sum_{k=0}^{n-1}\cos\bigl(\tfrac{\pi}2\cdot\tfrac kn\bigr)
-  \Arrow{$\cos x = \Re(e^{ix})$}\\
-...........
-\end{Verbatim}
-
-\WithArrowsNewStyle{MonStyle}       
-{displaystyle,
- ygap = 2mm,
- xoffset = 0pt,
- ystart = 0mm,
- tikz-code = {\path let \p1 = (##1)
-                    in (##1)
-                        -- node [anchor = west, 
-                                 text width = {\WithArrowsRightX - \x1 - 0.5 em}] {##3} 
-                       (##2) ;
-              \draw let \p1 = (##1) 
-                    in (##1) -- ++(\WithArrowsRightX - \x1,0) |- (##2) ; }}
-
-\begin{DispWithArrows}[MonStyle]
-S_n
-& = \frac1n \sum_{k=0}^{n-1}\cos\bigl(\tfrac{\pi}2\cdot\tfrac kn\bigr)
-\Arrow{$\cos x = \Re(e^{ix})$}\\
-& = \frac1n\sum_{k=0}^{n-1} \Re\left(e^{i\frac{k\pi}{2n}}\right)
-\Arrow{$\Re(z+z')=\Re(z)+\Re(z')$}\\
-& = \frac1n \Re\left(\sum_{k=0}^{n-1} e^{i\frac{k\pi}{2n}}\right)
-\Arrow{$\exp$ est un morphisme pour $\times$ et $+$} \\
-& = \frac1n \Re \left(\sum_{k=0}^{n-1}\bigl(e^{i\frac{\pi}{2n}}\bigr)^k\right)
-\Arrow{somme de termes d'une suite géométrique $e^{i\frac{2\pi}n}$}\\
-& = \frac1n \Re \left( \frac{1-\bigl(e^{i\frac{\pi}{2n}}\bigr)^n}{1-e^{i\frac{\pi}{2n}}}\right)\\
-& = \frac1n \Re \left(\frac{1-i}{1-e^{i\frac{\pi}{2n}}}\right) 
-\end{DispWithArrows}
-
-
-
-\bigskip
-\subsubsection{Exemple 3}
-
-Dans l'exemple suivant, nous changeons la forme de la flèche selon que la rangée de départ est plus longue ou
-plus courte que la rangée d'arrivée. Cet exemple nécessite l'extension \pkg{calc} de Tikz.
-
-
-\begin{Verbatim}
-\begin{WithArrows}[ll,interline=5mm,xoffset=5mm,
-      ~emphase#tikz-code  = {\draw[rounded corners,@
-      ~emphase#                    every node/.style = {circle,@
-      ~emphase#                                         draw,@
-      ~emphase#                                         auto = false,@
-      ~emphase#                                         inner sep = 1pt,@
-      ~emphase#                                         fill = gray!50,@
-      ~emphase#                                         font = \tiny }]@ 
-      ~emphase#                    let \p1 = (~#1),@
-      ~emphase#                        \p2 = (~#2)@
-      ~emphase#                    dans \ifdim \x1 > \x2@
-      ~emphase#                         (\p1) -- node {~#3} (\x1,\y2) -- (\p2)@
-      ~emphase#                       \else@
-      ~emphase#                         (\p1) -- (\x2,\y1) -- node {~#3} (\p2)@
-      ~emphase#                       \fi ;}@]
-E & \Longleftrightarrow \frac{(x+4)}3 + \frac{5x+3}5 = 7 
-\Arrow{$\times 15$}\\
-  & \Longleftrightarrow 5(x+4) + 3(5x+3) = 105 \\
-  & \Longleftrightarrow 5x+20 + 15x+9 = 105 \\
-  & \Longleftrightarrow 20x+29 = 105 
-\Arrow{$-29$}\\
-  & \Longleftrightarrow 20x = 76 
-\Arrow{$\div 20$}\\
-  & \Longleftrightarrow x = \frac{38}{10} 
-\end{WithArrows}
-\end{Verbatim}
-
-
-\[\begin{WithArrows}[ll,interline=5mm,xoffset=5mm,
-      tikz-code  = {\draw[rounded corners,
-                          every node/.style = {circle,
-                                               draw,
-                                               auto = false,
-                                               inner sep = 1pt,
-                                               fill = gray!50,
-                                               font = \tiny}] 
-                          let \p1 = (#1),
-                              \p2 = (#2)
-                          in \ifdim \x1 > \x2
-                               (\p1) -- node {#3} (\x1,\y2) -- (\p2)
-                             \else
-                               (\p1) -- (\x2,\y1) -- node {#3} (\p2)
-                             \fi ;}]
-E & \Longleftrightarrow \frac{(x+4)}3 + \frac{5x+3}5 = 7 
-\Arrow{$\times 15$}\\
-  & \Longleftrightarrow 5(x+4) + 3(5x+3) = 105 \\
-  & \Longleftrightarrow 5x+20 + 15x+9 = 105 \\
-  & \Longleftrightarrow 20x+29 = 105 
-\Arrow{$-29$}\\
-  & \Longleftrightarrow 20x = 76 
-\Arrow{$\div 20$}\\
-  & \Longleftrightarrow x = \frac{38}{10} 
-\end{WithArrows}\]
-
-
-
-\subsection{Boucle numérotée automatique}
-
-Supposons que nous voulions tracer une boucle avec des flèches numérotées. Dans ce but, il est
-possible d'écrire une commande dédiée \verb|\BoucleNumérotée| qui fera le travail quand elle 
-sera utilisée dans le \verb|code-after|. Dans l'exemple suivant, nous avons écrit cette commande avec
-\verb|\NewDocumentCommand| de \pkg{xparse} et \verb|\foreach| de \pkg{pgffor} (ces deux
-extensions sont chargées quand \pkg{witharrows} est chargé.).
-
-\begin{Verbatim}
-\NewDocumentCommande \NombreedLoop {}
-        {\foreach \j dans {2,...,\WithArrowsNbLines} 
-              { \pgfmathtruncatemacro{\i}{\j-1}
-                \Arrow[rr]{\i}{\j}{\i} }
-         \Arrow[rr,xoffset=1cm,tikz=<-]{1}{\WithArrowsNbLines}{\WithArrowsNbLines}}
-\end{Verbatim}
-
-La commande \verb|\WithArrowsNbLines| est une commande disponible dans le \verb|code-after| qui donne
-le nombre total de lignes (=rangées) dans l'environnement courant (pour TeX, il s'agit d'une commande et non d'un
-compteur).
-
-
-\bigskip
-\begin{Verbatim}
-$\begin{WithArrows}[~emphase#code-after = \BoucleNumérotée@]
-a.\;& f \text{ est continue sur } E \\
-b.\;& f \text{ est continue en } 0 \\
-c.\;& f \text{ est bornée sur la sphère unité} \\
-d.\;& \exists K > 0\quad \forall x \in E\quad \|f(x)\| \le K \|x\| \\
-e.\;& f \text{ est lipschitzienne} 
-\end{WithArrows}$
-\end{Verbatim}
-
-\bigskip
-\begin{scope}
-\NewDocumentCommand \BoucleNumérotée {}
-        {\foreach \j in {2,...,\WithArrowsNbLines} 
-              { \pgfmathtruncatemacro{\i}{\j-1}
-                \Arrow[rr]{\i}{\j}{\i} }
-         \Arrow[rr,xoffset=1cm,tikz=<-]{1}{\WithArrowsNbLines}{\WithArrowsNbLines}}
-
-
-$\begin{WithArrows}[code-after = \BoucleNumérotée]
-a.\;& f \text{ est continue sur } E \\
-b.\;& f \text{ est continue en } 0 \\
-c.\;& f \text{ est bornée sur la sphère unité} \\
-d.\;& \exists K > 0\quad \forall x \in E\quad \|f(x)\| \le K \|x\| \\
-e.\;& f \text{ est lipschitzienne} 
-\end{WithArrows}$
-
-
-\bigskip
-Comme d'habitude, il est possible changer les caractéristiques des flèches et des nœuds 
-avec l'option \verb|tikz|. Néanmoins, si nous voulons changer le style pour avoir, par
-exemple, les numéros entre parenthèses, le moyen le plus rapide est de changer la valeur de
-\verb|tikz-code|:
-
-\begin{Verbatim}
-tikz-code = {\draw (~#1) to node {\footnotesize (~#3)} (~#2) ;}
-\end{Verbatim}
-
-\WithArrowsOptions{tikz-code = {\draw (#1) to node {\footnotesize (#3)} (#2) ;}}
-
-$\begin{WithArrows}[code-after = \BoucleNumérotée]
-a.\;& f \text{ est continue on } E \\
-b.\;& f \text{ est continue dans } 0 \\
-c.\;& f \text{ est bornée sur la sphère unité} \\
-d.\;& \exists K > 0\quad \forall x \in E\quad \|f(x)\| \le K \|x\| \\
-e.\;& f \text{ est lipschitzienne}  
-\end{WithArrows}$
-
-\end{scope}
-
-
-
-
-
-\end{document}
diff --git a/Master/texmf-dist/doc/latex/witharrows/witharrows.pdf b/Master/texmf-dist/doc/latex/witharrows/witharrows.pdf
deleted file mode 100644
index a93bca1ae42..00000000000
--- a/Master/texmf-dist/doc/latex/witharrows/witharrows.pdf
+++ /dev/null
diff --git a/Master/texmf-dist/source/latex/witharrows/witharrows.dtx b/Master/texmf-dist/source/latex/witharrows/witharrows.dtx
deleted file mode 100644
index f814d93b32b..00000000000
--- a/Master/texmf-dist/source/latex/witharrows/witharrows.dtx
+++ /dev/null
@@ -1,6603 +0,0 @@
-% \iffalse meta-comment
-%
-% Copyright (C) 2017-2019 by F. Pantigny
-% -----------------------------------
-%
-% This file may be distributed and/or modified under the
-% conditions of the LaTeX Project Public License, either version 1.3
-% of this license or (at your option) any later version.
-% The latest version of this license is in:
-%
-% http://www.latex-project.org/lppl.txt
-%
-% and version 1.3 or later is part of all distributions of LaTeX
-% version 2005/12/01 or later.
-%
-% \fi
-% \iffalse
-\def\myfileversion{1.18}
-\def\myfiledate{2019/07/24}
-%
-%
-%<*batchfile>
-\begingroup
-\input l3docstrip.tex
-\keepsilent
-\usedir{tex/latex/witharrows}
-\preamble
-
-Copyright (C) 2017-2019 by F. Pantigny
------------------------------------
-
-This file may be distributed and/or modified under the
-conditions of the LaTeX Project Public License, either version 1.3
-of this license or (at your option) any later version.
-The latest version of this license is in:
-
-http://www.latex-project.org/lppl.txt
-
-and version 1.3 or later is part of all distributions of LaTeX
-version 2005/12/01 or later.
-
-\endpreamble
-\askforoverwritefalse
-\endgroup
-%</batchfile>
-%
-%<@@=wi>
-%<*driver>
-\documentclass[dvipsnames]{l3doc}% dvipsnames is for xcolor (loaded by Tikz, loaded by witharrows)
-\usepackage{xltxtra}
-\usepackage[xetex]{geometry}
-\geometry{left=2.8cm,right=2.8cm,top=2.5cm,bottom=2.5cm,papersize={21cm,29.7cm}}
-\usepackage[footnotehyper]{witharrows}
-\usetikzlibrary{calc}
-\usepackage{mathtools}
-\usepackage{amssymb}
-\usepackage[only,llbracket,rrbracket]{stmaryrd}
-\usepackage{varwidth}
-\NewDocumentEnvironment {scope} {} {} {}
-\def\interitem{\vskip 7mm plus 2 mm minus 3mm}          
-\def\emphase{\bgroup\color{RoyalPurple}\let\next=}
-\fvset{commandchars=\~\#\@,formatcom={\color{gray}}}
-\DeclareMathOperator{\re}{Re}
-\skip \footins = 2 \bigskipamount
-\parindent 0pt
-\DisableCrossrefs
-\begin{document}
-\DocInput{witharrows.dtx}
-\end{document}
-%</driver>
-% \fi 
-% \VerbatimFootnotes
-% \title{The package \pkg{witharrows}\thanks{This document corresponds to the
-% version~\myfileversion\space of \pkg{witharrows}, at the date
-% of~\myfiledate.}} \author{F. Pantigny \\ \texttt{fpantigny@wanadoo.fr}} 
-%
-% \maketitle
-%
-% \hypersetup{
-%   pdfinfo = {
-%      Title = { The extension 'witharrows' },
-%      Subject = { A LaTeX extension } ,
-%      Author = { F. Pantigny }
-%   }
-% }
-%
-%
-% \begin{abstract}
-% The LaTeX package \pkg{witharrows} provides environments |{WithArrows}| and
-% |{DispWithArrows}| similar to the environments |{aligned}| and |{align}| of
-% \pkg{amsmath} but with the possibility to draw arrows on the right side of the
-% alignment. These arrows are usually used to give explanations concerning the
-% mathematical calculus presented.
-% \end{abstract}
-%
-%
-% \vspace{1cm} 
-% This package can be used with |xelatex|, |lualatex|, |pdflatex|
-% but also by the classical workflow |latex|-|dvips|-|ps2pdf| (or Adobe
-% Distiller). Several compilations may be necessary. This package requires the
-% packages \pkg{expl3}, \pkg{xparse} and \pkg{tikz}. The Tikz libraries
-% \pkg{arrows.meta} and \pkg{bending} are also required.
-%
-% \bigskip
-% This package provides an environment |{WithArrows}| to construct alignments of
-% equations with arrows for the explanations on the right side:
-% 
-% \begin{Verbatim}
-% $\begin{WithArrows}
-% A & = (a+1)^2 ~emphase#\Arrow{we expand}@ \\
-%   & = a^2 + 2a + 1  % don't put \\ here
-% \end{WithArrows}$
-% \end{Verbatim}
-%
-% $\begin{WithArrows}
-% A & = (a+1)^2 \Arrow{we expand} \\
-%   & = a^2 + 2a + 1  
-% \end{WithArrows}$
-%
-%
-%
-% \medskip
-% The arrow has been drawn with the command |\Arrow| on the row from which it
-% starts. The command |\Arrow| must be used in the second column (the best way
-% is to put it at the end of the second cell of the row as in the previous
-% example).
-%
-% \medskip
-% The environment |{WithArrows}| bears similarities with the environment
-% |{aligned}| of \pkg{amsmath} (and |mathtools|). The extension \pkg{witharrows}
-% also provides an environment |{DispWithArrows}| which is similar to the
-% environment |{align}| of \pkg{amsmath}: cf. p. \pageref{DispWithArrows}.
-% 
-%
-% \section{Options for the shape of the arrows}
-%
-% The command |\Arrow| has several options. These options can be put between
-% square brackets, before, or after the mandatory argument.
-%
-% The option |jump| gives the number\footnote{It's not possible to give a
-% non-positive value to |jump|. See below (p.~\pageref{Backwards}) the way to
-% draw an arrow which goes backwards.} of rows the arrow must jump (the default
-% value is, of course,~$1$).
-%
-% 
-% \begin{Verbatim}
-% $\begin{WithArrows}
-% A & = \bigl((a+b)+1\bigr)^2 \Arrow[~emphase#jump=2@]{we expand} \\
-%   & = (a+b)^2 +  2(a+b) +1 \\
-%   & = a^2 + 2ab + b^2 + 2a + 2b +1 
-% \end{WithArrows}$
-% \end{Verbatim}
-%
-% $\begin{WithArrows}
-% A & = \bigl((a+b)+1\bigr)^2 \Arrow[jump=1+1]{we expand} \\
-%   & = (a+b)^2 + 2(a+b) +1 \\
-%   & = a^2 + 2ab + b^2 + 2a + 2b +1 
-% \end{WithArrows}$
-%
-% \interitem
-% It's possible to put several arrows which start from the same row.
-% \begin{Verbatim}
-% $\begin{WithArrows}
-% A & = \bigl((a+b)+1\bigr)^2 ~emphase#\Arrow{}\Arrow{}[jump=2]@ \\
-%   & = (a+b)^2 + 2(a+b) +1 \\
-%   & = a^2 + 2ab + b^2 + 2a + 2b +1 
-% \end{WithArrows}$
-% \end{Verbatim}
-%
-% $\begin{WithArrows}
-% A & = \bigl((a+b)+1\bigr)^2 \Arrow{}\Arrow{}[jump=2] \\
-%   & = (a+b)^2 + 2(a+b) +1 \\
-%   & = a^2 + 2ab + b^2 + 2a + 2b +1 
-% \end{WithArrows}$
-%
-% \interitem
-% The option |xoffset| shifts the arrow to the right (we usually don't want the
-% arrows to be stucked on the text). The default value of |xoffset| is $3$~mm.
-% \begin{Verbatim}
-% $\begin{WithArrows}
-% A & = \bigl((a+b)+1\bigr)^2 
-% \Arrow[~emphase#xoffset=1cm@]{with \texttt{xoffset=1cm}} \\
-%   & = (a+b)^2 + 2(a+b) +1 
-% \end{WithArrows}$
-% \end{Verbatim}
-%
-% $\begin{WithArrows}
-% A & = \bigl((a+b)+1\bigr)^2 
-% \Arrow[xoffset=1cm]{with \texttt{xoffset=1cm}} \\
-%   & = (a+b)^2 + 2(a+b) +1 
-% \end{WithArrows}$
-%
-%
-% \interitem 
-% The arrows are drawn with Tikz. That's why the command |\Arrow| has an option
-% |tikz| which can be used to give to the arrow (in fact, the command |\path| of
-% Tikz) the options proposed by Tikz for such an arrow. The following example
-% gives an thick arrow.
-% \begin{Verbatim}
-% $\begin{WithArrows}
-% A & = (a+1)^2 \Arrow[~emphase#tikz=thick@]{we expand} \\
-%   & = a^2 + 2a + 1 
-% \end{WithArrows}$
-% \end{Verbatim}
-%
-% $\begin{WithArrows}
-% A & = (a+1)^2 \Arrow[tikz=thick]{we expand} \\
-%   & = a^2 + 2a + 1 
-% \end{WithArrows}$
-%
-% \interitem
-% It's also possible to change the arrowheads. For example, we can draw an arrow
-% which goes backwards with the Tikz option~|<-|.
-% \label{Backwards} 
-%
-% \begin{Verbatim}
-% $\begin{WithArrows}
-% A & = (a+1)^2 \Arrow~emphase#[tikz=<-]@{we factorize} \\
-%   & = a^2 + 2a + 1 
-% \end{WithArrows}$
-% \end{Verbatim}
-%
-% $\begin{WithArrows}
-% A & = (a+1)^2 \Arrow[tikz=<-]{we factorize} \\
-%   & = a^2 + 2a + 1 
-% \end{WithArrows}$
-%
-% \interitem
-% It's also possible to suppress both tips of the arrow with the Tikz option
-% ``|-|''.
-% \begin{Verbatim}
-% $\begin{WithArrows}
-% A & = (a+1)^2 \Arrow[~emphase#tikz=-@]{very classical} \\
-%   & = a^2 + 2a + 1 
-% \end{WithArrows}$
-% \end{Verbatim}
-%
-% $\begin{WithArrows}
-% A & = (a+1)^2 \Arrow[tikz=-]{very classical} \\
-%   & = a^2 + 2a + 1 
-% \end{WithArrows}$
-%
-% \interitem
-% In order to have straight arrows instead of curved ones, we must use the Tikz
-% option ``|bend left = 0|''.
-% \begin{Verbatim}
-% $\begin{WithArrows}
-% A & = (a+1)^2 \Arrow~emphase#[tikz={bend left=0}]@{we expand} \\
-%   & = a^2 + 2a + 1 
-% \end{WithArrows}$
-% \end{Verbatim}
-%
-% $\begin{WithArrows}
-% A & = (a+1)^2 \Arrow[tikz={bend left=0}]{we expand} \\
-%   & = a^2 + 2a + 1 
-% \end{WithArrows}$
-%
-% \smallskip 
-% In fact, it's possible to change more drastically the shape or the arrows with
-% the option |tikz-code| (presented p.~\pageref{tikz-code}).
-%
-% \interitem
-% It's possible to use the Tikz option ``|text width|'' to control the width of
-% the text associated to the arrow.\footnote{It's possible to avoid the
-% hyphenations of the words with the option ``|align = flush left|'' of Tikz.}
-% %
-% \begin{Verbatim}
-% $\begin{WithArrows}
-% A & = \bigl((a+b)+1\bigr)^2 
-% \Arrow[jump=2,~emphase#tikz={text width=5.3cm}@]{We have done...} \\
-%   & = (a+b)^2 + 2(a+b) +1 \\
-%   & = a^2 + 2ab + b^2 + 2a + 2b +1 
-% \end{WithArrows}$
-% \end{Verbatim}
-%
-% $\begin{WithArrows}
-% A & = \bigl((a+b)+1\bigr)^2 
-% \Arrow[jump=2,tikz={text width=5.3cm}]{We have done a two-stages expansion but
-% it would have been clever
-% to expand with the multinomial theorem.} \\
-% & = (a+b)^2 + 2(a+b) +1 \\
-% & = a^2 + 2ab + b^2 + 2a + 2b +1
-% \end{WithArrows}$
-%
-%
-% \bigskip
-% In the environments |{DispWithArrows}| and |{DispWithArrows*}|, there is an
-% option |wrap-lines|. With this option, the lines of the labels are
-% automatically wrapped on the right: see p.~\pageref{wrap-lines}.
-% 
-% \interitem
-% If we want to change the font of the text associated to the arrow, we can, of
-% course, put a command like |\bfseries|, |\large| or |\sffamily| at the
-% beginning of the text. But, by default, the texts are composed with a
-% combination of |\small| and |\itshape|. When adding |\bfseries| at the
-% beginning of the text, we won't suppress the |\small| and the |\itshape| and
-% we will consequently have a text in a bold, italic and small font.
-% %
-% \begin{Verbatim}
-% $\begin{WithArrows}
-% A & = (a+1)^2 \Arrow{~emphase#\bfseries@ we expand} \\
-%   & = a^2 + 2a + 1 
-% \end{WithArrows}$
-% \end{Verbatim}
-%
-% $\begin{WithArrows}
-% A & = (a+1)^2 \Arrow{\bfseries we expand} \\
-%   & = a^2 + 2a + 1 
-% \end{WithArrows}$
-%
-% \interitem 
-% It's possible to put commands |\\| in the text to force new lines\footnote{By
-% default, this is not possible in a Tikz node. However, in \pkg{witharrows},
-% the nodes are created with the option |align=left|, and, thus, it becomes
-% possible.}. However, if we put a |\\| , a command of font placed in the
-% beginning of the text will have effect only until the first command |\\| (like
-% in an environment |{tabular}|). That's why Tikz gives an option |font| to
-% modify the font of the whole text. Nevertheless, if we use the option
-% |tikz={font={\bfseries}}|, the default specification of |\small| and
-% |\itshape| will be overwritten.
-% %
-% \begin{Verbatim}
-% $\begin{WithArrows}
-% A & = (a+1)^2 \Arrow[~emphase#tikz={font={\bfseries}}@]{we expand} \\
-%   & = a^2 + 2a + 1 
-% \end{WithArrows}$
-% \end{Verbatim}
-%
-% $\begin{WithArrows}
-% A & = (a+1)^2 \Arrow[tikz={font={\bfseries}}]{we expand} \\
-%   & = a^2 + 2a + 1 
-% \end{WithArrows}$
-%
-% \medskip
-% If we want exactly the same result as previously, we have to give to the
-% option |font| the value |\itshape\small\bfseries|.
-%
-%
-% \interitem 
-% The options can be given directly between square brackets to the environment
-% |{WithArrows}|. There must be no space between the |\begin{WithArrows}| and
-% the opening bracket (|[|) of the options of the environment. Such options
-% apply to all the arrows of the environment.\footnote{They also apply to the
-% nested environments |{WithArrows}| (with the logical exceptions of
-% |interline|, |code-before| and |code-after|).}
-% %
-% \begin{Verbatim}
-% $\begin{WithArrows}[~emphase#tikz=blue@]
-% A & = \bigl((a+b)+1\bigr)^2 \Arrow{first expansion.} \\
-%   & = (a+b)^2 + 2(a+b) +1 \Arrow{second expansion.} \\
-%   & = a^2 + 2ab + b^2 + 2a + 2b +1 
-% \end{WithArrows}$
-% \end{Verbatim}
-%
-% $\begin{WithArrows}[tikz=blue]
-% A & = \bigl((a+b)+1\bigr)^2 \Arrow{first expansion.} \\
-%   & = (a+b)^2 + 2(a+b) +1 \Arrow{second expansion.} \\
-%   & = a^2 + 2ab + b^2 + 2a + 2b +1 
-% \end{WithArrows}$
-%
-%
-% \interitem
-% The environment |{WithArrows}| has an option |displaystyle|. With this option,
-% all the elements are composed in |\displaystyle| (like in an environment
-% |{aligned}| of \pkg{amsmath}).
-%
-% \medskip
-% Without the option |displaystyle|:
-% %
-% \begin{Verbatim}
-% $\begin{WithArrows}
-% \int_0^1 (x+1)^2 dx 
-% & = \int_0^1 (x^2+2x+1) dx
-% \Arrow{linearity of integration}     \\
-% & = \int_0^1 x^2 dx + 2 \int_0^1 x dx + \int_0^1 dx \\
-% & = \frac13 + 2\frac12 + 1 \\
-% & = \frac73
-% \end{WithArrows}$
-% \end{Verbatim}
-%
-% $\begin{WithArrows}
-% \int_0^1 (x+1)^2 dx 
-% & = \int_0^1 (x^2+2x+1) dx
-% \Arrow{linearity of integration}     \\
-% & = \int_0^1 x^2 dx + 2 \int_0^1 x dx + \int_0^1 dx \\
-% & = \frac13 + 2\frac12 + 1 \\
-% & = \frac73
-% \end{WithArrows}$
-%
-%
-% \medskip
-% The same example with the option |displaystyle|:\par\nobreak
-%
-% $\begin{WithArrows}[displaystyle]
-% \int_0^1 (x+1)^2 dx 
-% & = \int_0^1 (x^2+2x+1) dx
-% \Arrow{linearity of integration}     \\
-% & = \int_0^1 x^2 dx + 2 \int_0^1 x dx + \int_0^1 dx \\
-% & = \frac13 + 2\frac12 + 1 \\
-% & = \frac73
-% \end{WithArrows}$
-%
-%
-%
-% \interitem 
-% Almost all the options can also be set at the document level with the command
-% |\WithArrowsOptions|. In this case, the scope of the declarations is the
-% current TeX group (these declarations are ``semi-global''). For example, if we
-% want all the environments |{WithArrows}| composed in |\displaystyle| with blue
-% arrows, we can write
-% |\WithArrowsOptions{displaystyle,tikz=blue}|.\footnote{It's also possible to
-% configure \pkg{witharrows} by modifying the Tikz style |WithArrows/arrow|
-% which is the style used by \pkg{witharrows} when drawing an arrow. For
-% example, to have the labels in blue with roman (upright) types, one can use
-% the following instruction: 
-% |\tikzset{WithArrows/arrow/.append style = {blue,font = {}}}|.}
-% 
-% \begin{Verbatim}
-% ~emphase#\WithArrowsOptions{displaystyle,tikz=blue}@
-% $\begin{WithArrows}
-% \sum_{i=1}^n (x_i+1)^2 
-% & = \sum_{i=1}^n (x_i^2+2x_i+1) \Arrow{by linearity}\\
-% & = \sum_{i=1}^n x_i^2 + 2\sum_{i=1}^nx_i+ n
-% \end{WithArrows}$
-% \end{Verbatim}
-%
-% \begin{scope}
-% \WithArrowsOptions{displaystyle,tikz=blue}
-% $\begin{WithArrows}
-% \sum_{i=1}^n (x_i+1)^2 
-% & = \sum_{i=1}^n (x_i^2+2x_i+1) \Arrow{by linearity}\\
-% & = \sum_{i=1}^n x_i^2 + 2\sum_{i=1}^nx_i+ n
-% \end{WithArrows}$
-% \end{scope}
-%
-%
-% \interitem
-% The command |\Arrow| is recognized only in the environments |{WithArrows}|. If
-% we have a command |\Arrow| previously defined, it's possible to go on using it
-% outside the environments |{WithArrows}|.
-%
-% However, a previouly defined command |\Arrow| may still be useful in an
-% environment |{WithArrows}|. If we want to use it in such an environment, it's
-% possible to change the name of the command |\Arrow| of the package
-% \pkg{witharrows}: there is an option |command-name|\footnote{For historical
-% reasons, there is an alias for this option: |CommandName|.} for this purpose.
-% The new name of the command must be given to the option \emph{without} the
-% leading backslash.
-% %
-% \begin{Verbatim}
-% \NewDocumentCommand {\Arrow} {} {\longmapsto}
-% $\begin{WithArrows}[~emphase#command-name=Explanation@]
-% f & = \bigl(x \Arrow (x+1)^2\bigr)
-% ~emphase#\Explanation{we work directly on fonctions}@\\
-% & = \bigl(x \Arrow x^2+2x+1\bigr)
-% \end{WithArrows}$
-% \end{Verbatim}
-% %
-% \begin{scope}
-% \NewDocumentCommand {\Arrow} {} {\longmapsto}
-% $\begin{WithArrows}[command-name=Explanation]
-% f & = \bigl(x \Arrow (x+1)^2\bigr)
-% \Explanation{we work directly on fonctions}\\
-% & = \bigl(x \Arrow x^2+2x+1\bigr)
-% \end{WithArrows}$
-% \end{scope}
-%
-%
-% \interitem 
-% The environment |{WithArrows}| provides also two options |code-before| and
-% |code-after|\footnote{For historical reasons, there are aliases for these
-% options: |CodeBefore| and |CodeAfter|.} for LaTeX code that will be executed
-% at the beginning and at the end of the environment. These options are not
-% designed to be hooks (they are available only at the environment level and
-% they do not apply to the nested environments).
-% %
-% \begin{Verbatim}
-% $\begin{WithArrows}[~emphase#code-before = \color{blue}@]
-% A & = (a+b)^2 \Arrow{we expand} \\
-%   & = a^2 + 2ab + b^2 
-% \end{WithArrows}$
-% \end{Verbatim}
-%
-% $\begin{WithArrows}[code-before = \color{blue}]
-% A & = (a+b)^2 \Arrow{we expand} \\
-%   & = a^2 + 2ab + b^2 
-% \end{WithArrows}$
-% 
-% \medskip 
-% Special commands are available in |code-after|: a command |\WithArrowsNbLines|
-% which gives the number of lines (=rows) of the current environment (this is a
-% command and not a counter), a special form of the command |\Arrow| and the
-% command |\MultiArrow|: these commands are described in the section concerning
-% the nested environments, p.~\pageref{NestedEnv}.
-%
-% \section{Numbers of columns}
-%
-% So far, we have used the environment |{WithArrows}| with two columns. However,
-% it's possible to use the environment with an arbitrary number of columns with
-% the option |format|. The value given to this option is like the preamble of an
-% environment |{array}|, that is to say a sequence of letters |r|, |c| and |l|.
-% The default value of the option |format| is, in fact, |rl|.
-%
-% \bigskip
-% For exemple, if we want only one column left-aligned, we use the option |format=l|.
-% \begin{Verbatim}
-% $\begin{WithArrows}[~emphase#format = l@]
-% f(x) \ge g(x) \Arrow{by squaring both sides} \\
-% f(x)^2 \ge g(x)^2 \Arrow{by moving to left side} \\
-% f(x)^2 - g(x)^2 \ge 0 
-% \end{WithArrows}$
-% \end{Verbatim}
-%
-% $\begin{WithArrows}[format = l]
-% f(x) \ge g(x) \Arrow{by squaring both sides} \\
-% f(x)^2 \ge g(x)^2 \Arrow{by moving to left side} \\
-% f(x)^2 - g(x)^2 \ge 0 
-% \end{WithArrows}$
-%
-% \interitem
-% In the following example, we use five columns all centered (the environment
-% |{DispWithArrows*}| is  presented p.~\pageref{DispWithArrows}).
-%
-% \begin{Verbatim}
-% \begin{DispWithArrows*}[~emphase#format = ccccc@,
-%                         wrap-lines,
-%                         tikz = {align = flush left},
-%                         interline=1mm]
-% k & \;\le\; & t & \;\le\; & k+1 \\
-% \frac{1}{k+1} & \le & \frac{1}{t} & \le & \frac{1}{k} 
-% \Arrow{we can integrate the inequalities since $k \leq k+1$ } \\
-% \int\limits_k^{k+1} \frac{d t}{k+1} 
-% & \le & \int\limits_k^{k+1} \frac{dt}{t} 
-% & \le & \int\limits_k^{k+1} \frac{dt}{k} \\
-% \frac{1}{k+1} & \le & \ln(k+1)-\ln(k) & \le & \frac{1}{k} 
-% \end{DispWithArrows*}
-% \end{Verbatim}
-% \begin{DispWithArrows*}[format = ccccc,
-%                         wrap-lines,
-%                         tikz = {align = flush left},
-%                         interline=1mm]
-% k & \;\le\; & t & \;\le\; & k+1 \\
-% \frac{1}{k+1} & \le & \frac{1}{t} & \le & \frac{1}{k} 
-% \Arrow{we can integrate the inequalities since $k \leq k+1$ } \\
-% \int\limits_k^{k+1} \frac{d t}{k+1} 
-% & \le & \int\limits_k^{k+1} \frac{dt}{t} 
-% & \le & \int\limits_k^{k+1} \frac{dt}{k} \\
-% \frac{1}{k+1} & \le & \ln(k+1)-\ln(k) & \le & \frac{1}{k} 
-% \end{DispWithArrows*}
-% 
-%
-% \section{Precise positioning of the arrows}
-%
-%
-% The environment |{WithArrows}| defines, during the composition of the array,
-% two series of nodes materialized in red in the following example.\footnote{The
-% option |show-nodes| can be used to materialize the nodes. The nodes are in
-% fact Tikz nodes of shape ``rectangle'', but with zero width. An arrow between
-% two nodes starts at the \emph{south} anchor of the first node and arrives at
-% the \emph{north} anchor of the second node.}
-%
-% \smallskip
-% $\begin{WithArrows}[displaystyle,show-nodes]
-% I
-% & = \int_{\frac{\pi}4}^0 \ln\Bigl(1+\tan\left(\tfrac{\pi}4-u\right)\Bigr)(-d u) \\
-% & = \int_0^{\frac{\pi}4} \ln\Bigl(1+\tan\left(\tfrac{\pi}4-u\right)\Bigr)d u \\
-% & = \int_0^{\frac{\pi}4}\ln\left(1+\frac{1-\tan u}{1+\tan u}\right)\, d u \\
-% & =\int_0^{\frac{\pi}4}\ln\left(\frac{1+\tan u+1-\tan u}{1+\tan u}\right) d u \\
-% & =\int_0^{\frac{\pi}4} \ln\left(\frac2{1+\tan u}\right)\, d u\\
-% & =\int_0^{\frac{\pi}4}\bigl(\ln2-\ln(1+\tan u)\bigr)\, d u \\
-% & =\frac{\pi}4\ln2-\int_0^{\frac{\pi}4}\ln(1+\tan u)\, d u  \\
-% & =\frac{\pi}4\ln2-I 
-% \end{WithArrows}$
-%
-% \bigskip
-% The nodes of the left are at the end of each line of text. These nodes will be
-% called \emph{left nodes}. The nodes of the right side are aligned vertically
-% on the right side of the array. These nodes will be called \emph{right nodes}.
-%
-% By default, the arrows use the right nodes. We will say that they are in |rr|
-% mode ($r$ for \emph{right}). These arrows are vertical (we will say that an
-% arrow is \emph{vertical} when its two ends have the same abscissa).
-%
-%
-% \smallskip
-% However, it's possible to use the left nodes, or a combination of left and
-% right nodes, with one of the options |lr|, |rl| and |ll| ($l$ for
-% \emph{left}). Those arrows are, usually, not vertical.
-%
-%
-% Therefore
-% $\begin{WithArrows}[displaystyle]
-% I
-% & = \int_{\frac{\pi}4}^0 \ln\Bigl(1+\tan\left(\tfrac{\pi}4-u\right)\Bigr)(-d u) 
-% \Arrow[lr]{This arrow uses the |lr| option.}\\
-% & = \int_0^{\frac{\pi}4} \ln\Bigl(1+\tan\left(\tfrac{\pi}4-u\right)\Bigr)d u \\
-% & = \int_0^{\frac{\pi}4}\ln\left(1+\frac{1-\tan u}{1+\tan u}\right)\, d u \\
-% & =\int_0^{\frac{\pi}4}\ln\left(\frac{1+\tan u+1-\tan u}{1+\tan u}\right) d u 
-% \Arrow[ll,jump=2,tikz={text width = 5cm}]{This arrow uses a |ll| option
-% and a |jump| equal to $2$}\\ 
-% & =\int_0^{\frac{\pi}4} \ln\left(\frac2{1+\tan u}\right)\, d u\\
-% & =\int_0^{\frac{\pi}4}\bigl(\ln2-\ln(1+\tan u)\bigr)\, d u \\
-% & =\frac{\pi}4\ln2-\int_0^{\frac{\pi}4}\ln(1+\tan u)\, d u  \\
-% & =\frac{\pi}4\ln2-I 
-% \end{WithArrows}$
-%
-%
-%
-% \interitem
-% There is also an option called |i| (\emph{i} for \emph{intermediate}). With
-% this option, the arrow is vertical and at the leftmost position.
-%
-% \begin{Verbatim}
-% $\begin{WithArrows}
-% (a+b)(a+ib)(a-b)(a-ib) 
-% & = (a+b)(a-b)\cdot(a+ib)(a-ib) \\
-% & = (a^2-b^2)(a^2+b^2) \Arrow~emphase#[i]@{because $(x-y)(x+y)=x^2-y^2$}\\
-% & = a^4-b^4 
-% \end{WithArrows}$
-% \end{Verbatim}
-%
-% $\begin{WithArrows}
-% (a+b)(a+ib)(a-b)(a-ib) 
-% & = (a+b)(a-b)\cdot(a+ib)(a-ib) \\
-% & = (a^2-b^2)(a^2+b^2) \Arrow[i]{because $(x-y)(x+y)=x^2-y^2$}\\
-% & = a^4-b^4 
-% \end{WithArrows}$
-%
-%
-% \interitem 
-% The environment |{WithArrows}| gives also a |group| option. With this option,
-% \emph{all} the arrows of the environment are grouped on a same vertical line
-% and at a leftmost position.
-% %
-% \begin{Verbatim}[formatcom=\small\color{gray}]
-% $\begin{WithArrows}[~emphase#displaystyle,group@]
-% 2xy'-3y=\sqrt x
-% & \Longleftrightarrow 2x(K'y_0+Ky_0')-3Ky_0 = \sqrt x \\
-% & \Longleftrightarrow 2xK'y_0 + K(2xy_0'-3y_0) = \sqrt x \\
-% & \Longleftrightarrow 2x K'y_0 = \sqrt x \Arrow{...}\\
-% ...
-% \end{WithArrows}$
-% \end{Verbatim}
-%
-%
-% $\begin{WithArrows}[displaystyle,group]
-% 2xy'-3y=\sqrt x
-% & \Longleftrightarrow 2x(K'y_0+Ky_0')-3Ky_0 = \sqrt x \\
-% & \Longleftrightarrow 2xK'y_0 + K(2xy_0'-3y_0) = \sqrt x \\
-% & \Longleftrightarrow 2x K'y_0 = \sqrt x \Arrow{we replace $y_0$ by its value}\\
-% & \Longleftrightarrow 2xK'x^{\frac32} = x^{\frac12} \Arrow{simplification of the $x$}\\
-% & \Longleftrightarrow K' = \tfrac1{2x^2} \Arrow{antiderivation}\\
-% & \Longleftrightarrow K = -\tfrac1{2x} 
-% \end{WithArrows}$
-%
-%
-% \bigskip
-% The environment |{WithArrows}| gives also a |groups| option (with a \emph{s}
-% in the name). With this option, the arrows are divided into several
-% ``groups''. Each group is a set of connected\footnote{More precisely: for each
-% arrow $a$, we note $i(a)$ the number of its initial row and $f(a)$ the number
-% of its final row; for two arrows $a$ and $b$, we say that $a \sim b$ when
-% $\llbracket i(a),f(a)\rrbracket \cap \llbracket i(b),f(b)\rrbracket \neq
-% \varnothing$; the groups are the equivalence classes of the transitive closure
-% of $\sim$.} arrows. All the arrows of a given group are grouped on a same
-% vertical line and at a leftmost position.
-%
-% \bigskip
-% $\begin{WithArrows}[groups]
-% A & = B \Arrow{one} \\
-%   & = C+D \Arrow{two} \\
-%   & = D' \\
-%   & = E+F+G+H+I \\
-%   & = K + L + M \Arrow{three}\\
-%   & = N \Arrow{four}\\
-%   & = O
-% \end{WithArrows}$
-%
-% \bigskip 
-% In an environment which uses the option |group| or the option |groups|, it's
-% still possible to give an option of position (|ll|, |lr|, |rl|, |rr| or |i|)
-% to an individual arrow. Such arrow will be drawn irrespective of the groups.
-% It's also possible to start a new group by applying the option |new-group| to
-% an given arrow.
-% 
-% \bigskip
-% If desired, the option |group| or the option |groups| can be given to the
-% command |\WithArrowsOptions| so that it will become the default value. In this
-% case, it's still possible to come back to the default behaviour for a given
-% environment |{WithArrows}| with the option |rr|: |\begin{WithArrows}[rr]|
-%
-%
-% \vspace{1cm}
-% In the following example, we have used the option |group| for the environment
-% and the option |rr| for the last arrow (that's why the last arrow is not
-% aligned with the others).
-%
-% $\begin{WithArrows}[interline=1mm,group]
-% \sum\limits_{k=0}^n\frac{\cos kx}{\cos^k x}
-% & = \sum\limits_{k=0}^n \frac{\Re (e^{ikx})}{(\cos x)^k} 
-% \Arrow{$(\cos x)^k$ is real} \\
-% & = \sum\limits_{k=0}^n \Re\left(\frac{e^{ikx}}{(\cos x)^k}\right)
-% \Arrow{$\Re(z+z')=\Re(z)+\Re(z')$}\\
-% & = \Re \left(\sum\limits_{k=0}^n \left(\frac{e^{ix}}{\cos x}\right)^k\right)
-% \Arrow{sum of terms of a geometric progression} \\
-% & = \Re \left(\frac{1-\left(\frac{e^{ix}}{\cos x}\right)^{n+1}}{1-\frac{e^{ix}}{\cos x}} \right)
-% \Arrow{algebraic calculation} \\
-% & = \Re \left(\frac{1-\frac{e^{i(n+1)x}}{\cos^{n+1}x}}{1-\frac{e^{ix}}{\cos x}}\right)
-% \Arrow{reduction to common denominator} \\
-% & = \Re \left(\frac{\frac{\cos^{n+1}x-e^{i(n+1)x}}{\cos^{n+1}x}}{\frac{\cos x-e^{ix}}{\cos x}}\right)
-% \Arrow{$\Re(kz) = k\cdot\Re(z)$ if $k$ is real} \\
-% & = \frac1{\cos^n x}\Re \left(\frac{\cos^{n+1}x-e^{i(n+1)x}}{\cos x-e^{ix}}\right)
-% \Arrow[rr]{algebraic form of the complexes} \\
-% & =\frac1{\cos^n x}\Re\left(\frac{\cos^{n+1}x-(\cos(n+1)x+i\sin(n+1)x)}{\cos x-(\cos x+i\sin x)}\right) \\
-% & =\frac1{\cos^n x}\Re\left(\frac{(\cos^{n+1}x-\cos(n+1)x)-i\sin(n+1)x}{-i\sin x}\right) \\
-% & = \frac1{\cos^nx}\cdot\frac{\sin(n+1)x}{\sin x}
-% \end{WithArrows}$
-%
-% \interitem
-%
-% \section[The options 'up' and 'down' for individual arrows]%
-%     {The options ``up'' and ``down'' for individual arrows} 
-%
-% \label{up-and-down}
-% At the local level, there are also two options for individuals arrows, called
-% ``|up|'' and ``|down|''. The following example illustrates these types of
-% arrows:
-% 
-% \begin{Verbatim}
-% \(\begin{WithArrows}
-% A & = B 
-% \Arrow~emphase#[up]@{an arrow of type \texttt{up}} \\
-%   & = C + C + C + C + C + C + C + C  \\
-%   & = C + C + C + C + C + C + C + C  
-% \Arrow~emphase#[down]@{an arrow of type \texttt{down}} \\
-%   & = E + E 
-% \end{WithArrows}\)
-% \end{Verbatim}
-% 
-% \vspace{1cm}
-% \(\begin{WithArrows}
-% A & = B 
-% \Arrow[up]{an arrow of type \texttt{up}} \\
-%   & = C + C + C + C + C + C + C + C  \\
-%   & = C + C + C + C + C + C + C + C  
-% \Arrow[down]{an arrow of type \texttt{down}} \\
-%   & = E + E 
-% \end{WithArrows}\)
-%
-%
-% \vspace{1cm}
-% The options |up| and |down| require the package \pkg{varwidth} and the Tikz
-% library \pkg{calc}. It they are not loaded, an error will be raised.
-%
-%
-% \interitem
-%
-% \section{Comparison with the environment \{aligned\}}
-%
-% |{WithArrows}| bears similarities with the environment |{aligned}| of the
-% extension \pkg{amsmath}. These are only similarities because |{WithArrows}|
-% has not been written upon the environment |{aligned}|.\footnote{In fact, it's
-% possible to use the package \pkg{witharrows} without the package
-% \pkg{amsmath}.}
-%
-% \interitem
-% As in the environments of \pkg{amsmath}, it's possible to change the spacing
-% between two given rows with the option of the command |\\| of end of line
-% (it's also possible to use |\\*| but it has exactly the same effect as |\\|
-% since an environment |{WithArrows}| is always unbreakable). This option is
-% designed to be used with positive values only.
-% %
-% \begin{Verbatim}
-% $\begin{WithArrows}
-% A & = (a+1)^2 \Arrow{we expand} ~emphase#\\[2ex]@
-%   & = a^2 + 2a + 1 
-% \end{WithArrows}$
-% \end{Verbatim}
-%
-% $\begin{WithArrows}
-% A & = (a+1)^2 \Arrow{we expand} \\*[2ex]
-% \noalign{\vspace{3mm}}
-%   & = a^2 + 2a + 1 
-% \end{WithArrows}$
-%
-%
-% \interitem 
-% In the environments of \pkg{amsmath} (or \pkg{mathtools}), the spacing between
-% rows is fixed by a parameter called |\jot| (it's a dimension and not a skip).
-% That's also the case for the environment |{WithArrows}|. An option |jot| has
-% been given to the environment |{WithArrows}| in order to change the value of
-% this parameter |\jot| for a given environment.\footnote{It's also possible to
-% change |\jot| with the environment |{spreadlines}| of \pkg{mathtools}.}
-% %
-% \begin{Verbatim}
-% $\begin{WithArrows}[displaystyle,~emphase#jot=2ex@]
-% F & = \frac12G     \Arrow{we expand}\\
-%   & = H + \frac12K \Arrow{we go on}\\
-%   & = K 
-% \end{WithArrows}$
-% \end{Verbatim}
-%
-%
-% $\begin{WithArrows}[displaystyle,jot=2ex]
-% F & = \frac12G     \Arrow{we expand}\\
-%   & = H + \frac12K \Arrow{we go on}\\
-%   & = K 
-% \end{WithArrows}$
-%
-%
-% \bigskip
-% However, this new value of |\jot| will also be used in other alignments
-% included in the environment~|{WithArrows}|:
-% %
-% \begin{Verbatim}
-% $\begin{WithArrows}[jot=2ex]
-% \varphi(x,y) = 0  & \Leftrightarrow (x+y)^2 + (x+2y)^2 = 0 
-% \Arrow{$x$ and $y$ are real}\\
-% & \Leftrightarrow \left\{
-% \begin{aligned}
-% x+y & = 0 \\
-% x+2y & = 0 
-% \end{aligned}
-% \right.
-% \end{WithArrows}$
-% \end{Verbatim}
-%
-%
-% $\begin{WithArrows}[jot=2ex]
-% \varphi(x,y) = 0  & \Leftrightarrow (x+y)^2 + (x+2y)^2 = 0 
-% \Arrow{$x$ and $y$ are real}\\
-% & \Leftrightarrow \left\{
-% \begin{aligned}
-% x+y & = 0 \\
-% x+2y & = 0 
-% \end{aligned}
-% \right.
-% \end{WithArrows}$
-%
-% \bigskip
-% Maybe this doesn't correspond to the desired outcome. That's why an option
-% |interline| is proposed. It's possible to use a skip (=glue) for this option.
-% %
-% \begin{Verbatim}
-% $\begin{WithArrows}[~emphase#interline=2ex@]
-% \varphi(x,y) = 0  & \Leftrightarrow (x+y)^2 + (x+2y)^2 = 0 
-% \Arrow{$x$ and $y$ are real}\\
-% & \Leftrightarrow \left\{
-% \begin{aligned}
-% x+y & = 0 \\
-% x+2y & = 0 \\
-% \end{aligned}
-% \right.
-% \end{WithArrows}$
-% \end{Verbatim}
-%
-%
-% $\begin{WithArrows}[interline=2ex]
-% \varphi(x,y) = 0  & \Leftrightarrow (x+y)^2 + (x+2y)^2 = 0 
-% \Arrow{$x$ and $y$ are real}\\
-% & \Leftrightarrow \left\{
-% \begin{aligned}
-% x+y & = 0 \\
-% x+2y & = 0 \\
-% \end{aligned}
-% \right.
-% \end{WithArrows}$
-%
-%
-% \interitem
-% Like the environment |{aligned}|, |{WithArrows}| has an option of placement
-% which can assume the values |t|, |c| or |b|. However, the default value is not
-% |c| but |t|. If desired, it's possible to have the |c| value as the default
-% with the command |\WithArrowsOptions{c}| at the beginning of the document.
-% %
-% \begin{Verbatim}
-% So\enskip
-% $\begin{WithArrows}
-% A & = (a+1)^2 \Arrow{we expand} \\
-%   & = a^2 + 2a + 1 
-% \end{WithArrows}$
-% \end{Verbatim}
-%
-% So\enskip 
-% $\begin{WithArrows}
-% A & = (a+1)^2 \Arrow{we expand} \\
-%   & = a^2 + 2a + 1 
-% \end{WithArrows}$
-%
-% \bigskip
-% The value |c| may be useful, for example, if we want to add curly braces:
-%
-% \smallskip
-% \begin{Verbatim}
-% Let's set\enskip $~emphase#\left\{@
-% \begin{WithArrows}[~emphase#c@]
-% f(x) & = 3x^3+2x^2-x+4 
-% \Arrow[tikz=-]{both are polynoms}\\
-% g(x) & = 5x^2-5x+6
-% \end{WithArrows}
-% ~emphase#\right.@$
-% \end{Verbatim}
-%
-%
-% Let's set\enskip $\left\{
-% \begin{WithArrows}[c]
-% f(x) & = 3x^3+2x^2-x+4 
-% \Arrow[tikz=-]{both are polynoms}\\
-% g(x) & = 5x^2-5x+6
-% \end{WithArrows}
-% \right.$
-%
-%
-% \interitem
-% Unlike |{aligned}|, the environment |{WithArrows}| uses |\textstyle| by
-% default.
-%
-% Once again, it's possible to change this behaviour with |\WithArrowsOptions|:
-%
-% \quad |\WithArrowsOptions{displaystyle}|.
-%
-%
-% \smallskip
-% The following example is composed with |{aligned}|:\par\nobreak
-%
-% \smallskip
-% $\left\{
-% \begin{aligned}
-% \sum_{i=1}^n (x_i+1)^2  
-% & = \sum_{i=1}^n (x_i^2 + 2x_i+1) \\
-% & = \sum_{i=1}^n x_i^2 + 2 \sum_{i=1}^nx_i + n 
-% \end{aligned}
-% \right.$
-%
-%
-% \medskip 
-% The following is composed with |{WithArrows}[c,displaystyle]|. The results are
-% strictly identical.\footnote{In versions of \pkg{amsmath} older than the
-% 5~nov.~2016, a thin space was added on the left of an environment |{aligned}|.
-% The new versions do not add this space and neither do
-% |{WithArrows}|.}\par\nobreak
-%
-% \smallskip
-% $\left\{
-% \begin{WithArrows}[c,displaystyle]
-% \sum_{i=1}^n (x_i+1)^2 
-% & = \sum_{i=1}^n (x_i^2 + 2x_i+1) \\
-% & = \sum_{i=1}^n x_i^2 + 2 \sum_{i=1}^nx_i + n 
-% \end{WithArrows}
-% \right.$
-%
-%
-% \section{Arrows in nested environments}
-%
-% \label{NestedEnv}
-%
-% The environments |{WithArrows}| can be nested. In this case, the options given
-% to the encompassing environment applies also to the inner ones (with logical
-% exceptions for |interline|, |code-before| and |code-after|). The command |Arrow|
-% can be used as usual in each environment |{WithArrows}|.
-% 
-% \begin{Verbatim}[formatcom=\small\color{gray}]
-% $~emphase#\begin{WithArrows}@
-% \varphi(x,y)=0
-%   & \Leftrightarrow (x+2y)^2+(2x+4y)^2 = 0 \Arrow{the numbers are real}\\
-%   & \Leftrightarrow
-%   \left\{~emphase#\begin{WithArrows}@[c]
-%   x+2y & = 0 \\
-%   2x+4y & = 0 
-%   ~emphase#\end{WithArrows}@\right. \\
-%   & \Leftrightarrow
-%   \left\{~emphase#\begin{WithArrows}@[c]
-%   x+2y & = 0 \Arrow[tikz=-]{the same equation}\\
-%   x+2y & = 0 
-%   ~emphase#\end{WithArrows}@\right. \\
-%   & \Leftrightarrow x+2y=0 
-% ~emphase#\end{WithArrows}@$
-% \end{Verbatim}
-%
-% $\begin{WithArrows}
-% \varphi(x,y)=0
-%   & \Leftrightarrow (x+2y)^2+(2x+4y)^2 = 0 \Arrow{the numbers are real}\\
-%   & \Leftrightarrow
-%   \left\{\begin{WithArrows}[c]
-%   x+2y & = 0 \\
-%   2x+4y & = 0 
-%   \end{WithArrows}\right. \\
-%   & \Leftrightarrow
-%   \left\{\begin{WithArrows}[c]
-%   x+2y & = 0 \Arrow[tikz=-]{the same equation}\\
-%   x+2y & = 0 
-%   \end{WithArrows}\right. \\
-%   & \Leftrightarrow x+2y=0 
-% \end{WithArrows}$
-%
-% \bigskip
-% However, one may want to draw an arrow between rows that are not in the same
-% environment. For example, one may want to draw the following arrow :
-%
-% \bigskip
-% $\begin{WithArrows}[code-after = \Arrow[v]{1-2}{2-2}{division by $2$} ]
-% \varphi(x,y)=0
-%   & \Leftrightarrow (x+2y)^2+(2x+4y)^2 = 0 \\
-%   & \Leftrightarrow
-%   \left\{\begin{WithArrows}[c]
-%   x+2y & = 0 \\
-%   2x+4y & = 0 
-%   \end{WithArrows}\right. \\
-%   & \Leftrightarrow
-%   \left\{\begin{WithArrows}[c]
-%   x+2y & = 0 \\
-%   x+2y & = 0 
-%   \end{WithArrows}\right. \\
-%   & \Leftrightarrow x+2y=0 
-% \end{WithArrows}$
-%
-%
-% \bigskip
-% Such a construction is possible by using |\Arrow| in the |code-after| option.
-% Indeed, in |code-after|, a special version of |\Arrow| is available (we will
-% call it ``|\Arrow| in |code-after|'').
-%
-% \smallskip
-% A command |\Arrow| in |code-after| takes three arguments :
-% \begin{itemize}
-% \item a specification of the start row of the arrow ;
-% \item a specification of the end row of the arrow ;
-% \item the label of the arrow.
-% \end{itemize}
-% As usual, it's also possible to give options within square brackets before or
-% after the three arguments. However, these options are limited (see below).
-% 
-% \bigskip
-% The specification of the row is constructed with the position of the concerned
-% environment in the nesting tree, followed (after an hyphen) by the number of
-% the row.
-%
-% \bigskip
-% In the previous example, there are two environments |{WithArrows}| nested in
-% the main environment |{WithArrows}|.
-%
-% $\begin{WithArrows}[tikz-code = {\path (#1) to node {#3} (#2) ; }]
-% \varphi(x,y)=0
-%   & \Leftrightarrow (x+2y)^2+(2x+4y)^2 = 0 \\
-%   & \Leftrightarrow \color{blue}
-%   \left\{\begin{WithArrows}[c]
-%   x+2y & = 0 \Arrow{environment number 1}\\
-%   2x+4y & = 0 
-%   \end{WithArrows}\right. \\
-%   & \Leftrightarrow \color{red}
-%   \left\{\begin{WithArrows}[c]
-%   x+2y & = 0 \Arrow{environment number 2}\\
-%   x+2y & = 0 
-%   \end{WithArrows}\right. \\
-%   & \Leftrightarrow x+2y=0 
-% \end{WithArrows}$
-%
-% \bigskip
-% The arrow we want to draw starts in the row~$2$ of the sub-environment
-% number~$1$ (and therefore, the specification is |1-2|) and ends in the row~$2$
-% of the sub-environment number~$2$ (and therefore, the specification is |2-2|).
-% We can draw the arrow with the following command |\Arrow| in |code-after| :
-% \begin{Verbatim}
-% $\begin{WithArrows}[~emphase#code-after = \Arrow{1-2}{2-2}{division by $2$}@ ]
-% \varphi(x,y)=0
-%   & \Leftrightarrow (x+2y)^2+(2x+4y)^2 = 0 \\
-% .........
-% \end{WithArrows}$
-% \end{Verbatim}
-%
-% $\begin{WithArrows}[code-after = \Arrow{1-2}{2-2}{division by $2$} ]
-% \varphi(x,y)=0
-%   & \Leftrightarrow (x+2y)^2+(2x+4y)^2 = 0 \\
-%   & \Leftrightarrow
-%   \left\{\begin{WithArrows}[c]
-%   x+2y & = 0 \\
-%   2x+4y & = 0 
-%   \end{WithArrows}\right. \\
-%   & \Leftrightarrow
-%   \left\{\begin{WithArrows}[c]
-%   x+2y & = 0 \\
-%   x+2y & = 0 
-%   \end{WithArrows}\right. \\
-%   & \Leftrightarrow x+2y=0 
-% \end{WithArrows}$
-% 
-% \bigskip
-% The options allowed for a command |\Arrow| in |code-after| are : |ll|, |lr|,
-% |rl|, |rr|, |v|, |xoffset|, |tikz| and |tikz-code|. Except |v|, which is
-% specific to |\Arrow| in |code-after|, all these options have their usual
-% meaning.
-%
-% With the option |v|, the arrow drawn is vertical to an abscissa computed with
-% the start row and the end row only : the intermediate lines are not taken into
-% account unlike with the option |i|. Currently, the option |i| is not available
-% for the command~|\Arrow| in |code-after|. However, it's always possible to
-% translate an arrow with |xoffset| (or |xshift| of Tikz).
-% \begin{Verbatim}
-% $\begin{WithArrows}[code-after=\Arrow~emphase#[v]@{1-2}{2-2}{division by $2$}]
-% \varphi(x,y)=0
-%   & \Leftrightarrow (x+2y)^2+(2x+4y)^2 = 0 \\
-% .........
-% \end{WithArrows}$
-% \end{Verbatim}
-%
-% $\begin{WithArrows}[code-after = \Arrow[v]{1-2}{2-2}{division by $2$} ]
-% \varphi(x,y)=0
-%   & \Leftrightarrow (x+2y)^2+(2x+4y)^2 = 0 \\
-%   & \Leftrightarrow
-%   \left\{\begin{WithArrows}[c]
-%   x+2y & = 0 \\
-%   2x+4y & = 0 
-%   \end{WithArrows}\right. \\
-%   & \Leftrightarrow
-%   \left\{\begin{WithArrows}[c]
-%   x+2y & = 0 \\
-%   x+2y & = 0 
-%   \end{WithArrows}\right. \\
-%   & \Leftrightarrow x+2y=0 
-% \end{WithArrows}$
-%
-%  
-% \interitem
-% The package \pkg{witharrows} gives also another command available only in
-% |code-after|: the command |\MultiArrow|. This command draws a ``rak''. The list
-% of the rows of the environment concerned by this rak are given in the first
-% argument of the command |\MultiArrow|. This list is given with the syntax of
-% the list in a |\foreach| command of \pkg{pgffor}.
-%
-%
-% \begin{Verbatim}
-% $\begin{WithArrows}[tikz = rounded corners,
-%                     code-after = {~emphase#\MultiArrow{1,...,4}{text}@} ]
-% A & = B \\
-%   & = C \\
-%   & = D \\
-%   & = E \\
-%   & = F
-% \end{WithArrows}$
-% \end{Verbatim}
-% 
-% 
-% $\begin{WithArrows}[tikz = rounded corners,
-%                     code-after = {\MultiArrow{1,...,4}{text}}]
-% A & = B \\
-%   & = C \\
-%   & = D \\
-%   & = E \\
-%   & = F
-% \end{WithArrows}$
-%
-% \medskip
-% As of now, there is no option available for the command |\MultiArrow| (maybe
-% in a future release).
-% 
-% 
-% \bigskip
-% \section{Arrows from outside environments \{WithArrows\}}
-%
-% If someone wants to draw arrows from outside the environments |{WithArrows}|,
-% he can use the Tikz nodes created in the environments.
-% 
-% The Tikz name of a node created by \pkg{witharrows} is prefixed by |wa-|.
-% Then, we have a list of numbers which give the position in the nesting tree
-% and the row number in the environment. At the end, we have the suffixe |l| for
-% a ``left node'' and |r| for a ``right node''.
-% 
-% \smallskip
-% For illustrative purposes, we give an example of nested environments
-% |{WithArrows}|, and, for each ``right node'', the name of that
-% node.\footnote{There is an option |show-node-names| to show the names of these
-% nodes.}
-% 
-% \medskip
-% \[\begin{WithArrows}[show-nodes,show-node-names]
-% A & \vartriangleleft B+B+B+B+B+B+B+B+B+B+B+B+B \\
-% & \vartriangleleft \left\{
-% \begin{WithArrows}[c]
-% C & \vartriangleleft D \\
-% E & \vartriangleleft F 
-% \end{WithArrows}
-% \right. \\
-%  & \vartriangleleft 
-% \left\{
-% \begin{WithArrows}[c]
-% G & \vartriangleleft H+H+H+H+H+H+H \\
-% I & \vartriangleleft 
-% \left\{
-% \begin{WithArrows}
-% J &\vartriangleleft K \\
-% L &\vartriangleleft M 
-% \end{WithArrows}
-% \right.
-% \end{WithArrows}
-% \right. \\
-%  & \vartriangleleft 
-% \left\{
-% \begin{WithArrows}[c]
-% N & \vartriangleleft O \\
-% P & \vartriangleleft Q 
-% \end{WithArrows}
-% \right.
-% \end{WithArrows}\]
-%
-% \medskip
-% The package \pkg{witharrows} provides some tools facilitating the use of these
-% nodes:
-% \begin{itemize}
-% \item the command |\WithArrowsLastEnv| gives the number of the last
-% environment of level~$0$ (\emph{i.e.} which is not included in another
-% environnment of the package \pkg{witharrows});
-%
-% \item a name can be given to a given environment with the option |name| and,
-% in this case, the nodes created in the environment will have aliases
-% constructed with this name;
-%
-% \item the Tikz style |WithArrows/arrow| is the style used by \pkg{witharrows}
-% when drawing an arrow\footnote{More precisely, this style is given to the Tikz
-% option ``|every path|'' before drawing the arrow with the code of the option
-% |tikz-code|. This style is modified (in TeX scopes) by the option |tikz| of
-% \pkg{witharrows}.};
-%
-% \item the Tikz style |WithArrows/arrow/tips| is the style for the tip of the
-% arrow (loaded by |WithArrows/arrow|).
-% \end{itemize}
-%
-% For example, we can draw an arrow from \texttt{wa-\WithArrowsLastEnv-2-1-2-r.south}
-% to \texttt{wa-\WithArrowsLastEnv-3-2-r.north} with the following Tikz command. 
-%
-% \begin{Verbatim}
-% \begin{tikzpicture}[remember picture,overlay]
-% \draw [WithArrows/arrow] 
-%       ([xshift=3mm]wa-\WithArrowsLastEnv-2-1-2-r.south)
-%    to ([xshift=3mm]wa-\WithArrowsLastEnv-3-2-r.north) ;
-% \end{tikzpicture}
-% \end{Verbatim}
-%
-% \[\begin{WithArrows}
-% A & \vartriangleleft B+B+B+B+B+B+B+B+B+B+B+B+B \\
-% & \vartriangleleft \left\{
-% \begin{WithArrows}[c]
-% C & \vartriangleleft D \\
-% E & \vartriangleleft F 
-% \end{WithArrows}
-% \right. \\
-%  & \vartriangleleft 
-% \left\{
-% \begin{WithArrows}[c]
-% G & \vartriangleleft H+H+H+H+H+H+H \\
-% I & \vartriangleleft 
-% \left\{
-% \begin{WithArrows}
-% J &\vartriangleleft K \\
-% L &\vartriangleleft M 
-% \end{WithArrows}
-% \right.
-% \end{WithArrows}
-% \right. \\
-%  & \vartriangleleft 
-% \left\{
-% \begin{WithArrows}[c]
-% N & \vartriangleleft O \\
-% P & \vartriangleleft Q 
-% \end{WithArrows}
-% \right.
-% \end{WithArrows}\]
-%
-% \begin{tikzpicture}[remember picture,overlay]
-% \draw [WithArrows/arrow] 
-%       ([xshift=3mm]wa-\WithArrowsLastEnv-2-1-2-r.south)
-%    to ([xshift=3mm]wa-\WithArrowsLastEnv-3-2-r.north) ;
-% \end{tikzpicture}
-%
-% \medskip
-% In this case, it would be easier to use a command |\Arrow| in |code-after| but
-% this is an example to explain how the Tikz nodes created by \pkg{witharrows}
-% can be used.
-% 
-% \bigskip
-% In the following example, we create two environments |{WithArrows}| named
-% ``|first|'' and ``|second|'' and we draw a line between a node of the first
-% and a node of the second.
-%
-% \begin{Verbatim}
-% $\begin{WithArrows}[~emphase#name=first@]
-% A & = B \\
-%   & = C 
-% \end{WithArrows}$
-%
-% \bigskip
-% $\begin{WithArrows}[~emphase#name=second@]
-% A' & = B' \\
-%    & = C'
-% \end{WithArrows}$
-%
-% \begin{tikzpicture}[remember picture,overlay]
-% \draw [WithArrows/arrow] 
-%       ([xshift=3mm]~emphase#first@-1-r.south)
-%    to ([xshift=3mm]~emphase#second@-1-r.north) ;
-% \end{tikzpicture}
-% \end{Verbatim}
-% 
-%
-% \begin{center}
-% $\begin{WithArrows}[name=first]
-% A & = B \\
-%   & = C 
-% \end{WithArrows}$
-% 
-% \bigskip
-% $\begin{WithArrows}[name=second]
-% A' & = B' \\
-%    & = C' 
-% \end{WithArrows}$
-% \end{center}
-%
-% \begin{tikzpicture}[remember picture,overlay]
-% \draw [WithArrows/arrow] 
-%       ([xshift=3mm]first-1-r.south)
-%    to ([xshift=3mm]second-1-r.north) ;
-% \end{tikzpicture}
-% 
-% \section{The environment \{DispWithArrows\}}
-% \label{DispWithArrows}
-% 
-% As previously said, the environment |{WithArrows}| bears similarities with the
-% environment |{aligned}| of \pkg{amsmath} (and |mathtools|). This extension also
-% provides an environment |{DispWithArrows}| which is similar to the
-% environments |{align}| and |{flalign}| of \pkg{amsmath}.
-%
-% \medskip
-% The environment |{DispWithArrows}| must be used \emph{outside} math mode. Like
-% |{align}|, it should be used in horizontal mode.
-% \begin{Verbatim}
-% \begin{~emphase#DispWithArrows@}
-% A & = (a+1)^2 \Arrow{we expand} \\
-%   & = a^2 + 2a + 1 
-% \end{~emphase#DispWithArrows@}
-% \end{Verbatim}
-% \begin{DispWithArrows}
-% A & = (a+1)^2 \Arrow{we expand} \\
-%   & = a^2 + 2a + 1 
-% \end{DispWithArrows}
-%
-% \medskip
-% It's possible to use the command |\notag| (or |\nonumber|) to suppress a tag. 
-% 
-% It's possible to use the command |\tag| to put a special tag (e.g. $\star$).
-%
-% It's also possible to put a label to the line of an equation with the command
-% |\label|.
-% 
-% These commands must be in the second column of the environment.
-% \begin{Verbatim}
-% \begin{DispWithArrows}
-% A & = (a+1)^2 \Arrow{we expand} ~emphase#\notag@ \\
-%   & = a^2 + 2a + 1 ~emphase#\tag{$\star$} \label{my-equation}@
-% \end{DispWithArrows}
-% \end{Verbatim}
-% \begin{DispWithArrows}
-% A & = (a+1)^2 \Arrow{we expand} \notag \\
-%   & = a^2 + 2a + 1 \tag{$\star$} \label{my-equation}
-% \end{DispWithArrows}
-% A link to the equation \eqref{my-equation}. This link has been composed with
-% |\eqref{my-equation}| (the command |\eqref| is a command of \pkg{amsmath}).
-% 
-% \medskip
-% If \pkg{amsmath} (or \pkg{mathtools}) is loaded, it's also possible to use
-% |\tag*| which, as in \pkg{amsmath}, typesets the tag without the parenthesis.
-% For example, it's possible to use it to put the symbol |\square| of
-% \pkg{amssymb}. This symbol is often used to mark the end of a
-% proof.\footnote{Notice that the environment |{DispWithArrows}| is compatible
-% with the command |\qedhere| of \pkg{amsthm}.}
-% \begin{Verbatim}
-% \begin{DispWithArrows}
-% A & = (a+1)^2 \Arrow{we expand} \notag \\
-%   & = a^2 + 2a + 1 ~emphase#\tag*{$\square$}@
-% \end{DispWithArrows}
-% \end{Verbatim}
-% \begin{DispWithArrows}
-% A & = (a+1)^2 \Arrow{we expand} \notag \\
-%   & = a^2 + 2a + 1 \tag*{$\square$} 
-% \end{DispWithArrows}
-%
-% \medskip
-% It's also possible to suppress all the autogenerated numbers with the boolean
-% option |notag| (or |nonumber|), at the global or environment level. There is
-% also an environment |{DispWithArrows*}| which suppresses all these
-% numbers.\footnote{Even in this case, it's possible to put a ``manual tag''
-% with the command |\tag|.}
-% \begin{Verbatim}
-% \begin{~emphase#DispWithArrows*@}
-% A & = (a+1)^2 \Arrow{we expand} \\
-%   & = a^2 + 2a + 1 
-% \end{~emphase#DispWithArrows*@}
-% \end{Verbatim}
-% \begin{DispWithArrows*}
-% A & = (a+1)^2 \Arrow{we expand} \\
-%   & = a^2 + 2a + 1 
-% \end{DispWithArrows*}
-%
-% \medskip
-% In fact, there is also another option |tagged-lines| which can be used to
-% control the lines that will be tagged. The value of this option is a list of
-% the numbers of the lines that must to be tagged. For example, with the option
-% |tagged-lines = {first,3,last}|, only the first, the third and the last line
-% of the environment will be tagged. There is also the special value |all| which
-% means that all the lines will be tagged.
-% \begin{Verbatim}
-% \begin{DispWithArrows}[~emphase#tagged-lines = last@]
-% A & = A_1 \Arrow{first stage} \\
-%   & = A_2 \Arrow{second stage} \\
-%   & = A_3 
-% \end{DispWithArrows}
-% \end{Verbatim}
-% \begin{DispWithArrows}[tagged-lines = last]
-% A & = A_1 \Arrow{first stage} \\
-%   & = A_2 \Arrow{second stage} \\
-%   & = A_3 
-% \end{DispWithArrows}
-%
-% \bigskip
-% With the option |fleqn|, the environment is composed flush left (in a way
-% similar to the option |fleqn| of the standard classes of LaTeX). In this case,
-% the left margin can be controlled with the option |mathindent| (with a name
-% inspired by the parameter |\mathindent| of standard LaTeX). The default value
-% of this parameter is 25~pt.
-%
-% \begin{Verbatim}
-% \begin{DispWithArrows}[~emphase#fleqn,mathindent = 1cm@]
-% A & = (a+1)^2 \Arrow{we expand} \\
-%   & = a^2 + 2a + 1 
-% \end{DispWithArrows}
-% \end{Verbatim}
-% \begin{DispWithArrows}[fleqn,mathindent = 1cm]
-% A & = (a+1)^2 \Arrow{we expand} \\
-%   & = a^2 + 2a + 1 
-% \end{DispWithArrows}
-%
-% \medskip
-% \emph{Remark} : By design, the option |fleqn| of \pkg{witharrows} is
-% independent of the option |fleqn| of LaTeX. Indeed, since the environments of
-% \pkg{witharrows} are meant to be used with arrows on the right side, the user
-% may want to use \pkg{witharrows} with the option |fleqn| (in order to have
-% more space on the right of the equations for the arrows) while still centering
-% the classical equations.
-%
-% \medskip
-% If the option |leqno| is used as a class option, the labels will be composed
-% on the left also for the environments |{DispWithArrows}| and
-% |{DispWithArrows*}|.\footnote{The package \pkg{amsmath} has an option |leqno|
-% but \pkg{witharrows}, of course, is not aware of that option: \pkg{witharrows}
-% only checks the option |leqno| of the document class.}
-%
-% \medskip
-% If the package \pkg{amsmath} is loaded, it's possible to use the command
-% |\intertext| in the environments |{DispWithArrows}|. It's also possible to use
-% the environment |{subequations}|. However, there is, for the environments
-% |{DispWithArrows}| an option |subequations| to encapsulate the environment in
-% an environment |{subequations}|.
-%
-% \medskip
-% In the following example, the key |{subequations}| is fixed by the command
-% |\WithArrowsOptions|. Each environment |{DispWithArrows}| will subnumerated
-% (in the scope of the |\WithArrowsOptions|)
-% \begin{Verbatim}
-% ~emphase#\WithArrowsOptions{subequations}@
-% First environment.
-% \begin{DispWithArrows}
-% A & = B \\
-%   & = C 
-% \end{DispWithArrows}
-% Second environment.
-% \begin{DispWithArrows}
-% D & = E \\
-%   & = F 
-% \end{DispWithArrows}
-% \end{Verbatim}
-% %
-% \begin{scope}
-% \WithArrowsOptions{subequations}
-% First environment.
-% \begin{DispWithArrows}
-% A & = B \\
-%   & = C 
-% \end{DispWithArrows}
-% Second environment.
-% \begin{DispWithArrows}
-% D & = E \\
-%   & = F 
-% \end{DispWithArrows}
-% \end{scope}
-%
-% \bigskip
-% If there is not enough space to put the tag at the end of a line, there is no
-% automatic positioning of the label on the next line (as in the environments of
-% \pkg{amsmath}). However, in |{DispWithArrows}|, the user can use the command
-% |\tagnextline| to manually require the composition of the tag on the following
-% line.
-% \begin{Verbatim}
-% \begin{DispWithArrows}[displaystyle]
-% S_{2(p+1)}
-% & =\sum_{k=1}^{2(p+1)} (-1)^k k^2 \\
-% & \smash[b]{=\sum_{k=1}^{2p}(-1)^kk²
-%    +(-1)^{2p+1}(2p+1)^2+(-1)^{2p+2}(2p+2)^2} ~emphase#\tagnextline@ \\
-% &= S_{2p}-(2p+1)^2+(2p+2)^2\\
-% &=p(2p+1)-(2p+1)^2+(2p+2)^2\\
-% &= 2p^2+5p+3 
-% \end{DispWithArrows}
-% \end{Verbatim}
-% \begin{center}
-% \color{gray}\vrule%
-% \begin{minipage}{275pt}\color{black}
-% \begin{DispWithArrows}[displaystyle]
-% S_{2(p+1)}
-% & =\sum_{k=1}^{2(p+1)} (-1)^k k^2 \\
-% & \smash[b]{=\sum_{k=1}^{2p}(-1)^kk^2+(-1)^{2p+1}(2p+1)^2+(-1)^{2p+2}(2p+2)^2}
-% \tagnextline \\ 
-% &= S_{2p}-(2p+1)^2+(2p+2)^2\\
-% &= 2p^2+p-4p^2-4p-1+4p^2+8p+4\\
-% &= 2p^2+5p+3 
-% \end{DispWithArrows}
-% \end{minipage}%
-% \color{gray}\vrule
-% \end{center}
-% 
-%
-%
-% \bigskip
-% The environments |{DispWithArrows}| and |{DispWithArrows*}| provide an option
-% |wrap-lines|. With this option, the lines of the label are automatically
-% wrapped on the right.\footnote{It's possible to avoid the hyphenations of the
-% words with the option ``|align = flush left|'' of Tikz.}\label{wrap-lines}
-%
-% \begin{Verbatim}
-% \begin{DispWithArrows*}[displaystyle,~emphase#wrap-lines@]
-% S_n
-% & = \frac1n \Re \left(\sum_{k=0}^{n-1}\bigl(e^{i\frac{\pi}{2n}}\bigr)^k\right)
-% \Arrow{sum of terms of a geometric progression of ratio $e^{i\frac{2\pi}n}$}\\
-% & = \frac1n \Re \left( \frac{1-\bigl(e^{i\frac{\pi}{2n}}\bigr)^n}
-%                             {1-e^{i\frac{\pi}{2n}}}\right)
-% \Arrow{This line has been wrapped automatically.} \\
-% & = \frac1n \Re \left(\frac{1-i}{1-e^{i\frac{\pi}{2n}}}\right) 
-% \end{DispWithArrows*}
-% \end{Verbatim}
-% \begin{DispWithArrows*}[displaystyle,wrap-lines]
-% S_n
-% & = \frac1n \Re \left(\sum_{k=0}^{n-1}\bigl(e^{i\frac{\pi}{2n}}\bigr)^k\right)
-% \Arrow{sum of terms of a geometric progression of ratio $e^{i\frac{2\pi}n}$}\\
-% & = \frac1n \Re \left(
-% \frac{1-\bigl(e^{i\frac{\pi}{2n}}\bigr)^n}{1-e^{i\frac{\pi}{2n}}} \right) 
-% \Arrow{This line has been wrapped automatically.} \\
-% & = \frac1n \Re \left(\frac{1-i}{1-e^{i\frac{\pi}{2n}}}\right) 
-% \end{DispWithArrows*}
-% 
-% \bigskip
-% The option |wrap-lines| doesn't apply to the environments |{WithArrows}|
-% nested in an environment |{DispWithArrows}| or |{DispWithArrows*}|. However,
-% it applies to the instructions |\Arrow| and |\MultiArrow| of the |code-after|
-% of the environments |{DispWithArrows}| or |{DispWithArrows*}|.
-% 
-% \vspace{1cm}
-% We have said that the environments |{DispWithArrows}| and |{DispWithArrows*}|
-% should be used in horizontal mode and not in vertical mode. However, there is
-% an exception. These environments can be used directly after a |\item| of a
-% LaTeX list. In this case, no vertical space is added before the
-% environment.\footnote{It's possible to disable this feature with the option |standard-behaviour-with-items|.}
-%
-% \medskip
-% Here is an example. The use of |{DispWithArrows}| gives the ability to tag an
-% equation (and also to use |wrap-lines|).
-%
-% \begin{Verbatim}
-% ~emphase#\begin{enumerate}@
-% ~emphase#\item @
-% \begin{DispWithArrows}%
-%   [displaystyle, wrap-lines, tagged-lines = last, fleqn, mathindent = 0 pt]
-% S_n
-% & = \frac1n \Re \left(\sum_{k=0}^{n-1}\bigl(e^{i\frac{\pi}{2n}}\bigr)^k\right)
-% \Arrow{we use the formula for a sum of terms of a geometric progression of
-% ratio $e^{i\frac{2\pi}n}$}\\ 
-% & = \frac1n \Re \left( \frac{1-\bigl(e^{i\frac{\pi}{2n}}\bigr)^n}
-%                             {1-e^{i\frac{\pi}{2n}}}\right)
-% \Arrow{$\bigl(e^{i\frac{\pi}{2n}}\bigr)^n = e^{i\frac{\pi}2}=i$} \\
-% & = \frac1n \Re \left(\frac{1-i}{1-e^{i\frac{\pi}{2n}}}\right) 
-% \end{DispWithArrows}
-% ~emphase#\end{enumerate}@
-% \end{Verbatim}
-% \begin{enumerate}
-% \item 
-% \begin{DispWithArrows}[displaystyle, wrap-lines, tagged-lines = last, fleqn, mathindent = 0 pt]
-% S_n
-% & = \frac1n \Re \left(\sum_{k=0}^{n-1}\bigl(e^{i\frac{\pi}{2n}}\bigr)^k\right)
-% \Arrow{we use the formula for a sum of terms of a geometric progression of
-% ratio $e^{i\frac{2\pi}n}$}\\ 
-% & = \frac1n \Re \left(
-% \frac{1-\bigl(e^{i\frac{\pi}{2n}}\bigr)^n}{1-e^{i\frac{\pi}{2n}}} \right) 
-% \Arrow{$\bigl(e^{i\frac{\pi}{2n}}\bigr)^n = e^{i\frac{\pi}2}=i$} \\
-% & = \frac1n \Re \left(\frac{1-i}{1-e^{i\frac{\pi}{2n}}}\right) 
-% \end{DispWithArrows}
-% \end{enumerate}
-% 
-% \vspace{1cm}
-% The environment |{DispWithArrows}| is similar to the environment |{align}| of
-% \pkg{amsmath}. However, |{DispWithArrows}| is not constructed upon |{align}|
-% (in fact, it's possible to use \pkg{witharrows} without \pkg{amsmath}).
-%
-% There are differences between |{DispWithArrows}| and |{align}|. 
-% \begin{itemize}
-% \item The environment |{DispWithArrows}| cannot be inserted in an environment
-% |{gather}| of \pkg{amsmath}.
-% \item An environment |{DispWithArrows}| is always unbreakable (even with
-% |\allowdisplaybreaks| of \pkg{amsmath}).
-% \item The commands |\label|, |\tag|, |\notag| and |\nonumber| are allowed only
-% in the last column.
-% \item After an |\item| of a LaTeX list, no vertical space is added (this can
-% be changed with the option |standard-behaviour-with-items|).
-% \item 
-% \begin{bfseries}
-% Last but not least, by default, the elements of a |\{DispWithArrows\}|
-% are composed in |textstyle| and not in |displaystyle| (it's possible to change
-% this point with the option |displaystyle|). 
-% \end{bfseries}
-% \end{itemize}
-% 
-% \bigskip 
-% Concerning the references, the package \pkg{witharrows} is compatible with the
-% extensions \pkg{autonum}, \pkg{cleveref}, \pkg{fancyref}, \pkg{fncylab},
-% \pkg{hyperref}, \pkg{listlbls}, \pkg{prettyref}, \pkg{refcheck},
-% \pkg{refstyle}, \pkg{showlabels}, \pkg{smartref}, \pkg{typedref} and
-% \pkg{varioref}, and with the options |showonlyrefs| and |showmanualtags| of
-% \pkg{mathtools}.\footnote{We recall that \pkg{varioref}, \pkg{hyperref},
-% \pkg{cleveref} and \pkg{autonum} must be loaded in this order. The package
-% \pkg{witharrows} can be loaded anywhere.}
-%
-% It is not compatible with \pkg{showkeys} (not all the labels are shown).
-%
-% 
-%
-%
-% \subsection{The option <...> of DispWithArrows}
-%
-% The environment |{DispWithArrows}| provides an option |left-brace|. When present,
-% the value of this option is composed on the left, followed by a curly brace
-% (hence the name) and the body of the environment.\footnote{The option
-% |left-brace| can also be used without value: in this case, only the brace is drawn...}
-%
-% For lisibility, this option |left-brace| is also available with a special
-% syntax: it's possible to give this option between angle brackets  
-% (\verb|<| and \verb|>|) just after \verb|{DispWithArrows}| (before the optional
-% arguments between square brackets).
-%
-% \bigskip 
-% The following code is an example of multi-case equations.\footnote{The
-% environment |{cases}| of \pkg{amsmath} is a way to compose such multi-cases
-% equations. However, it's not possible to use the automatic numbering of
-% equations with this environment. The environment |{numcases}| of the extension
-% \pkg{cases} (written by Donald Arseneau) provides this possibility but, of
-% course, it's not possible to draw arrows with this extension.}
-%
-% \medskip
-%
-% \begin{BVerbatim}
-% \begin{DispWithArrows}~emphase#< \binom{n}{p} = >@[format = ll,fleqn,displaystyle]
-% 0 & \quad \text{if } p > n  
-% \Arrow{if fact, it's a special case\\ of the following one} \\
-% \frac{n(n-1)\cdots(n-p+1)}{p!} & \quad \text{if } 0 \leq p \leq n  \\
-% 0 & \quad \text{if } p < 0 
-% \end{DispWithArrows}
-% \end{BVerbatim}
-% %
-% \begin{DispWithArrows}< \binom{n}{p} = >[format = ll,fleqn,displaystyle]
-% 0 & \quad \text{if } p > n  
-% \Arrow{if fact, it's a special case\\ of the following one} \\
-% \frac{n(n-1)\cdots(n-p+1)}{p!} & \quad \text{if } 0 \leq p \leq n  \\
-% 0 & \quad \text{if } p < 0 
-% \end{DispWithArrows}
-%
-% \interitem
-% It's possible to use the environment |{subequations}| of \pkg{amsmath}. 
-%
-% \begin{Verbatim}
-% \begin{subequations}
-% \label{system}
-% \begin{DispWithArrows}<  (\ref*{system}) \Leftrightarrow >[format = l]
-% x+y+z = -3 \Arrow[tikz=-,jump=2]{3 equations} \\
-% xy+xz+yz=-2 \\
-% xyz = -15 \label{last-equation}
-% \end{DispWithArrows}
-% \end{subequations}
-% \end{Verbatim}
-% %
-% \begin{subequations}
-% \label{system}
-% \begin{DispWithArrows}< (\ref*{system}) \Leftrightarrow >[format = l]
-% x+y+z = -3 \Arrow[tikz=-,jump=2]{3 equations} \\
-% xy+xz+yz=-2 \\
-% xyz = -15 \label{last-equation} 
-% \end{DispWithArrows}
-% \end{subequations}
-%
-% \bigskip
-% The whole system is the equation \eqref{system} (this reference has been coded
-% by |\eqref{system}|) whereas the last equation is the equation
-% \eqref{last-equation} (this reference has been coded by
-% |\eqref{last-equation}|). The command |\ref*| used in the code above is
-% provided by \pkg{hyperref}. It's a variant of |\ref| which doesn't create 
-% interactive link.
-%
-% \bigskip
-% With the option \verb|replace-curly-brace-by|, it's possible to replace the
-% left curly brace can be replaced by another extensible delimiter.
-% 
-% \bigskip
-% \section{Advanced features}
-%
-% \subsection{The option tikz-code : how to change the shape of the arrows}
-%
-% \label{tikz-code}
-%
-% The option |tikz-code|\footnote{For historical reasons, the option |tikz-code|
-% has an alias: |TikzCode|.} allows the user to change the shape of the 
-% arrows.\footnote{If the option |wrap-lines| is used in an environment
-% |{DispWithArrows}| or |{DispWithArrows*}|, the option |tikz-code| will have no
-% effect for the arrows of this environment but only for the arrows in the
-% nested environments |{WithArrows}|.}
-%
-% \smallskip
-% For example, the options ``|up|'' and ``|down|'' described previously (cf.
-% p.~\pageref{up-and-down}) are programmed internally with |tikz-code|.
-% 
-% \smallskip
-% The value of this option must be a valid Tikz drawing instruction (with the
-% final semicolon) with three markers |#1|, |#2| and |#3| for the start point,
-% the end point and the label of the arrow.
-%
-% \bigskip
-% By default, the value is the following:
-% 
-% \smallskip
-% \qquad \verb|\draw (#1) to node {#3} (#2) ;|
-%
-%
-% \bigskip
-% In the following example, we replace this default path by a path with three
-% segments (and the node overwriting the second segment).
-% \begin{Verbatim}
-% \begin{WithArrows}[format=c,ygap=5pt,interline=4mm,
-%       ~emphase#tikz-code = {\draw[rounded corners]@
-%       ~emphase#                  (~#1) -- ([xshift=5mm]~#1)@
-%       ~emphase#                  -- node[circle,@
-%       ~emphase#                          draw,@
-%       ~emphase#                          auto = false,@
-%       ~emphase#                          fill = gray!50,@
-%       ~emphase#                          inner sep = 1pt] {\tiny ~#3}@ 
-%       ~emphase#                  ([xshift=5mm]~#2)@
-%       ~emphase#                  -- (~#2) ; }@]
-% 3 (2x+4) = 6   \Arrow{$\div 3$} \\
-% 2x+4 = 2       \Arrow{$-4$}     \\
-% 2x = -2        \Arrow{$\div 2$} \\
-%  x = -1
-% \end{WithArrows}
-% \end{Verbatim}
-%
-% 
-% \[\begin{WithArrows}[format=c,
-%       ygap=5pt,
-%       interline=4mm,
-%       tikz-code = {\draw[rounded corners]
-%                         (#1) 
-%                         --
-%                         ([xshift=5mm]#1)
-%                         -- node[circle,
-%                                 draw,
-%                                 auto=false,
-%                                 fill=gray!50,
-%                                 inner sep = 1pt] {\tiny #3} 
-%                         ([xshift=5mm]#2)
-%                         --
-%                         (#2) ; }]
-% 3 (2x+4) = 6   \Arrow{$\div 3$} \\
-% 2x+4 = 2       \Arrow{$-4$}     \\
-% 2x = -2        \Arrow{$\div 2$} \\
-%  x = -1
-% \end{WithArrows}\]
-%
-% \bigskip
-% The environments |{DispWithArrows}| and its starred version
-% |{DispWithArrows*}| provide a command |\WithArrowsRightX| which can be used in
-% a definition of |tikz-code|. This command gives the $x$-value of the right side
-% of the composition box (taking into account the eventual tags of the
-% equations). For an example of use, see p.~\pageref{example-WithArrowsRightX}.
-%
-%
-% \bigskip
-% \subsection{The command \textbackslash WithArrowsNewStyle}
-%
-% The extension \pkg{witharrows} provides a command |\WithArrowsNewStyle| to
-% define styles in a way similar to the ``styles'' of Tikz.
-%
-% The command |\WithArrowsNewStyle| takes two mandatory arguments. The first is
-% the name of the style and the second is a list of key-value pairs. The scope
-% of the definition done by |\WithArrowsNewStyle| is the current TeX scope.
-%
-% The style can be used as a key at the document level (with
-% |\WithArrowsOptions|) or at the environment level (in the optional arguments
-% of |{WithArrows}| and |{DispWithArrows}|). The style can also be used in
-% another command |\WithArrowsNewStyle|.
-%
-% For an example of use, see p.~\pageref{example-WithArrowsRightX}.
-%
-%
-% \bigskip
-% \subsection{Vertical positioning of the arrows}
-% 
-% There are four parameters for fine tuning of the vertical positioning of the
-% arrows : |ygap|, |ystart|, |start-adjust| and |end-adjust|.
-% 
-% \medskip
-% We first explain the behaviour when the parameters |start-adjust| and
-% |end-adjust| are equal to zero:
-% \begin{itemize}
-% \item the option |ystart| sets the vertical distance between the base line of
-% the text and the start of the arrow (default value: 0.4 ex);
-% \item the option |ygap| sets the vertical distance between two consecutive
-% arrows (default value: 0.4~ex).
-% \end{itemize}
-%
-%
-% \bigskip
-% $\begin{WithArrows}[interline=1mm, adjust = 0pt]
-%  (\cos x + \sin x)^2 & = \cos^2 x +2 \cos x \sin x + \sin^2 x\Arrow{}\tikz[remember picture] \coordinate (A) ; \\
-%    & = \cos^2x + \sin^2x + 2\sin x\cos x \Arrow{} \\
-%    & = 1 + \sin(2x) 
-% \end{WithArrows}$
-%
-% \begin{tikzpicture}[remember picture,overlay,blue]
-% \draw (wa-\WithArrowsLastEnv-1-r.south) to ++(1,0) coordinate (B) to ++(0.1,0) ;;
-% \draw (A) to ++(1,0) coordinate (C) to ++(0.1,0) ;;
-% \draw (B) -- (C) ;
-% \draw[<-] (B) to ++(0,0.2) ;
-% \draw[<-] (C) to ++(0,-0.2) ;
-% \path (C) node[right=1mm] {|ystart|} ;
-% \draw (wa-\WithArrowsLastEnv-2-r.north) to ++(3,0) coordinate (E) to ++(0.1,0);
-% \draw (wa-\WithArrowsLastEnv-2-r.south) to ++(3,0) coordinate (F) to ++(0.1,0);
-% \draw (E) -- (F) ;
-% \draw[<-] (E) to ++(0,0.2) ;
-% \draw[<-] (F) to ++(0,-0.2) ;
-% \path (F) node[right=1mm] {|ygap|} ;
-% \end{tikzpicture}
-%
-% \interitem 
-% However, for aesthetic reasons, when it's possible, \pkg{witharrows} starts
-% the arrow a bit higher (by an amount |start-adjust|) and ends the arrow a bit
-% lower (by an amount |end-adjust|). By default, both parameters |start-adjust|
-% and |end-adjust| are equal to $0.4$~ex.
-%
-% \bigskip
-% Here is for example the behaviour without the mechanism of |start-adjust| and
-% |end-adjust| (this was the standard behaviour for versions prior to 1.13).
-% % \begin{Verbatim}
-% $\begin{WithArrows}~emphase#[start-adjust=0pt, end-adjust=0pt]@
-% A & = (a+1)^2 \Arrow{we expand} \\
-%   & = a^2 + 2a + 1  
-% \end{WithArrows}$
-% \end{Verbatim}
-%
-% $\begin{WithArrows}[start-adjust=0pt, end-adjust=0pt]
-% A & = (a+1)^2 \Arrow{we expand} \\
-%   & = a^2 + 2a + 1  
-% \end{WithArrows}$
-%
-%
-% \bigskip
-% Here is the standard behaviour since version 1.13 (the parameters
-% |start-adjust| and |end-ajust| are used with the default value $0.4$~ex). The
-% arrow is longer and the result is more aesthetic.
-% 
-% \medskip
-% $\begin{WithArrows}
-% A & = (a+1)^2 \Arrow{we expand} \\
-%   & = a^2 + 2a + 1  
-% \end{WithArrows}$
-%
-%
-% \bigskip
-% It's also possible to use the option |adjust| which sets both |start-adjust|
-% and |end-ajust|.
-%
-% \bigskip
-% Since the mechanism of |start-adjust| and |end-ajust| has been added in
-% version 1.13 of \pkg{witharrows}, that version is not stricty compatible with
-% older versions. However, it's possible to restore the previous behaviour
-% simply by setting |start-adjust| and |end-adjust| to $0$~pt:
-% \begin{Verbatim}
-% \WithArrowsOptions{adjust = 0pt}
-% \end{Verbatim}
-% 
-% \bigskip
-% \subsection{Footnotes in the environments of witharrows}
-% 
-% If you want to put footnotes in an environment |{WithArrows}| or
-% |{DispWithArrows}|, you can use a pair |\footnotemark|--|\footnotetext|.
-%
-% \smallskip
-% It's also possible to extract the footnotes with the help of the package
-% \pkg{footnote} or the package \pkg{footnotehyper}.
-%
-% \smallskip
-% If \pkg{witharrows} is loaded with the option |footnote| (with
-% |\usepackage[footnote]{witharrows}| or with |\PassOptionsToPackage|), the
-% package \pkg{footnote} is loaded (if it is not yet loaded) and it is used to
-% extract the footnotes.
-%
-% \smallskip
-% If \pkg{witharrows} is loaded with the option |footnotehyper|, the package
-% \pkg{footnotehyper} is loaded (if it is not yet loaded) ant it is used to
-% extract footnotes.
-%
-% \smallskip
-% Caution: The packages \pkg{footnote} and \pkg{footnotehyper} are incompatible.
-% The package \pkg{footnotehyper} is the successor of the package \pkg{footnote}
-% and should be used preferently. The package \pkg{footnote} has some drawbacks,
-% in particular: it must be loaded after the package \pkg{xcolor} and it is not
-% perfectly compatible with \pkg{hyperref}.
-%
-% \medskip
-% In this document, the package \pkg{witharrows} has been loaded with the option
-% |footnotehyper| and we give an example with a footnote in the label of an
-% arrow:
-%
-% \smallskip
-% $\begin{WithArrows}
-% A & = (a+b)^2 
-% \Arrow{We expand\,\footnote{A footnote.}} \\
-%    & = a^2+b^2+2ab
-% \end{WithArrows}$
-%
-% \bigskip
-% \subsection{Option no-arrows}
-%
-% The option |no-arrows| is a convenience given to the user. With this option
-% the arrows are not drawn. However, an analyse of the arrows is done and some
-% errors can be raised, for example if an arrow would arrive after the last row
-% of the environment.
-%
-%
-% \bigskip
-% \subsection{Note for developpers}
-%
-% If you want to construct an environment upon an environment of
-% \pkg{witharrows}, we recommand to call the environment with the construction
-% |\WithArrows|-|\endWithArrows| or |\DispWithArrows|-|\endDispWithArrows| (and
-% not |\begin{WithArrows}|-|\end{WithArrows}|, etc.).
-%
-% \smallskip
-% By doing so, the error messages generated by \pkg{witharrows} will (usually)
-% mention the name of your environment and they will be easier to understand by
-% the final user.
-%
-% \smallskip
-% By example, you can define an environment |{DWA}| which is an alias of
-% |{DispWithArrows}|:
-% \begin{BVerbatim}
-% \NewDocumentEnvironment {DWA} {} {\DispWithArrows}{\endDispWithArrows}
-% \end{BVerbatim}
-% 
-% \smallskip
-% If you use this environment |{DWA}| in math mode, you will have the following
-% error message:
-% 
-% \begin{BVerbatim}
-% The environment {DWA} should be used only outside math mode.
-% \end{BVerbatim}
-% 
-% \interitem
-% Another example is the definition of the environment |{DispWithArrows*}|
-% internally in the package \pkg{witharrows} by the following code:
-% \begin{Verbatim}
-% \NewDocumentEnvironment {DispWithArrows*} {}
-%     {\WithArrowsOptions{notag}%
-%      \DispWithArrows}
-%     {\endDispWithArrows}
-% \end{Verbatim}
-%
-%
-%
-% \section{Examples}
-%
-% \subsection{\textbackslash MoveEqLeft}
-%
-% It's possible to use |\MoveEqLeft| of \pkg{mathtools}. Don't forget that
-% |\MoveEqLeft| has also the value of an ampersand (|&|). That's important for the
-% placement of an eventual command |\Arrow|.
-% 
-% 
-% 
-% \begin{Verbatim}[formatcom=\small\color{gray}]
-% $\begin{WithArrows}[interline=0.5ex]
-% ~emphase#\MoveEqLeft@ \arccos(x) = \arcsin \frac45 + \arcsin \frac5{13} 
-% \Arrow{because both are in $[-\frac{\pi}2,\frac{\pi}2]$} \\
-% & \Leftrightarrow x = \sin\left(\arcsin\frac45 + \arcsin\frac5{13}\right) \\
-% & \Leftrightarrow x = \frac45\cos\arcsin\frac5{13} + \frac5{13} \cos\arcsin\frac45 
-% \Arrow{$\forall x \in [-1,1], \cos(\arcsin x) = \sqrt{1-x^2}$} \\
-% & \Leftrightarrow x = \frac45\sqrt{1-\bigl(\frac5{13}\bigr)^2}
-% + \frac5{13}\sqrt{1-\bigl(\frac45\bigr)^2} 
-% \end{WithArrows}$
-% \end{Verbatim}
-%
-%
-% \medskip
-% $\begin{WithArrows}[interline=0.5ex]
-% \MoveEqLeft \arccos(x) = \arcsin \frac45 + \arcsin \frac5{13} 
-% \Arrow{because both are in $[-\frac{\pi}2,\frac{\pi}2]$} \\
-% & \Leftrightarrow x = \sin\left(\arcsin\frac45 + \arcsin\frac5{13}\right) \\
-% & \Leftrightarrow x = \frac45\cos\arcsin\frac5{13} + \frac5{13} \cos\arcsin\frac45 
-% \Arrow{$\forall x \in [-1,1], \cos(\arcsin x) = \sqrt{1-x^2}$} \\
-% & \Leftrightarrow x = \frac45\sqrt{1-\bigl(\frac5{13}\bigr)^2}
-% + \frac5{13}\sqrt{1-\bigl(\frac45\bigr)^2} 
-% \end{WithArrows}$
-%
-%
-% \bigskip
-% \subsection{Modifying the shape of the nodes}
-%
-% It's possible to change the shape of the labels, which are Tikz nodes, by
-% modifying the key ``|every node|'' of Tikz.
-%
-% \begin{Verbatim}
-% \begin{WithArrows}%
-%      [format = c,
-%       interline = 4mm,
-%       tikz = {~emphase#every node/.style = {circle,@
-%               ~emphase#                     draw,@
-%               ~emphase#                     auto = false,@
-%               ~emphase#                     fill = gray!50,@
-%               ~emphase#                     inner sep = 1pt,@
-%               ~emphase#                     font = \tiny}@}]
-%  3 (2x+4) = 6 \Arrow{$\div 3$} \\
-%  2x+4 = 2     \Arrow{$-4$} \\
-%  2x = -2      \Arrow{$\div 2$} \\
-%  2x = -1
-% \end{WithArrows}
-% \end{Verbatim}
-%
-% \[\begin{WithArrows}[%
-%       format = c,
-%       interline = 4mm,
-%       tikz = {every node/.style = {circle,
-%                                    draw,
-%                                    auto = false,
-%                                    fill = gray!50,
-%                                    inner sep = 1pt,
-%                                    font = \tiny}}]
-%  3 (2x+4) = 6 \Arrow{$\div 3$} \\
-%  2x+4 = 2     \Arrow{$-4$}     \\
-%  2x = -2      \Arrow{$\div 2$} \\
-%  2x = -1
-% \end{WithArrows}\]
-%
-%
-% \bigskip
-% \subsection{Examples with the option tikz-code}
-%
-% We recall that the option |tikz-code| is the Tikz code used by \pkg{witharrows}
-% to draw the arrows.\footnote{If an environment |{DispWithArrows}| or
-% |{DispWithArrows*}| is used with the option |wrap-lines|, the value of the
-% option |tikz-code| is not used for this environment (but is used for the
-% environments nested inside).}
-%
-% \smallskip
-% The value by defaut of |tikz-code| is \verb|\draw (#1) to node {#3} (#2) ;|
-% where the three markers |#1|, |#2| and |#3| represent the start row, the end
-% row and the label of the arrow.
-%
-%
-% \bigskip
-% \subsubsection{Example 1}
-% In the following example, we define the value of |tikz-code| with two
-% instructions |\path| : the first instruction draws the arrow itself and the
-% second puts the label in a Tikz node in the rectangle delimited by the arrow.
-%
-% \begin{Verbatim}
-% \begin{DispWithArrows*}%
-%       [displaystyle,
-%        ygap = 2mm,
-%        ystart = 0mm,
-%        ~emphase#tikz-code = {\draw (~#1) -- ++(4.5cm,0) |- (~#2) ;@
-%        ~emphase#             \path (~#1) -- (~#2) @
-%        ~emphase#                    node[text width = 4.2cm, right, midway] {~#3} ;}@]
-% S_n
-% & = \frac1n \sum_{k=0}^{n-1}\cos\bigl(\tfrac{\pi}2\cdot\tfrac kn\bigr)
-% ...........
-% \end{Verbatim}
-%
-%
-% \bigskip
-% \begin{DispWithArrows*}[
-%        displaystyle,
-%        ygap = 2mm,
-%        ystart = 0mm,
-%        tikz-code = {\draw (#1) -- ++(4.5cm,0) |- (#2) ;
-%                     \path (#1) -- (#2) 
-%                            node[text width = 4.2cm, right, midway] {#3} ;}]
-% S_n
-% & = \frac1n \sum_{k=0}^{n-1}\cos\bigl(\tfrac{\pi}2\cdot\tfrac kn\bigr)
-% \Arrow{$\cos x = \Re(e^{ix})$}\\
-% & = \frac1n\sum_{k=0}^{n-1} \Re\left(e^{i\frac{k\pi}{2n}}\right)
-% \Arrow{$\Re(z+z')=\Re(z)+\Re(z')$}\\
-% & = \frac1n \Re\left(\sum_{k=0}^{n-1} e^{i\frac{k\pi}{2n}}\right)
-% \Arrow{$\exp$ is a morphism for $\times$ et $+$} \\
-% & = \frac1n \Re \left(\sum_{k=0}^{n-1}\bigl(e^{i\frac{\pi}{2n}}\bigr)^k\right)
-% \Arrow{sum of terms of a geometric progression of ratio $e^{i\frac{2\pi}n}$}\\
-% & = \frac1n \Re \left( \frac{1-\bigl(e^{i\frac{\pi}{2n}}\bigr)^n}{1-e^{i\frac{\pi}{2n}}}\right)\\
-% & = \frac1n \Re \left(\frac{1-i}{1-e^{i\frac{\pi}{2n}}}\right) 
-% \end{DispWithArrows*}
-%
-% \bigskip
-% \subsubsection{Example 2}
-%
-% \label{example-WithArrowsRightX}
-% It's possible to modify the previous example to have the ``|text width|''
-% automatically computed with the right margin (in a way similar as the
-% |wrap-lines| option) in the environments |{DispWithArrows}| and
-% |{DispWithArrows*}|. In the definition of |tikz-code|, we use the command
-% |\WithArrowsRightX| which is the $x$-value of the right margin of the current
-% composition box (it's a TeX command and not a dimension). For lisibility, we
-% use a style. This example requires the Tikz library \pkg{calc}.
-%
-% \begin{Verbatim}
-% \WithArrowsNewStyle{MyStyle}       
-%   {displaystyle,
-%    ygap = 2mm,
-%    xoffset = 0pt,
-%    ystart = 0mm,
-%    tikz-code = {\path let \p1 = (~#~#1)
-%                       in (~#~#1)
-%                           -- node [anchor = west, 
-%                                    text width = {~emphase#\WithArrowsRightX@ - \x1 - 0.5 em}] 
-%                                   {~#~#3} 
-%                          (~#~#2) ;
-%                 \draw let \p1 = (~#~#1) 
-%                       in (~#~#1) -- ++(~emphase#\WithArrowsRightX@ - \x1,0) |- (~#~#2) ; }}
-% \end{Verbatim}
-%
-% \begin{Verbatim}
-%\begin{DispWithArrows}[MyStyle]
-%   S_n
-%   & = \frac1n \sum_{k=0}^{n-1}\cos\bigl(\tfrac{\pi}2\cdot\tfrac kn\bigr)
-%   \Arrow{$\cos x = \Re(e^{ix})$}\\
-% ...........
-% \end{Verbatim}
-% 
-% \WithArrowsNewStyle{MyStyle}       
-% {displaystyle,
-%  ygap = 2mm,
-%  xoffset = 0pt,
-%  ystart = 0mm,
-%  tikz-code = {\path let \p1 = (##1)
-%                     in (##1)
-%                         -- node [anchor = west, 
-%                                  text width = {\WithArrowsRightX - \x1 - 0.5 em}] {##3} 
-%                        (##2) ;
-%               \draw let \p1 = (##1) 
-%                     in (##1) -- ++(\WithArrowsRightX - \x1,0) |- (##2) ; }}
-%
-%\begin{DispWithArrows}[MyStyle]
-% S_n
-% & = \frac1n \sum_{k=0}^{n-1}\cos\bigl(\tfrac{\pi}2\cdot\tfrac kn\bigr)
-% \Arrow{$\cos x = \Re(e^{ix})$}\\
-% & = \frac1n\sum_{k=0}^{n-1} \Re\left(e^{i\frac{k\pi}{2n}}\right)
-% \Arrow{$\Re(z+z')=\Re(z)+\Re(z')$}\\
-% & = \frac1n \Re\left(\sum_{k=0}^{n-1} e^{i\frac{k\pi}{2n}}\right)
-% \Arrow{$\exp$ is a morphism for $\times$ et $+$} \\
-% & = \frac1n \Re \left(\sum_{k=0}^{n-1}\bigl(e^{i\frac{\pi}{2n}}\bigr)^k\right)
-% \Arrow{sum of terms of a geometric progression of ratio $e^{i\frac{2\pi}n}$}\\
-% & = \frac1n \Re \left( \frac{1-\bigl(e^{i\frac{\pi}{2n}}\bigr)^n}{1-e^{i\frac{\pi}{2n}}}\right)\\
-% & = \frac1n \Re \left(\frac{1-i}{1-e^{i\frac{\pi}{2n}}}\right) 
-% \end{DispWithArrows}
-% 
-%
-% 
-% \bigskip
-% \subsubsection{Example 3}
-% 
-% In the following example, we change the shape of the arrow depending on whether
-% the start row is longer than the end row or not. This example requires the
-% Tikz library \pkg{calc}.
-% 
-% \begin{Verbatim}
-% \begin{WithArrows}[ll,interline=5mm,xoffset=5mm,
-%       ~emphase#tikz-code  = {\draw[rounded corners,@
-%       ~emphase#                    every node/.style = {circle,@
-%       ~emphase#                                         draw,@
-%       ~emphase#                                         auto = false,@
-%       ~emphase#                                         inner sep = 1pt,@
-%       ~emphase#                                         fill = gray!50,@
-%       ~emphase#                                         font = \tiny }]@ 
-%       ~emphase#                    let \p1 = (~#1),@
-%       ~emphase#                        \p2 = (~#2)@
-%       ~emphase#                    in \ifdim \x1 > \x2@
-%       ~emphase#                         (\p1) -- node {~#3} (\x1,\y2) -- (\p2)@
-%       ~emphase#                       \else@
-%       ~emphase#                         (\p1) -- (\x2,\y1) -- node {~#3} (\p2)@
-%       ~emphase#                       \fi ;}@]
-% E & \Longleftrightarrow \frac{(x+4)}3 + \frac{5x+3}5 = 7 
-% \Arrow{$\times 15$}\\
-%   & \Longleftrightarrow 5(x+4) + 3(5x+3) = 105 \\
-%   & \Longleftrightarrow 5x+20 + 15x+9 = 105 \\
-%   & \Longleftrightarrow 20x+29 = 105 
-% \Arrow{$-29$}\\
-%   & \Longleftrightarrow 20x = 76 
-% \Arrow{$\div 20$}\\
-%   & \Longleftrightarrow x = \frac{38}{10} 
-% \end{WithArrows}
-% \end{Verbatim}
-%
-%
-% \[\begin{WithArrows}[ll,interline=5mm,xoffset=5mm,
-%       tikz-code  = {\draw[rounded corners,
-%                           every node/.style = {circle,
-%                                                draw,
-%                                                auto = false,
-%                                                inner sep = 1pt,
-%                                                fill = gray!50,
-%                                                font = \tiny}] 
-%                           let \p1 = (#1),
-%                               \p2 = (#2)
-%                           in \ifdim \x1 > \x2
-%                                (\p1) -- node {#3} (\x1,\y2) -- (\p2)
-%                              \else
-%                                (\p1) -- (\x2,\y1) -- node {#3} (\p2)
-%                              \fi ;}]
-% E & \Longleftrightarrow \frac{(x+4)}3 + \frac{5x+3}5 = 7 
-% \Arrow{$\times 15$}\\
-%   & \Longleftrightarrow 5(x+4) + 3(5x+3) = 105 \\
-%   & \Longleftrightarrow 5x+20 + 15x+9 = 105 \\
-%   & \Longleftrightarrow 20x+29 = 105 
-% \Arrow{$-29$}\\
-%   & \Longleftrightarrow 20x = 76 
-% \Arrow{$\div 20$}\\
-%   & \Longleftrightarrow x = \frac{38}{10} 
-% \end{WithArrows}\]
-%
-%
-% 
-% \subsection{Automatic numbered loop}
-%
-% Assume we want to draw a loop of numbered arrows. In this purpose, it's
-% possible to write a dedicated command |\NumberedLoop| which will do the job
-% when used in |code-after|. In the following example, we write this command with
-% |\NewDocumentCommand| of \pkg{xparse} and |\foreach| of \pkg{pgffor} (both
-% packages are loaded when \pkg{witharrows} is loaded).
-%
-% \begin{Verbatim}
-% \NewDocumentCommand \NumberedLoop {}
-%         {\foreach \j in {2,...,\WithArrowsNbLines} 
-%               { \pgfmathtruncatemacro{\i}{\j-1}
-%                 \Arrow[rr]{\i}{\j}{\i} }
-%          \Arrow[rr,xoffset=1cm,tikz=<-]{1}{\WithArrowsNbLines}{\WithArrowsNbLines}}
-% \end{Verbatim}
-% 
-% The command |\WithArrowsNbLines| is a command available in |code-after| which
-% gives the total number of lines (=rows) of the current environment (it's a
-% command and not a counter).
-%
-%
-% \bigskip
-% \begin{Verbatim}
-% $\begin{WithArrows}[~emphase#code-after = \NumberedLoop@]
-% a.\;& f \text{ est continuous on } E \\
-% b.\;& f \text{ est continuous in } 0 \\
-% c.\;& f \text{ is bounded on the unit sphere} \\
-% d.\;& \exists K > 0\quad \forall x \in E\quad \|f(x)\| \le K \|x\| \\
-% e.\;& f \text{ is lipschitzian} 
-% \end{WithArrows}$
-% \end{Verbatim}
-% 
-% \bigskip
-% \begin{scope}
-% \NewDocumentCommand \NumberedLoop {}
-%         {\foreach \j in {2,...,\WithArrowsNbLines} 
-%               { \pgfmathtruncatemacro{\i}{\j-1}
-%                 \Arrow[rr]{\i}{\j}{\i} }
-%          \Arrow[rr,xoffset=1cm,tikz=<-]{1}{\WithArrowsNbLines}{\WithArrowsNbLines}}
-%
-%
-% $\begin{WithArrows}[code-after = \NumberedLoop]
-% a.\;& f \text{ est continuous on } E \\
-% b.\;& f \text{ est continuous in } 0 \\
-% c.\;& f \text{ is bounded on the unit sphere} \\
-% d.\;& \exists K > 0\quad \forall x \in E\quad \|f(x)\| \le K \|x\| \\
-% e.\;& f \text{ is lipschitzian} 
-% \end{WithArrows}$
-%
-%
-% \bigskip
-% As usual, it's possible to change the characteristic of both arrows and nodes
-% with the option |tikz|. However, if we want to change the style to have, for
-% example, numbers in parenthesis, the best way is to change the value of
-% |tikz-code|:
-%
-% \begin{Verbatim}
-% tikz-code = {\draw (~#1) to node {\footnotesize (~#3)} (~#2) ;}
-% \end{Verbatim}
-%
-% \WithArrowsOptions{tikz-code = {\draw (#1) to node {\footnotesize (#3)} (#2) ;}}
-%
-% $\begin{WithArrows}[code-after = \NumberedLoop]
-% a.\;& f \text{ est continuous on } E \\
-% b.\;& f \text{ est continuous in } 0 \\
-% c.\;& f \text{ is bounded on the unit sphere} \\
-% d.\;& \exists K > 0\quad \forall x \in E\quad \|f(x)\| \le K \|x\| \\
-% e.\;& f \text{ is lipschitzian}  
-% \end{WithArrows}$
-%
-% \end{scope}
-%
-% \vspace{2cm}
-% 
-% \section{Implementation}
-%
-% \subsection{Declaration of the package and extensions loaded}
-%
-%
-% First, \pkg{tikz} and some Tikz libraries are loaded before the
-% |\ProvidesExplPackage|. They are loaded this way because |\usetikzlibrary| in
-% |expl3| code fails.\footnote{cf.
-%   |tex.stackexchange.com/questions/57424/using-of-usetikzlibrary-in-an-expl3-package-fails|}
-% 
-%    \begin{macrocode}
-\RequirePackage{tikz}
-\usetikzlibrary{arrows.meta,bending}
-\RequirePackage{expl3}[2019/02/15]
-%    \end{macrocode}
-%
-% \bigskip
-% Then, we can give the traditional declaration of a package written with
-% |expl3|:
-%    \begin{macrocode}
-\RequirePackage{l3keys2e}
-\ProvidesExplPackage
-  {witharrows}
-  {\myfiledate}
-  {\myfileversion}
-  {Draws arrows for explanations on the right}
-%    \end{macrocode}
-%
-% \bigskip
-% The package \pkg{xparse} will be used to define the environments
-% |{WithArrows}|, |{DispWithArrows}|, |{DispWithArrows*}| and the commands
-% |\Arrow|, |\WithArrowsOptions| and |\WithArrowsNewStyle|.
-%    \begin{macrocode}
-\RequirePackage { xparse } [ 2018-10-17 ]
-%    \end{macrocode}
-%
-% \bigskip
-% \subsection{The packages footnote and footnotehyper}
-%
-% A few options can be given to the package \pkg{witharrows} when it is loaded
-% (with |\usepackage|, |\RequirePackage| or |\PassOptionsToPackage|). Currently
-% (version \myfileversion), there are two such options: |footnote| and
-% |footnotehyper|. With the option |footnote|, \pkg{witharrows} loads
-% \pkg{footnote} and uses it to extract the footnotes from the environments
-% |{WithArrows}|. Idem for the option |footnotehyper|.
-%
-% \medskip
-% The boolean |\g_@@_footnotehyper_bool| will indicate if the option
-% |footnotehyper| is used.
-%    \begin{macrocode}
-\bool_new:N \g_@@_footnotehyper_bool
-%    \end{macrocode}
-%
-% \medskip
-% The boolean |\g_@@_footnote_bool| will indicate if the option |footnote| is
-% used, but quicky, it will also be set to |true| if the option |footnotehyper|
-% is used.
-%    \begin{macrocode}
-\bool_new:N \g_@@_footnote_bool
-%    \end{macrocode}
-%
-% \bigskip
-%    \begin{macrocode}
-\cs_new_protected:Npn \@@_msg_new:nn { \msg_new:nnn { witharrows } }
-\cs_new_protected:Npn \@@_msg_new:nnn { \msg_new:nnnn { witharrows } }
-\cs_new_protected:Npn \@@_msg_redirect_name:nn 
-  { \msg_redirect_name:nnn { witharrows } }
-\cs_new_protected:Npn \@@_error:n { \msg_error:nn { witharrows } }
-\cs_new_protected:Npn \@@_warning:n { \msg_error:nn { witharrows } }
-\cs_new_protected:Npn \@@_fatal:n { \msg_fatal:nn { witharrows } }
-\cs_new_protected:Npn \@@_error:nn  { \msg_error:nnn { witharrows } }
-\cs_generate_variant:Nn \@@_error:nn { n x }
-%    \end{macrocode}
-% 
-% \medskip
-% We define a set of keys |WithArrows/package| for these options.
-%    \begin{macrocode}
-\keys_define:nn { WithArrows / package }
-  { 
-    footnote .bool_gset:N = \g_@@_footnote_bool ,
-    footnotehyper .bool_gset:N = \g_@@_footnotehyper_bool ,
-    unknown .code:n = 
-      \@@_fatal:n { Option~unknown~for~package } 
-  }
-%    \end{macrocode}
-%
-%    \begin{macrocode}          
-\@@_msg_new:nn { Option~unknown~for~package }
-  { 
-    You~can't~use~the~option~'\l_keys_key_tl'~when~loading~the~
-    package~witharrows.~Try~to~use~the~command~
-    \token_to_str:N\WithArrowsOptions. 
-  }
-%    \end{macrocode}
-%
-%
-% \bigskip
-% We process the options when the package is loaded (with |\usepackage|).
-%    \begin{macrocode}
-\ProcessKeysOptions { WithArrows / package }
-%    \end{macrocode}
-% 
-%
-% \medskip
-%    \begin{macrocode}
-\@@_msg_new:nn { Option~incompatible~with~Beamer }
-  { 
-    The~option~'\l_keys_key_tl'\ is~incompatible~
-    with~Beamer~because~Beamer~has~its~own~system~to~extract~footnotes.
-  }
-%    \end{macrocode}
-%
-%    \begin{macrocode}
-\@@_msg_new:nn { footnote~with~footnotehyper~package }
-  { 
-    You~can't~use~the~option~'footnote'~because~the~package~
-    footnotehyper~has~already~been~loaded.~
-    If~you~want,~you~can~use~the~option~'footnotehyper'~and~the~footnotes~  
-    within~the~environments~of~witharrows~will~be~extracted~with~the~tools~
-    of~the~package~footnotehyper.\\
-    If~you~go~on,~the~package~footnote~won't~be~loaded.
-  }
-%    \end{macrocode}
-%
-%    \begin{macrocode}
-\@@_msg_new:nn { footnotehyper~with~footnote~package }
-  { 
-    You~can't~use~the~option~'footnotehyper'~because~the~package~
-    footnote~has~already~been~loaded.~
-    If~you~want,~you~can~use~the~option~'footnote'~and~the~footnotes~  
-    within~the~environments~of~witharrows~will~be~extracted~with~the~tools~
-    of~the~package~footnote.\\ 
-    If~you~go~on,~the~package~footnotehyper~won't~be~loaded.
-  }
-%    \end{macrocode}
-%
-% \medskip
-%    \begin{macrocode}
-\bool_if:NT \g_@@_footnote_bool 
-  { 
-    \@ifclassloaded { beamer }
-      { \msg_info:nn { witharrows } { Option~incompatible~with~Beamer } }
-      { 
-        \@ifpackageloaded { footnotehyper }
-          { \@@_error:n { footnote~with~footnotehyper~package } }
-          { \usepackage { footnote } }
-      }
-  }
-%    \end{macrocode}
-%
-%    \begin{macrocode}
-\bool_if:NT \g_@@_footnotehyper_bool 
-  { 
-    \@ifclassloaded { beamer }
-      { \@@_info:n  { Option~incompatible~with~Beamer } }
-      { 
-        \@ifpackageloaded { footnote }
-          { \@@_error:n { footnotehyper~with~footnote~package } }
-          { \usepackage { footnotehyper } }
-      }
-    \bool_gset_true:N \g_@@_footnote_bool 
-  }
-%    \end{macrocode}
-% The flag |\g_@@_footnote_bool| is raised and so, we will only have to test
-% |\g_@@_footnote_bool| in order to know if we have to insert an environnement
-% |{savenotes}| (the |\begin{savenotes}| is in |\@@_pre_halign:n| and
-% |\end{savenotes}| at the end of the environments |{WithArrows}| and
-% |{DispWithArrows}|).
-%
-% \bigskip
-% \subsection{The class option leqno}
-%
-% The boolean |\c_@@_leqno_bool| will indicate if the class option |leqno| is
-% used. When this option is used in LaTeX, the command |\@eqnnum| is redefined
-% (as one can see in the file |leqno.clo|). That's enough to put the labels on
-% the left in our environments |{DispWithArrows}| and |{DispWithArrows*}|.
-% However, that's not enough when our option |wrap-lines| is used. That's why we
-% have to know if this option is used as a class option. With the following
-% programmation, |leqno| \emph{can't} be given as an option of \pkg{witharrows}
-% (by design).
-%    \begin{macrocode}
-\bool_new:N \c_@@_leqno_bool
-\DeclareOption { leqno } { \bool_set_true:N \c_@@_leqno_bool }
-\DeclareOption* { }
-\ProcessOptions* 
-%    \end{macrocode}
-%
-% 
-%
-% \bigskip
-% \subsection{Some technical definitions}
-%
-% 
-%    \begin{macrocode}
-\cs_generate_variant:Nn \tl_put_right:Nn { N v }
-\cs_generate_variant:Nn \seq_set_split:Nnn { N x x }
-%    \end{macrocode}
-% 
-% \medskip
-% We create booleans in order to know if some packages are loaded. For example,
-% for the package \pkg{amsmath}, the boolean is called
-% |\c_@@_amsmath_loaded_bool|.\footnote{It's not possible to use
-%   |\@ifpackageloaded| in the core of the functions because |\@ifpackageloaded|
-%   is available only in the preamble.}
-%    \begin{macrocode}
-\AtBeginDocument 
-  { 
-    \clist_map_inline:nn
-      { 
-        amsmath, amsthm, autonum, cleveref, hyperref, mathtools, showlabels,
-        typedref, unicode-math, varwidth 
-      }
-      {
-        \bool_new:c { c_@@_#1_loaded_bool }
-        \@ifpackageloaded { #1 }
-          { \bool_set_true:c { c_@@_#1_loaded_bool } }
-          { } 
-      }
-  }
-%    \end{macrocode}
-%
-% \bigskip
-% We define a command |\@@_strcmp:nn| to compare two token lists. It will be
-% available whether the engine is pdfTeX, XeTeX or LuaTeX.
-%    \begin{macrocode}
-\sys_if_engine_luatex:TF
-  { 
-    \cs_new_protected:Npn \@@_strcmp:nn  #1 #2
-      { \lua_now:e { l3kernel.strcmp('#1','#2') } } 
-  }
-  { 
-    \cs_new_protected:Npn \@@_strcmp:nn #1 #2 
-      { \pdftex_strcmp:D { #1 } { #2 } } 
-  } 
-%    \end{macrocode}
-%
-% \bigskip
-% We can now define a command |\@@_sort_seq:N| which will sort a sequence.
-%    \begin{macrocode}
-\cs_new_protected:Npn \@@_sort_seq:N #1
-  { 
-    \seq_sort:Nn #1
-      { 
-        \int_compare:nNnTF 
-          { 
-            \@@_strcmp:nn 
-              { \str_lower_case:n { ##1 } } 
-              { \str_lower_case:n { ##2 } } 
-          } 
-          > 0
-          \sort_return_swapped:
-          \sort_return_same:    
-      } 
-  }
-%    \end{macrocode}
-% 
-% \bigskip
-% The following command converts each item of a sequence from |tl| to |str|. It
-% will be used when creating list of keys (a key name is always a |str|).
-%    \begin{macrocode}
-\cs_new_protected:Npn \@@_convert_to_str_seq:N #1
-  {
-    \seq_clear:N \l_tmpa_seq
-    \seq_map_inline:Nn #1 
-      {
-        \seq_put_left:Nx \l_tmpa_seq { \tl_to_str:n { ##1 } }
-      }
-    \seq_set_eq:NN #1 \l_tmpa_seq
-  }
-\cs_new_protected:Npn \@@_set_seq_of_str_from_clist:Nn #1 #2
-  {
-    \seq_set_from_clist:Nn #1 { #2 }
-    \@@_convert_to_str_seq:N #1
-  }
-%    \end{macrocode}
-% 
-% \bigskip
-% The command |\@@_save:N| saves a \pkg{expl3} variable by creating a global
-% version of the variable. For a variable named |\l_|\texttt{\slshape
-%   name}|_|\texttt{\slshape type}, the corresponding global variable will be
-% named |\g_|\texttt{\slshape name}|_|\texttt{\slshape type}. The type of the
-% variable is determinated by the suffix \texttt{\slshape type} and is used to
-% apply the corresponding \pkg{expl3} commands.
-%    \begin{macrocode}
-\cs_new_protected:Npn \@@_save:N #1
-  { 
-    \seq_set_split:Nxx \l_tmpa_seq 
-       { \char_generate:nn { `_ } { 12 } } 
-       { \cs_to_str:N #1 }
-    \seq_pop_left:NN \l_tmpa_seq \l_tmpa_tl
-%    \end{macrocode}
-% The string |\l_tmpa_str| will contains the \emph{type} of the variable.
-%    \begin{macrocode}
-    \str_set:Nx \l_tmpa_str { \seq_item:Nn \l_tmpa_seq { -1 } }
-    \use:c { \l_tmpa_str _if_exist:cF }
-      { g _\seq_use:Nnnn \l_tmpa_seq _ _ _ }
-      { 
-        \use:c { \l_tmpa_str _new:c }
-          { g _\seq_use:Nnnn \l_tmpa_seq _ _ _ } 
-      }
-    \use:c { \l_tmpa_str _gset_eq:cN } 
-      { g _\seq_use:Nnnn \l_tmpa_seq _ _ _ } #1 
-  }
-%    \end{macrocode}
-% 
-% \medskip
-% The command |\@@_restore:N| affects to the \pkg{expl3} variable the value of
-% the (previously) set value of the corresponding \emph{global} variable.
-%    \begin{macrocode}  
-\cs_new_protected:Npn \@@_restore:N #1
-  { 
-    \seq_set_split:Nxx \l_tmpa_seq 
-      { \char_generate:nn { `_ } { 12 } } 
-      { \cs_to_str:N #1 }
-    \seq_pop_left:NN \l_tmpa_seq \l_tmpa_tl
-    \str_set:Nx \l_tmpa_str { \seq_item:Nn \l_tmpa_seq { -1 } }
-    \use:c { \l_tmpa_str _set_eq:Nc } 
-      #1 { g_\seq_use:Nnnn \l_tmpa_seq _ _ _ } 
-  }
-%    \end{macrocode}
-% 
-% 
-% \bigskip
-% We define a Tikz style |@@_node_style| for the |l|-nodes and |r|-nodes that
-% will be created in the |\halign|. These nodes are Tikz nodes of shape
-% ``rectangle'' but with zero width. An arrow between two nodes starts from the
-% \emph{south} anchor of the first node and arrives at the \emph{north} anchor
-% of the second node.
-%    \begin{macrocode}
-\tikzset
-  { 
-    @@_node_style / .style = 
-      { 
-        above = \l_@@_ystart_dim ,
-        inner~sep = \c_zero_dim ,
-        minimum~width = \c_zero_dim ,
-        minimum~height = \l_@@_ygap_dim
-      }
-  }
-%    \end{macrocode}
-% If the user uses the option |show-nodes| (it's a \pkg{l3keys} option), the
-% Tikz options |draw| and |red| will be appended to this style. This feature may
-% be useful for debugging.\footnote{The |v|-nodes, created near the end of line
-%   in |{DispWithArrows}| and |{DispWithArrows*}| are not shown with the option
-%   |show-nodes|.}
-%
-% 
-% \bigskip
-% The style |@@_standard| is loaded in standard in the |{tikzpicture}| we need.
-% The names of the nodes are prefixed by |wa| (by security) but also by a prefix
-% which is the position-in-the-tree of the nested environments.
-%    \begin{macrocode}
-\tikzset
-  { 
-    @@_standard / .style = 
-      { 
-        remember~picture ,
-        overlay ,
-        name~prefix = wa - \l_@@_prefix_str -
-      }
-  }
-%    \end{macrocode}
-% 
-% \bigskip
-% We also define a style for the tips of arrow. The final user of the extension
-% \pkg{witharrows} will use this style if he wants to draw an arrow directly
-% with a Tikz command in his document (probably using the Tikz nodes created by
-% |{WithArrows}| in the |\halign|).
-%    \begin{macrocode}
-\tikzset
-  { 
-    WithArrows / arrow / tips / .style = 
-      { > = { Straight~Barb [ scale = 1.2 , bend ] } } 
-  }
-%    \end{macrocode}
-%
-% \bigskip
-% The style |WithArrows/arrow| will be used to draw the arrows (more precisely,
-% it will be passed to |every~path|).
-%    \begin{macrocode}
-\tikzset 
- { 
-   WithArrows / arrow / .style  = 
-     { 
-       align = left ,
-%    \end{macrocode}
-%
-% We have put the option |align = left| because we want to give the user the
-% possibility of using |\\| in the labels.
-%    \begin{macrocode}
-       auto = left ,
-       font = \small \itshape ,
-       WithArrows / arrow / tips ,
-       bend~left = 45 ,
-       -> 
-     } 
- }
-%    \end{macrocode}
-%
-% \bigskip
-% The option |subequations| is an option which uses the environment
-% |{subequations}| of \pkg{amsmath}. That's why, if \pkg{amsmath} is loaded, we
-% add the key |subequations| to the list of the keys available in
-% |\WithArrowsOptions| and |{DispWithArrows}|.
-%    \begin{macrocode}
-\AtBeginDocument 
-  {
-    \bool_if:NTF \c_@@_amsmath_loaded_bool
-      {
-        \seq_put_right:Nn \l_@@_options_WithArrowsOptions_seq { subequations }
-        \seq_put_right:Nn \l_@@_options_DispWithArrows_seq { subequations }
-      }
-%    \end{macrocode}
-%
-% \bigskip
-% In order to increase the interline in the environments |{WithArrows}|,
-% |{DispWithArrows}|, etc., we will use the command |\spread@equation| of
-% \pkg{amsmath}. When used, this command becomes no-op (in the current TeX
-% group). Therefore, it will be possible to use the environments of
-% \pkg{amsmath} (e.g. |{aligned}|) in an environment |{WithArrows}|.
-% 
-% Nevertheless, we want the extension \pkg{witharrows} available without
-% \pkg{amsmath}. That's why we give a definition of |\spread@equation| if
-% \pkg{amsmath} is not loaded (we put the code in a |\AtBeginDocument| because
-% the flag |\c_@@_amsmath_loaded_bool| is itself set in a |\AtBeginDocument|).
-%    \begin{macrocode}
-      { 
-        \cs_new_protected:Npn \spread@equation
-          { 
-            \openup \jot   
-            \cs_set_eq:NN \spread@equation \prg_do_nothing:
-          }
-      } 
-  }
-%    \end{macrocode}
-%
-% \bigskip
-%    \begin{macrocode}
-\tl_new:N \l_@@_left_brace_tl
-\tl_set_eq:NN \l_@@_left_brace_tl \c_novalue_tl
-%    \end{macrocode}
-%
-% \bigskip
-% \subsection{Variables}
-%
-% The boolean |\l_@@_in_WithArrows_bool| will be raised in an environment
-% |{WithArrows}| and the boolean |\l_@@_in_dispwitharrows_bool| will be raised
-% in an environment |{DispWithArrows}| or |{DispWithArrows*}|. The boolean
-% |\l_@@_in_code_after_bool| will be raised during the execution of the
-% |code-after| (option |code-after|).
-%    \begin{macrocode}
-\bool_new:N \l_@@_in_WithArrows_bool
-\bool_new:N \l_@@_in_DispWithArrows_bool
-\bool_new:N \l_@@_in_code_after_bool
-%    \end{macrocode}
-%
-% \bigskip
-% The following sequence is the position of the last environment |{WithArrows}|
-% in the tree of the nested environments |{WithArrows}|.
-%    \begin{macrocode}
-\seq_new:N \g_@@_position_in_the_tree_seq
-\seq_gput_right:Nn \g_@@_position_in_the_tree_seq 1
-%    \end{macrocode}
-%
-% \bigskip
-% The following counter will give the number of the last environment
-% |{WithArrows}| of level~$0$. This counter will be used only in the definition
-% of |\WithArrowsLastEnv|.
-%    \begin{macrocode}
-\int_new:N \g_@@_last_env_int
-%    \end{macrocode}
-%
-% \bigskip
-% The following integer indicates the position of the box that will be created
-% for an environment |{WithArrows}| (not an environment |{DispWithArrows}|) :
-% 0 (=|t|=|\vtop|), 1~(=|c|=|\vcenter|) or 2 (=|b|=|\vbox|).
-%    \begin{macrocode}
-\int_new:N \l_@@_pos_env_int 
-%    \end{macrocode}
-%
-% \bigskip
-% The integer |\l_@@_pos_arrow_int| indicates the position of the arrow with the
-% following code (the option |v| is accessible only for the arrows in
-% |code-after| where the options |i|, |group| et |groups| are not available).
-%
-% \begin{center}
-% \begin{tabular}{l}
-% \begin{tabular}{@{}l*8c@{}}
-% \toprule
-% option                 & |lr| & |ll| & |rl| & |rr| & |v| & |i| & |groups| & |group| \\
-% \midrule
-% |\l_@@_pos_arrow_int| & $0$  & $1$  & $2$  & $3$  & $4$ & $5$  & $6$  & $7$  \\
-% \bottomrule
-% \end{tabular} \\
-% \footnotesize The option |v| can be used only in |\Arrow| in |code-after| (see
-% below). 
-% \end{tabular}
-% \end{center}
-%
-%    \begin{macrocode}
-\int_new:N \l_@@_pos_arrow_int
-\int_set:Nn \l_@@_pos_arrow_int 3
-%    \end{macrocode}
-%
-%
-% \bigskip
-% In the |\halign| of an environment |{WithArrows}| or |{DispWithArrows}|, we
-% will have to use four counters:
-% \begin{itemize}
-% \item |\g_@@_arrow_int| to count the arrows created in the environment ;
-% \item |\g_@@_line_int| to count the lines of the |\halign| ;
-% \item |\g_@@_col_int| to count the column of the |\halign|.
-% \end{itemize}
-%
-%
-% These counters will be incremented in a cell of the |\halign| and, therefore,
-% the incrementation must be global. However, we want to be able to include a
-% |{WithArrows}| in another |{WithArrows}|. To do so, we must restore the
-% previous value of these counters at the end of an environment |{WithArrows}|
-% and we decide to manage a stack for each of these counters.
-%    \begin{macrocode}
-\seq_new:N \g_@@_arrow_int_seq
-\int_new:N \g_@@_arrow_int
-\seq_new:N \g_@@_line_int_seq
-\int_new:N \g_@@_line_int
-\seq_new:N \g_@@_col_int_seq
-\int_new:N \g_@@_col_int
-%    \end{macrocode}
-%
-% 
-% \bigskip
-% For the environment |{DispWithArrows}|, the comma list |\l_@@_tags_clist| will
-% be the list of the numbers of lines to be tagged (with the counter |equation|
-% of LaTeX). In fact, |\l_@@_tags_clist| may contain non negative integers but
-% also three special values, |first|, |last| and |all|.
-%    \begin{macrocode}
-\clist_new:N \l_@@_tags_clist
-\clist_set:Nn \l_@@_tags_clist { all }
-%    \end{macrocode}
-%
-% \bigskip
-% During the execution of an environment |{DispWithArrows}|, if a row must be
-% tagged, the (local) value of |\l_@@_tags_clist| will be put (by convention) to
-% |all|. 
-%    \begin{macrocode}
-\cs_new_protected:Npn \@@_test_if_to_tag:
-  { 
-    \clist_if_in:NVT \l_@@_tags_clist \g_@@_line_int
-      { \clist_set:Nn \l_@@_tags_clist { all } }
-  }
-%    \end{macrocode}
-%
-%
-% \bigskip
-% If the user has given a value for the option |command-name| (at the global or
-% at the \emph{environment} level), a command with this name is defined locally
-% in the environment with meaning |\@@_Arrow|. The default value of the option
-% |command-name| is ``|Arrow|'' and thus, by default, the name of the command
-% will be |\Arrow|.
-%    \begin{macrocode}
-\str_new:N \l_@@_command_name_str
-\str_set:Nn \l_@@_command_name_str { Arrow }
-%    \end{macrocode}
-%
-% \bigskip
-% The string |\l_@@_string_Arrow_for_msg_str| is only a string that will be
-% displayed in some error messages. For example, if |command-name| is defined to
-% be |Explanation|, this string will contain ``|\Arrow alias \Explanation|''. 
-%    \begin{macrocode}
-\str_new:N \l_@@_string_Arrow_for_msg_str 
-\str_set:Nx \l_@@_string_Arrow_for_msg_str { \token_to_str:N \Arrow }
-%    \end{macrocode}
-%
-% \bigskip
-% The sequence |\g_@@_names_seq| will be the list of all the names of
-% environments used (via the option |name|) in the document: two environments
-% must not have the same name. However, it's possible to use the option
-% |allow-duplicate-names|.
-%    \begin{macrocode}
-\seq_new:N \g_@@_names_seq
-%    \end{macrocode}
-% 
-% \bigskip
-% The boolean |\l_@@_sbwi_bool| corresponds to the option
-% |standard-behaviour-with-items|. Since the version 1.16 of \pkg{witharrows},
-% no vertical space is added between an |\item| of a LaTeX list and an
-% environment |{DispWithArrows}|. With the option
-% |standard-behaviour-with-items|, it's possible to restore the previous
-% behaviour (which corresponds to the standard behaviour of |{align}| of
-% \pkg{amsmath}). |\l_@@_sbwi_bool| is the boolean corresponding to this option.
-%    \begin{macrocode}
-\bool_new:N \l_@@_sbwi_bool 
-%    \end{macrocode}
-% 
-% \bigskip
-%    \begin{macrocode}
-\bool_new:N \l_@@_in_first_columns_bool
-\bool_new:N \l_@@_tag_star_bool
-\bool_new:N \l_@@_tag_next_line_bool
-\bool_new:N \l_@@_qedhere_bool
-\bool_new:N \l_@@_new_group_bool
-\bool_new:N \l_@@_initial_r_bool
-\bool_new:N \l_@@_final_r_bool
-\tl_new:N \l_@@_initial_tl
-\tl_new:N \l_@@_final_tl
-\int_new:N \l_@@_nb_cols_int
-%    \end{macrocode}
-% 
-% \bigskip
-% The string |\l_@@_format_str| will contain the \emph{format} of the array
-% which is a succession of letters |r|, |c| and |l| specifying the type of the
-% columns of the |\halign| (except the column for the labels of the equations
-% in the environment |{DispWithArrows}|). 
-%    \begin{macrocode}
-\str_new:N \l_@@_format_str
-%    \end{macrocode}
-% 
-% \bigskip
-% The option boolean corresponds to the option |subequations|.
-%    \begin{macrocode}
-\bool_new:N \l_@@_subequations_bool
-%    \end{macrocode}
-% 
-% \bigskip
-% \subsection{The definition of the options}
-%
-% There are four levels where options can be set:
-% \begin{itemize}
-% \item with |\usepackage[...]{witharrows}|: this level will be called
-% \emph{package} level;
-% \item with |\WithArrowsOptions{...}|: this level will be called \emph{global}
-% level\footnote{This level is called \emph{global level} but the settings done
-% by |\WithArrowsOptions| are local in the TeX sense: their scope corresponds to
-% the current TeX group.};
-% \item with |\begin{WithArrows}[...]|: this level will be called
-% \emph{environment} level;
-% \item with |\Arrow[...]| (included in |code-after|): this level will be called
-% \emph{local} level.
-% \end{itemize}
-%
-%
-% \bigskip
-% When we scan a list of options, we want to be able to raise an error if two
-% options of position (|ll|, |rl|, |i|, etc.) of the arrows are present. That's
-% why we keep the first option of position in a variable called
-% |\l_@@_previous_key_str|. The following function |\@@_eval_if_allowed:n| will
-% execute its argument only if a first key of position has not been set (and
-% raise an error elsewhere). 
-%
-%    \begin{macrocode}
-\cs_new_protected:Npn \@@_eval_if_allowed:n #1
-  { 
-    \str_if_empty:NTF \l_@@_previous_key_str
-      { 
-        \str_set_eq:NN \l_@@_previous_key_str \l_keys_key_tl
-        #1
-      }
-      { \@@_error:n { Incompatible~options } }
-  }
-%    \end{macrocode}
-%
-%
-%    \begin{macrocode}
-\cs_new_protected:Npn \@@_fix_pos_option:n #1
-  { \@@_eval_if_allowed:n { \int_set:Nn \l_@@_pos_arrow_int { #1 } } }
-%    \end{macrocode}
-%
-% \bigskip
-% First a set of keys that will be used at the global or environment level of
-% options.
-%    \begin{macrocode}
-\keys_define:nn { WithArrows / Global }
-  {
-    ygap .dim_set:N = \l_@@_ygap_dim ,
-    ygap .value_required:n = true ,
-    ygap .initial:n = 0.4 ex ,
-    ystart .dim_set:N = \l_@@_ystart_dim ,
-    ystart .value_required:n = true ,
-    ystart .initial:n = 0.4 ex ,
-    more-columns .code:n = 
-      \@@_msg_redirect_name:nn { Too~much~columns~in~WithArrows } { none } ,
-    more-columns .value_forbidden:n = true,
-    command-name .code:n =
-      \str_set:Nn \l_@@_command_name_str { #1 }
-      \str_set:Nx \l_@@_string_Arrow_for_msg_str
-        { \c_backslash_str Arrow~alias~\c_backslash_str #1 } ,
-    command-name .value_required:n = true ,
-    tikz-code .tl_set:N = \l_@@_tikz_code_tl,
-    tikz-code .initial:n = \draw~(#1)~to~node{#3}~(#2)~; ,
-    tikz-code .value_required:n = true ,
-    TikzCode .meta:n = { tikz-code = #1 } ,
-    displaystyle .bool_set:N = \l_@@_displaystyle_bool ,
-    displaystyle .default:n = true ,
-    show-nodes .code:n =  
-      \tikzset { @@_node_style / .append~style = { draw , red } } ,
-    show-nodes .value_forbidden:n = true,
-    show-node-names .bool_set:N = \l_@@_show_node_names_bool ,
-    show-node-names .default:n = true ,
-    group .code:n = 
-      \str_if_empty:NTF \l_@@_previous_key_str
-        {
-          \str_set:Nn \l_@@_previous_key_str { group }
-          \seq_remove_all:Nn \l_@@_options_Arrow_seq { xoffset }
-          \int_set:Nn \l_@@_pos_arrow_int 7 
-        }
-        { \@@_error:n { Incompatible~options } } ,
-    group .value_forbidden:n = true ,
-    groups .code:n = 
-      \str_if_empty:NTF \l_@@_previous_key_str
-        { 
-          \str_set:Nn \l_@@_previous_key_str { groups }
-          \seq_if_in:NnF \l_@@_options_Arrow_seq { new-group }
-            { \seq_put_right:Nn \l_@@_options_Arrow_seq { new-group } }
-          \seq_remove_all:Nn \l_@@_options_Arrow_seq { xoffset }
-          \int_set:Nn \l_@@_pos_arrow_int 6
-        }
-        { \@@_error:n { Incompatible~options } } ,
-    groups .value_forbidden:n = true ,
-    tikz   .code:n = \tikzset { WithArrows / arrow / .append~style = { #1 } } , 
-    tikz   .initial:n         = \c_empty_tl ,
-    tikz   .value_required:n  = true ,
-    rr     .value_forbidden:n = true ,
-    rr     .code:n            = \@@_fix_pos_option:n 3 ,
-    ll     .value_forbidden:n = true ,
-    ll     .code:n            = \@@_fix_pos_option:n 1 ,
-    rl     .value_forbidden:n = true ,
-    rl     .code:n            = \@@_fix_pos_option:n 2 ,
-    lr     .value_forbidden:n = true ,
-    lr     .code:n            = \@@_fix_pos_option:n 0 ,
-    i      .value_forbidden:n = true ,
-    i      .code:n            = \@@_fix_pos_option:n 5 ,
-    xoffset .dim_set:N  = \l_@@_xoffset_dim ,
-    xoffset .value_required:n  = true ,
-    xoffset .initial:n = 3 mm ,
-    jot .dim_set:N = \jot ,
-    jot .value_required:n = true ,
-    interline .skip_set:N = \l_@@_interline_skip ,
-    interline .value_required:n = true ,
-    start-adjust .dim_set:N = \l_@@_start_adjust_dim ,
-    start-adjust .value_required:n = true ,
-    start-adjust .initial:n = 0.4 ex ,
-    end-adjust .dim_set:N = \l_@@_end_adjust_dim ,
-    end-adjust .value_required:n = true ,
-    end-adjust .initial:n = 0.4 ex ,
-    adjust .meta:n  = { start-adjust = #1 , end-adjust = #1 } ,
-    adjust .value_required:n = true ,
-%    \end{macrocode}
-%
-% \medskip
-% With the option |no-arrows|, the arrows won't be drawn. However, the ``first
-% pass'' of the arrows is done and some errors may be detected. The
-% nullification of |\@@_draw_arrows:nn| is for the standard arrows and the
-% nullification of |\@@_draw_arrow:nnn| is for ``Arrow in |code-after|''.
-%    \begin{macrocode}
-    no-arrows .code:n = 
-      \cs_set_eq:NN \@@_draw_arrows:nn \use_none:nn
-      \cs_set_eq:NN \@@_draw_arrow:nnn \use_none:nnn  ,
-    no-arrows .value_forbidden:n = true ,
-  }
-%    \end{macrocode}
-% 
-% \bigskip
-% Now a set of keys specific to the environments |{WithArrows}| (and not
-% |{DispWithArrow}}|). Despite its name, this set of keys will also be used in
-% |\WithArrowsOptions|. 
-%    \begin{macrocode}
-\keys_define:nn { WithArrows / WithArrowsSpecific }
-  { 
-    t   .code:n            = \int_set:Nn \l_@@_pos_env_int O ,
-    t   .value_forbidden:n = true ,
-    c   .code:n            = \int_set:Nn \l_@@_pos_env_int 1 ,
-    c   .value_forbidden:n = true ,
-    b   .code:n            = \int_set:Nn \l_@@_pos_env_int 2 ,
-    b   .value_forbidden:n = true
-  }
-%    \end{macrocode}
-%
-% \bigskip
-% The following list of the (left) extensible delimiters of LaTeX is only for
-% the validation of the key |replace-left-brace-by|.
-%    \begin{macrocode}
-\clist_new:N \c_@@_extensible_delimiters_clist
-\clist_set:Nn \c_@@_extensible_delimiters_clist
-  { 
-    \{, (, [, \lbrace, \lbrack, \lgroup, \langle, \lmoustache, \lceil, \lfloor
-  }
-\AtBeginDocument
-  { 
-    \bool_if:nT 
-      { \c_@@_amsmath_loaded_bool || \use:c { c_@@_unicode-math_loaded_bool } } 
-      { 
-        \clist_put_right:Nn \c_@@_extensible_delimiters_clist { \lvert, \lVert }
-      }  
-  }
-%    \end{macrocode}
-%
-%
-% \bigskip
-% Now a set of keys specific to the environments |{DispWithArrows}| and
-% |{DispWithArrows*}| (and not |{WithArrows}|). Despite its name, this set of
-% keys will also be used in |\WithArrowsOptions|. 
-%    \begin{macrocode}
-\keys_define:nn { WithArrows / DispWithArrowsSpecific }
-  {  
-    fleqn .bool_set:N = \l_@@_fleqn_bool ,
-    fleqn .default:n = true ,
-    mathindent .dim_set:N = \l_@@_mathindent_dim ,
-    mathindent .value_required:n = true ,
-    mathindent .initial:n = 25 pt ,
-    notag .code:n = 
-      \str_if_eq:nnTF { #1 } { true }
-        { \clist_clear:N \l_@@_tags_clist }
-        { \clist_set:Nn \l_@@_tags_clist { all } } ,
-    notag .default:n = true ,
-%    \end{macrocode}
-% Since the option |subequations| is an option which insert the environment
-% |{DispWithArrows}| in an environment |{subequations}| of \pkg{amsmath}, we
-% must test whether the package \pkg{amsmath} is loaded. 
-%    \begin{macrocode}
-    subequations .code:n = 
-      \bool_if:NTF \c_@@_amsmath_loaded_bool
-        { \bool_set_true:N \l_@@_subequations_bool }
-        { 
-          \@@_error:n { amsmath~not~loaded } 
-          \group_begin:
-          \globaldefs = 1
-          \@@_msg_redirect_name:nn { amsmath~not~loaded } { info }
-          \group_end:
-        } ,
-    subequations .default:n = true ,
-    subequations .value_forbidden:n = true ,
-    nonumber .meta:n = notag ,
-    allow-multiple-labels .code:n = 
-      \@@_msg_redirect_name:nn { Multiple~labels } { none } ,
-    allow-multiple-labels .value_forbidden:n = true ,
-    wrap-lines .bool_set:N = \l_@@_wrap_lines_bool ,
-    wrap-lines .default:n = true ,
-    tagged-lines .code:n =   
-      \clist_set:Nn \l_@@_tags_clist { #1 }
-      \clist_if_in:NnT \l_@@_tags_clist { first }
-        {
-          \clist_remove_all:Nn \l_@@_tags_clist { first }
-          \clist_put_left:Nn \l_@@_tags_clist \c_one_int
-        } ,
-    tagged-lines .value_required:n = true ,
-    replace-left-brace-by .code:n = 
-      {
-        \clist_if_in:NnTF 
-          \c_@@_extensible_delimiters_clist
-          { #1 }
-          { \tl_set:Nn \l_@@_replace_left_brace_by_tl { #1 } }
-          { \@@_error:n { Bad~value~for~replace~brace~by } }
-      } ,
-    replace-left-brace-by .initial:n = \lbrace ,
-%    \end{macrocode}
-%
-% Since the version 1.16 of \pkg{witharrows}, no vertical space is added between
-% an |\item| of a LaTeX list and an environment |{DispWithArrows}|. With the
-% option |standard-behaviour-with-items|, it's possible to restore the previous
-% behaviour (which corresponds to the standard behaviour of |{align}| of
-% \pkg{amsmath}).
-%    \begin{macrocode}
-    standard-behaviour-with-items .bool_set:N = \l_@@_sbwi_bool ,
-    standard-behaviour-with-items .default:n = true 
-  }
-%    \end{macrocode}
-%
-%
-% \bigskip
-% Now a set of keys which will be used in all the environments (but not in
-% |\WithArrowsOptions}|). 
-%
-%    \begin{macrocode}
-\keys_define:nn { WithArrows / Env } 
-  { 
-    name .code:n = 
-%    \end{macrocode}
-% First, we convert the value in a |str| because the list of the names will be a
-% list of |str|.
-%    \begin{macrocode}
-      \str_set:Nn \l_tmpa_str { #1 }
-      \seq_if_in:NVTF \g_@@_names_seq \l_tmpa_str
-        { \@@_error:n { Duplicate~name } }
-        { \seq_gput_left:NV \g_@@_names_seq \l_tmpa_str }
-      \str_set_eq:NN \l_@@_name_str \l_tmpa_str ,
-    name .value_required:n = true ,
-    code-before .code:n = \tl_put_right:Nn \l_@@_code_before_tl { #1 } ,
-    code-before .value_required:n = true,
-    CodeBefore .meta:n = { code-before = #1 } ,
-    code-after .code:n = \tl_put_right:Nn \l_@@_code_after_tl { #1 } ,
-    code-after .value_required:n = true ,
-    CodeAfter  .meta:n = { code-after = #1 } ,
-    format .code:n = 
-      \tl_if_empty:nTF { #1 } 
-        { \@@_error:n { Invalid~option~format } }
-        {
-          \regex_match:nnTF { \A[rcl]*\Z } { #1 }
-            { \tl_set:Nn \l_@@_format_str { #1 } }
-            { \@@_error:n { Invalid~option~format } }
-        } ,
-    format .value_required:n = true ,
-  }
-%    \end{macrocode}
-%
-% 
-% \bigskip
-% Now, we begin the construction of the major sets of keys, named
-% ``|WithArrows / WithArrows|'', ``|WithArrows / DispWithArrows|'' and 
-% ``|WithArrows / WithArrowsOptions|''. Each of these sets of keys will be
-% completed after.
-%    \begin{macrocode}
-\keys_define:nn { WithArrows } 
-  { 
-    WithArrows .inherit:n = 
-      { 
-        WithArrows / Global , 
-        WithArrows / WithArrowsSpecific , 
-        WithArrows / Env
-      } , 
-    DispWithArrows .inherit:n = 
-      { 
-        WithArrows / DispWithArrowsSpecific , 
-        WithArrows / Global ,
-        WithArrows / Env ,
-      } ,
-    WithArrowsOptions .inherit:n = 
-      { 
-        WithArrows / Global , 
-        WithArrows / WithArrowsSpecific , 
-        WithArrows / DispWithArrowsSpecific 
-      } 
-  }
-%    \end{macrocode}
-% 
-% 
-% \bigskip
-% A sequence of |str| for the options available in |{WithArrows}|. This sequence
-% will be used in the error messages and can be modified dynamically.
-%    \begin{macrocode}
-\seq_new:N \l_@@_options_WithArrows_seq
-\@@_set_seq_of_str_from_clist:Nn \l_@@_options_WithArrows_seq
-  { 
-    adjust, b, c, code-after, code-before, command-name,
-    displaystyle, end-adjust, 
-    format, group, groups, i,
-    interline, jot, ll,
-    lr, more-columns, name, 
-    no-arrows, rl, rr, 
-    show-node-names, show-nodes, start-adjust,
-    t, tikz, tikz-code, 
-    xoffset, ygap, ystart 
-  } 
-\@@_convert_to_str_seq:N \l_@@_options_WithArrows_seq
-%    \end{macrocode}
-%
-% \medskip
-%    \begin{macrocode}
-\keys_define:nn { WithArrows / WithArrows } 
-  { 
-    unknown .code:n  = 
-      \@@_sort_seq:N \l_@@_options_WithArrows_seq 
-      \@@_error:n { Unknown~option~WithArrows } 
-  }
-%    \end{macrocode}
-%
-% \bigskip
-%    \begin{macrocode}
-\keys_define:nn { WithArrows / DispWithArrows } 
-  { 
-    left-brace .tl_set:N = \l_@@_left_brace_tl ,
-    unknown .code:n  = 
-      \@@_sort_seq:N \l_@@_options_DispWithArrows_seq
-      \@@_error:n { Unknown~option~DispWithArrows } 
-  }
-%    \end{macrocode}
-%
-% \bigskip
-% A sequence of the options available in |{DispWithArrows}|. This sequence will
-% be used in the error messages and can be modified dynamically.
-%    \begin{macrocode}
-\seq_new:N \l_@@_options_DispWithArrows_seq
-\@@_set_seq_of_str_from_clist:Nn \l_@@_options_DispWithArrows_seq
-  { 
-    allow-multiple-labels, code-after, code-before, command-name, tikz-code, adjust,
-    displaystyle, end-adjust, fleqn, group, format, groups, i, interline, jot,
-    left-brace, ll, lr, mathindent, name, no-arrows, nonumber, notag, 
-    replace-left-brace-by, rl, rr, show-node-names, show-nodes, start-adjust, 
-    tagged-lines, tikz, wrap-lines, xoffset, ygap, ystart 
-  }
-%    \end{macrocode}
-% 
-%
-%    \begin{macrocode}
-\keys_define:nn { WithArrows / WithArrowsOptions } 
-  { 
-    allow-duplicate-names .code:n = 
-      \@@_msg_redirect_name:nn { Duplicate~name } { none } ,
-    allow-duplicate-names .value_forbidden:n = true ,
-    unknown .code:n  = 
-      \@@_sort_seq:N \l_@@_options_WithArrowsOptions_seq
-      \@@_error:n { Unknown~option~WithArrowsOptions } 
-  }
-%    \end{macrocode}
-% 
-%
-% \bigskip
-% A sequence of the options available in |\WithArrowsOptions|. This sequence
-% will be used in the error messages and can be modified dynamically.
-%    \begin{macrocode}
-\seq_new:N \l_@@_options_WithArrowsOptions_seq
-\@@_set_seq_of_str_from_clist:Nn \l_@@_options_WithArrowsOptions_seq
-  { 
-    allow-duplicate-names, allow-multiple-labels, b, c, command-name,
-    more-columns, tikz-code, adjust, displaystyle, end-adjust, fleqn, group,
-    groups, i, interline, jot, ll, lr, mathindent, no-arrows, nonumber, notag,
-    rl, rr, show-node-names, show-nodes, standard-behaviour-with-items,
-    start-adjust, t, tagged-lines, tikz, wrap-lines, xoffset, ygap, ystart 
-  }
-%    \end{macrocode}
-% 
-% \bigskip
-% The command |\@@_set_independent:| is a command without argument that will be
-% used to specify that the arrow will be ``independent'' (of the potential
-% groups of the option |group| or |groups|). This information will be stored in
-% the field ``status'' of the arrow. Another value of the field ``status'' is
-% ``new-group''.
-%    \begin{macrocode}
-\cs_new_protected:Npn \@@_set_independent:
-  { 
-    \str_if_empty:NTF \l_@@_previous_key_str
-      {
-        \str_set_eq:NN \l_@@_previous_key_str \l_keys_key_tl
-        \str_set:Nn \l_@@_status_arrow_str { independent } 
-        \str_if_eq:VnF \l_keys_value_tl { NoValue }
-          { \@@_error:n { Value~for~a~key } }
-      }
-      { \@@_error:n { Incompatible~options~in~Arrow } }
-  }
-%    \end{macrocode}
-%
-% \bigskip
-% The options of an individual arrow are parsed twice. The first pass is when
-% the command |\Arrow| is read. The second pass is when the arrows are drawn
-% (after the end of the environment |{WithArrows}| or |{DispWithArrows}|). Now,
-% we present the keys set for the first pass. The main goal is to extract
-% informations which will be necessary during the scan of the arrows. For
-% instance, we have to know if some arrows are ``independent'' or use the
-% option ``new-group''.
-%    \begin{macrocode}
-\keys_define:nn { WithArrows / Arrow / FirstPass }
-  { 
-    jump .code:n = 
-      \int_compare:nTF { #1 > 0 }
-        { \int_set:Nn \l_@@_jump_int { #1 } }
-        { \@@_error:n { Negative~jump } } ,
-    jump .value_required:n  = true,
-    rr .code:n = \@@_set_independent: ,
-    ll .code:n = \@@_set_independent: ,
-    rl .code:n = \@@_set_independent: ,
-    lr .code:n = \@@_set_independent: ,
-    i  .code:n = \@@_set_independent: ,
-    rr .default:n = NoValue ,
-    ll .default:n = NoValue ,
-    rl .default:n = NoValue ,
-    lr .default:n = NoValue ,
-    i  .default:n = NoValue ,
-    new-group .value_forbidden:n = true,
-    new-group .code:n = 
-      \int_compare:nTF { \l_@@_pos_arrow_int = 6 }
-        { \str_set:Nn \l_@@_status_arrow_str { new-group } }
-        { \@@_error:n { new-group~without~groups } } , 
-%    \end{macrocode}
-%
-% \medskip
-% The other keys don't give any information necessary during the scan of the
-% arrows. However, you try to detect errors and that's why all the keys are
-% listed in this keys set. An unknown key will be detected at the point of the
-% command |\Arrow| and not at the end of the environment.
-%    \begin{macrocode}
-    tikz-code .code:n = \prg_do_nothing: ,
-    tikz-code .value_required:n = true ,
-    tikz .code:n = \prg_do_nothing: ,
-    tikz .value_required:n = true ,
-%    \end{macrocode}
-%
-% \medskip
-% The option |xoffset| is not allowed when the option |group| or the option
-% |groups| is used (since it would be meaningless).
-%    \begin{macrocode}
-    xoffset .code:n = 
-      \int_compare:nNnT \l_@@_pos_arrow_int > 5
-        { \@@_error:n { Option~xoffset~forbidden } } ,
-    xoffset .value_required:n = true ,
-    start-adjust .code:n = \prg_do_nothing: ,
-    start-adjust .value_required:n = true ,
-    end-adjust .code:n = \prg_do_nothing: ,
-    end-adjust .value_required:n = true ,
-    adjust .code:n  = \prg_do_nothing: ,
-    adjust .value_required:n = true ,
-    unknown .code:n = 
-      \@@_sort_seq:N \l_@@_options_Arrow_seq
-      \seq_if_in:NVTF \l_@@_options_WithArrows_seq \l_keys_key_tl
-        { 
-          \str_set:Nn \l_tmpa_str
-           { ~However,~this~key~can~be~used~in~the~options~of~\{WithArrows\}. } 
-        }
-        { \str_clear:N \l_tmpa_str }
-      \@@_error:n { Unknown~option~in~Arrow }
-  }
-%    \end{macrocode}
-%
-%
-% \bigskip
-% A sequence of the options available in |\Arrow|. This sequence will be used in
-% the error messages and can be modified dynamically.
-%    \begin{macrocode}
-\seq_new:N \l_@@_options_Arrow_seq
-\@@_set_seq_of_str_from_clist:Nn \l_@@_options_Arrow_seq
-  { 
-    adjust, end-adjust, i, jump, ll, lr, rl, rr, start-adjust, tikz, tikz-code,
-    xoffset 
-  }
-%    \end{macrocode}
-%
-% \bigskip
-%    \begin{macrocode}
-\cs_new_protected:Npn \@@_fix_pos_arrow:n #1
-  { 
-    \str_if_empty:NT \l_@@_previous_key_str
-      { 
-        \str_set_eq:NN \l_@@_previous_key_str \l_keys_key_tl
-        \int_set:Nn \l_@@_pos_arrow_int { #1 } 
-      }
-  }
-%    \end{macrocode}
-%
-% \bigskip
-% The options of the individual commands |\Arrows| are scanned twice. The second
-% pass is just before the drawing of the arrow. In this set of keys, we don't
-% put an item for the unknown keys because an unknown key would have been
-% already detected during the first pass.
-%
-%    \begin{macrocode} 
-\keys_define:nn {WithArrows / Arrow / SecondPass }
-  { 
-    tikz-code .tl_set:N = \l_@@_tikz_code_tl ,
-    tikz-code .initial:n = \draw~(#1)~to~node{#3}~(#2)~; ,
-    tikz .code:n = \tikzset { WithArrows / arrow / .append~style = { #1 } } ,
-    tikz .initial:n = \c_empty_tl ,
-    rr .code:n = \@@_fix_pos_arrow:n 3 ,
-    ll .code:n = \@@_fix_pos_arrow:n 1 ,
-    rl .code:n = \@@_fix_pos_arrow:n 2 ,
-    lr .code:n = \@@_fix_pos_arrow:n 0 ,
-    i  .code:n = \@@_fix_pos_arrow:n 5 ,
-%    \end{macrocode}
-%
-% \medskip
-% The option |xoffset| is not allowed when the option |group| or the option 
-% |groups| is used (since it would be meaningless). An error has been raised 
-% during the first pass. Here, we manage to avoid a second error which
-% would be redundant.
-%    \begin{macrocode}
-    xoffset .code:n  = 
-      \int_compare:nNnF \l_@@_pos_arrow_int > 5
-        { \dim_set:Nn \l_@@_xoffset_dim { #1 } } ,
-    start-adjust .dim_set:N = \l_@@_start_adjust_dim,
-    end-adjust .dim_set:N = \l_@@_end_adjust_dim,
-    adjust .code:n  =  
-      \dim_set:Nn \l_@@_start_adjust_dim { #1 }
-      \dim_set:Nn \l_@@_end_adjust_dim { #1 } ,
-  }
-%    \end{macrocode}
-% 
-% \bigskip
-% |\WithArrowsOptions| is the command of the \pkg{witharrows} package to fix
-% options at the document level. It's possible to fix in |\WithArrowsOptions|
-% some options specific to |{WithArrows}| (in contrast with |{DispWithArrows}|)
-% or specific to |{DispWithArrows}| (in contrast with |{WithArrows}|). That's
-% why we have constructed a set of keys specific to |\WithArrowsOptions|.
-%    \begin{macrocode}
-\NewDocumentCommand \WithArrowsOptions { m }
-  { 
-    \str_clear_new:N \l_@@_previous_key_str
-    \keys_set:nn { WithArrows / WithArrowsOptions } { #1 } 
-  }
-%    \end{macrocode}
-%
-% 
-% \bigskip
-% \subsection{The command \textbackslash Arrow}
-%
-% In fact, the internal command is not named |\Arrow| but |\@@_Arrow|. Usually,
-% at the beginning of an environment |{WithArrows}|, |\Arrow| is set to be
-% equivalent to |\@@_Arrow|. However, the user can change the name with the
-% option |command-name| and the user command for |\@@_Arrow| will be different.
-% This mechanism can be useful when the user has already a command named
-% |\Arrow| he still wants to use in the environments |{WithArrows}| or
-% |{DispWithArrows}|. 
-%
-% \medskip
-%    \begin{macrocode}
-\NewDocumentCommand \@@_Arrow { O { } m ! O { } }
-  {
-%    \end{macrocode}
-%
-% The counter |\g_@@_arrow_int| counts the arrows in the environment. The
-% incrementation must be global (|gincr|) because the command |\Arrow| will be
-% used in the cell of a |\halign|. It's recalled that we manage a stack for this
-% counter.
-%    \begin{macrocode}
-    \int_gincr:N \g_@@_arrow_int
-%    \end{macrocode}
-% 
-% \medskip
-% We will construct a global property list to store the informations of the
-% considered arrow. The six fields of this property list are ``initial'',
-% ``final'', ``status'', ``options'', ``label'' and ``input-line''. In order to
-% compute the value of ``final'' (the destination row of the arrow), we have to
-% take into account a potential option |jump|. In order to compute the value of
-% the field ``status'', we have to take into account options as |ll|, |rl|,
-% |rr|, |lr|, etc. or |new-group|.
-% 
-% We will do that job with a first analyze of the options of the command
-% |\Arrow| with a dedicated set of keys called |WithArrows/Arrow/FirstPass|.
-% 
-%    \begin{macrocode}
-    \str_clear_new:N \l_@@_previous_key_str
-    \keys_set:nn { WithArrows / Arrow / FirstPass } { #1 , #3 } 
-%    \end{macrocode}
-%
-% \medskip
-% We construct now a global property list to store the informations of the
-% considered arrow with the six fields ``initial'', ``final'', ``status'',
-% ``options'', ``label'' and ``input-line''.
-%
-% \smallskip
-% \begin{enumerate}
-% \item First, the row from which the arrow starts:
-%    \begin{macrocode}
-    \prop_put:NnV \l_tmpa_prop { initial } \g_@@_line_int
-%    \end{macrocode}
-%
-% \item The row where the arrow ends (that's why it was necessary to analyze the
-% key |jump|):
-%    \begin{macrocode}
-    \int_set:Nn \l_tmpa_int { \g_@@_line_int + \l_@@_jump_int }
-    \prop_put:NnV \l_tmpa_prop { final } \l_tmpa_int
-%    \end{macrocode}
-%
-% \item The ``status'' of the arrow, with 3 possible values: empty,
-% |independent|, or |new-group|.
-%    \begin{macrocode} 
-    \prop_put:NnV \l_tmpa_prop { status } \l_@@_status_arrow_str
-%    \end{macrocode}
-% 
-% \item The options of the arrow (it's a token list):
-%    \begin{macrocode}
-    \prop_put:Nnn \l_tmpa_prop { options } { #1 , #3 }
-%    \end{macrocode}
-%
-% \item The label of the arrow (it's also a token list):
-%    \begin{macrocode}
-    \prop_put:Nnn \l_tmpa_prop { label } { #2 }
-%    \end{macrocode}
-% 
-% \item The number of the line where the command |\Arrow| is issued in the TeX
-% source (as of now, this is only useful for an error message).
-%    \begin{macrocode}
-    \prop_put:Nnx \l_tmpa_prop { input-line } \msg_line_number:
-%    \end{macrocode}
-% \end{enumerate}
-%
-% The property list has been created in a local variable for convenience. Now,
-% it will be stored in a global variable indicating both the
-% position-in-the-tree and the number of the arrow.
-% 
-%    \begin{macrocode}
-    \prop_gclear_new:c 
-      { g_@@_arrow _ \l_@@_prefix_str _ \int_use:N \g_@@_arrow_int _ prop }
-    \prop_gset_eq:cN 
-      { g_@@_arrow _ \l_@@_prefix_str _ \int_use:N \g_@@_arrow_int _ prop } 
-      \l_tmpa_prop
-  }       
-%    \end{macrocode}
-%
-% \medskip
-% The command |\Arrow| (or the corresponding command with a name given by the
-% user with the option |command-name|) will be available only in the last column of
-% the environments |{WithArrows}| and |{DispWithArrows}|. In the other columns,
-% the command will be linked to the following command |\@@_Arrow_first_columns:|
-% which will raise an error.
-%    \begin{macrocode}
-\cs_new_protected:Npn \@@_Arrow_first_columns: 
-  { \@@_error:n { Arrow~not~in~last~column } \@@_Arrow }
-%    \end{macrocode}
-%                                
-%
-% \bigskip
-% \subsection{The environments \{WithArrows\} and \{DispWithArrows\}}
-%
-% \subsubsection{Code before the \textbackslash halign}
-%
-% The command |\@@_pre_halign:n| is a code common to the environments
-% |{WithArrows}| and |{DispWithArrows}|. The argument is the list of options
-% given to the environment.
-%    \begin{macrocode}
-\cs_new_protected:Npn \@@_pre_halign:n #1
-%    \end{macrocode}
-%
-% First, the initialisation of |\l_@@_type_env_str| which is the name of the
-% encompassing environment. In fact, this token list is used only in the error
-% messages.
-%    \begin{macrocode}
-  { 
-    \str_clear_new:N \l_@@_type_env_str
-    \str_set:NV \l_@@_type_env_str \@currenvir
-%    \end{macrocode}
-%
-% \bigskip
-% We deactivate the potential externalization of Tikz. The Tikz elements created
-% by \pkg{witharrows} can't be externalized since they are created in Tikz
-% pictures with |overlay| and |remember picture|.
-%    \begin{macrocode}
-    \cs_if_exist:NT \tikz@library@external@loaded
-      { \tikzset { external / export = false } }
-%    \end{macrocode}
-%
-% \bigskip
-% The token list |\l_@@_name_str| will contain the potential name of the
-% environment (given with the option |name|). This name will be used to create
-% aliases for the names of the nodes.
-%    \begin{macrocode}
-    \str_clear_new:N \l_@@_name_str
-%    \end{macrocode}
-%
-% \bigskip
-% The parameter |\l_@@_status_arrow_str| will be used to store the ``status'' of
-% an individual arrow. It will be used to fill the field ``status'' in the
-% property list describing an arrow.
-%    \begin{macrocode}
-    \str_clear_new:N \l_@@_status_arrow_str
-%    \end{macrocode}
-%
-% \bigskip
-% The dimension |\l_@@_x_dim| will be used to compute the $x$-value for some
-% vertical arrows when one of the options |i|, |group| and |groups| (values 5, 6
-% and 7 of |\l_@@_pos_arrow_int|) is used.
-%    \begin{macrocode}
-    \dim_zero_new:N \l_@@_x_dim
-%    \end{macrocode}
-%
-% \medskip
-% The variable |\l_@@_input_line_str| will be used only to store, for each
-% command |\Arrow| the line (in the TeX file) where the command is issued. This
-% information will be stored in the field ``input-line'' of the arrow. As of
-% now, this information is used only in the error message of a arrow impossible
-% to draw (because it arrives after the last row of the environment).
-%    \begin{macrocode}
-    \str_clear_new:N \l_@@_input_line_str
-%    \end{macrocode}
-%
-% 
-% The initialisation of the counters |\g_@@_arrow_int|, |\g_@@_line_int| and
-% |\g_@@_col_int|. However, we have to save their previous values with the
-% stacks created for this end. 
-%    \begin{macrocode}
-    \seq_gput_right:NV \g_@@_arrow_int_seq \g_@@_arrow_int
-    \int_gzero:N \g_@@_arrow_int 
-    \seq_gput_right:NV \g_@@_line_int_seq \g_@@_line_int
-    \int_gzero:N \g_@@_line_int 
-    \seq_gput_right:NV \g_@@_col_int_seq \g_@@_col_int
-    \int_gzero:N \g_@@_col_int 
-%    \end{macrocode}
-%
-% In the preamble of the |\halign|, there will be \emph{two} counters of the
-% columns. The aim of this programmation is to detect the utilisation of a
-% command |\omit| in a cell of the |\halign| (it should be forbidden).
-% For example, in the part of the preamble concerning the third column (if there
-% is a third column in the environment), we will have the following instructions :
-% \begin{Verbatim}
-%  \int_gincr:N \g_~@~@_col_int
-%  \int_gset:Nn \g_~@~@_static_col_int 3
-% \end{Verbatim}
-%  The counter |\g_@@_col_int| is incremented dynamically and the second is
-%  static. If the user has used a command |\omit|, the dynamic incrementation is
-%  not done in the cell and, at this end of the row, the difference between the
-%  counters may infer the presence of |\omit| at least once.
-%    \begin{macrocode}
-    \int_gzero_new:N \g_@@_static_col_int
-%    \end{macrocode}
-% 
-% \bigskip
-% We also have to update the position on the nesting tree.
-%    \begin{macrocode}
-    \seq_gput_right:Nn \g_@@_position_in_the_tree_seq 1
-%    \end{macrocode}
-%
-% The nesting tree is used to create a prefix which will be used in the names of
-% the Tikz nodes and in the names of the arrows (each arrow is a property list
-% of six fields). If we are in the second environment |{WithArrows}| nested in
-% the third environment |{WithArrows}| of the document, the prefix will be |3-2|
-% (although the position in the tree is $[3,2,1]$ since such a position always
-% ends with a~$1$). First, we do a copy of the position-in-the-tree and then we
-% pop the last element of this copy (in order to drop the last~$1$).
-%    \begin{macrocode}
-    \seq_set_eq:NN \l_tmpa_seq \g_@@_position_in_the_tree_seq
-    \seq_pop_right:NN \l_tmpa_seq \l_tmpa_tl
-    \str_clear_new:N \l_@@_prefix_str
-    \str_set:Nx \l_@@_prefix_str { \seq_use:Nnnn \l_tmpa_seq - - - }
-%    \end{macrocode}
-% 
-% \bigskip
-% We define the command |\\| to be the command |\@@_cr:| (defined below). 
-%    \begin{macrocode}
-    \cs_set_eq:NN \\ \@@_cr:
-    \dim_zero:N \mathsurround 
-%    \end{macrocode}
-%
-% \bigskip
-% These counters will be used later as variables.
-%    \begin{macrocode}
-    \int_zero_new:N \l_@@_initial_int
-    \int_zero_new:N \l_@@_final_int
-    \int_zero_new:N \l_@@_arrow_int
-    \int_zero_new:N \l_@@_pos_of_arrow_int
-    \int_zero_new:N \l_@@_jump_int
-%    \end{macrocode}
-%
-% \medskip
-% The counter |\l_@@_jump_int| corresponds to the option |jump|. Now, we set the
-% default value for this option.
-%    \begin{macrocode}
-    \int_set:Nn \l_@@_jump_int \c_one_int
-%    \end{macrocode}
-%
-% \medskip
-% The string |\l_@@_format_str| corresponds to the option |format|. Now, we set
-% the default value for this option.
-%    \begin{macrocode}
-    \str_set:Nn \l_@@_format_str { rl }
-%    \end{macrocode}
-% 
-%
-%
-% \bigskip
-% In (the last column of) |{DispWithArrows}|, it's possible to put several
-% labels (for the same number of equation). That's why these labels will be
-% stored in a sequence |\l_@@_labels_seq|.
-%    \begin{macrocode}
-    \seq_clear_new:N \l_@@_labels_seq
-%    \end{macrocode}
-%
-%    \begin{macrocode}
-    \bool_set_false:N \l_@@_tag_next_line_bool
-%    \end{macrocode}
-% 
-% \bigskip
-% The value corresponding to the key |interline| is put to zero before the
-% treatment of the options of the environment.\footnote{It's recalled that, by
-% design, the option |interline| of an environment doesn't apply in the nested
-% environments.}
-%    \begin{macrocode}
-    \skip_zero:N \l_@@_interline_skip
-%    \end{macrocode}
-%
-% \bigskip
-% The value corresponding to the key |code-before| is put to nil before the
-% treatment of the options of the environment, because, of course, we don't want
-% the code executed at the beginning of all the nested
-% environments~|{WithArrows}|. Idem for |code-after|. 
-%    \begin{macrocode}
-    \tl_clear_new:N \l_@@_code_before_tl
-    \tl_clear_new:N \l_@@_code_after_tl
-%    \end{macrocode}
-%
-% \bigskip
-% We process the options given to the environment |{WithArrows}| or
-% |{DispWithArrows}|.
-%    \begin{macrocode}
-    \str_clear_new:N \l_@@_previous_key_str 
-    \bool_if:NT \l_@@_in_WithArrows_bool
-      { \keys_set:nn { WithArrows / WithArrows } { #1 } }
-    \bool_if:NT \l_@@_in_DispWithArrows_bool
-      { \keys_set:nn { WithArrows / DispWithArrows } { #1 } }
-%    \end{macrocode}
-%
-% \medskip
-% Now we link the command |\Arrow| (or the corresponding command with a name
-% given by the user with the option |command-name|: that's why the following line
-% must be after the loading of the options) to the command
-% |\@@_Arrow_first_columns:| which will raise an error. 
-%    \begin{macrocode}
-    \cs_set_eq:cN \l_@@_command_name_str \@@_Arrow_first_columns: 
-%    \end{macrocode}
-% It's only in the last column of the environment that it will be linked to the
-% command |\@@_Arrow:|.
-%
-% \medskip
-% The counter |\l_@@_nb_cols_int| is the number of columns in the
-% |\halign| (excepted the column for the labels of equations in
-% |{DispWithArrows}| and excepted eventuals other columns in |{WithArrows}| allowed
-% by the option |more-columns|).
-%    \begin{macrocode}
-    \int_set:Nn \l_@@_nb_cols_int { \str_count:N \l_@@_format_str } 
-%    \end{macrocode}
-%   
-% \medskip
-% Be careful! The following counter |\g_@@_col_int| will be used for two usages:
-% \begin{itemize}
-% \item during, the construction of the preamble of the |\halign|, it will be
-% used as counter for the number of the column under construction in the
-% preamble (since the preamble is constructed backwards, |\g_@@_col_int| will go
-% decreasing from |\l_@@_nb_cols_int| to $1$) ;
-% \item once the preamble constructed, the primitive |\halign| is executed, and,
-% in each row of the |\halign|, the counter |\g_@@_col_int| will be increased
-% from column to column.
-% \end{itemize}
-%
-%    \begin{macrocode}
-    \int_gset_eq:NN \g_@@_col_int \l_@@_nb_cols_int
-%    \end{macrocode}
-% 
-% \medskip
-% We convert the format in a sequence because we use it as a stack (with the top
-% of the stack at the end of the sequence) in the construction of the preamble.
-%    \begin{macrocode}
-    \seq_clear_new:N \l_@@_format_seq
-    \seq_set_split:NnV \l_@@_format_seq { } \l_@@_format_str
-%    \end{macrocode}
-%
-% \bigskip
-% If the option |footnote| or the option |footnotehyper| is used, then we
-% extract the footnotes with an environment |{savenotes}| (of the package
-% \pkg{footnote} or the package \pkg{footnotehyper}).
-%    \begin{macrocode}
-    \bool_if:NT \g_@@_footnote_bool { \begin { savenotes } }
-%    \end{macrocode}
-%
-% \bigskip
-% We execute the code |\l_@@_code_before_tl| of the option |code-before| of the
-% environment after the eventual |\begin{savenotes}| and, symetrically, we will
-% execute the |\l_@@_code_after_tl| before the eventual |\end{savenotes}| (we
-% have a good reason for the last point: we want to extract the footnotes of the
-% arrows executed in the |code-after|).
-%    \begin{macrocode}
-    \l_@@_code_before_tl
-%    \end{macrocode}
-%
-% \bigskip
-% The command |\spread@equation| is the command used by \pkg{amsmath} in the
-% beginning of an alignment to fix the interline. When used, it becomes no-op.
-% However, it's possible to use \pkg{witharrows} without \pkg{amsmath} since we
-% have redefined |\spread@equation| (if it is not defined yet).
-%    \begin{macrocode}
-    \spread@equation
-%    \end{macrocode}
-%
-%
-%    \begin{macrocode}
-    \cs_set_eq:NN \notag \@@_notag:
-    \cs_set_eq:NN \nonumber \@@_nonumber:
-    \cs_set_eq:NN \tag \@@_tag
-    \cs_set_eq:NN \@@_old_label \label
-    \cs_set_eq:NN \label \@@_label:n
-    \cs_set_eq:NN \tagnextline \@@_tagnextline:
-  }
-%    \end{macrocode}
-% This is the end of |\@@_pre_halign:n|.
-%
-% \bigskip
-% \subsubsection{The construction of the preamble of the \textbackslash halign}
-%
-% The control sequence |\@@_construct_halign:| will ``start'' the |\halign| and
-% the preamble. In fact, it constructs all the preamble excepted the end of
-% the last column (more precisely: except the part concerning the construction
-% of the left node and the right node).
-%
-% The same function |\@@_construct_halign:| will be used both for the
-% environment |{WithArrows}| and the environment |{DispWithArrows}|.
-% 
-% Several important points must be noted concerning that construction of the
-% preamble.
-% \begin{itemize}
-% \item The construction of the preamble is done by reading backwards the
-% format |\l_@@_format_str| and adding the corresponding tokens in the input
-% stream of TeX. That means that the part of the preamble concerning the last
-% cell will be constructed first.
-% \item The function |\@@_construct_halign:| is recursive in order to treat
-% succesively all the letters of the preamble.
-% \item Each part of the preamble is created with a |\use:x| function. This
-% expansion of the preamble gives the ability of controlling which parts of the
-% code will be expanded during the construction of the preamble (other parts
-% will be expanded and executed only during the execution of the |\halign|).
-% \item The counter |\g_@@_col_int| is used during the loop of the construction
-% of the preamble but, it will also appears in the preamble (we could have
-% chosen two differents counters but this way saves a counter).
-% \end{itemize}
-% 
-%    \begin{macrocode}
-\cs_new_protected:Npn \@@_construct_halign:
-  {
-    \seq_pop_right:NNTF \l_@@_format_seq \l_@@_type_col_str
-      {
-%    \end{macrocode}
-% Here is the |\use:x| which is fundamental: it will really construct the part
-% of the preamble corresponding to a column by expanding only some parts of the
-% following code.
-%    \begin{macrocode}
-        \use:x
-          {
-%    \end{macrocode}
-% Before the recursive call of |\@@_construct_halign:|, we decrease the integer
-% |\g_@@_col_bool|. But, during the construction of the column which is
-% constructed first (that is to say which is the last column of the |\halign|),
-% it is \emph{not} lowered because |\int_decr:N|, which is protected, won't be
-% expanded by the |\use:x|.
-%
-% We begin the construction of a generic column.
-%    \begin{macrocode}
-            \int_gdecr:N \g_@@_col_int
-            \@@_construct_halign:
-            \int_compare:nNnT \g_@@_col_int = \l_@@_nb_cols_int
-              { 
-%    \end{macrocode}
-% We redefine the command |\Arrow| (or the name given to the corresponding
-% command by the option |command-name|) in each cell of the last column.
-% The braces around |\l_@@_command_name_str| are mandatory because
-% |\l_@@_command_name_str| will be expanded by the |\use:x| and the command
-% |\cs_set_eq:cN| must still be efficient during the execution of the |\halign|.
-%    \begin{macrocode}
-                \cs_set_eq:cN { \l_@@_command_name_str } \@@_Arrow
-                \bool_if:NT \l_@@_in_DispWithArrows_bool
-                  {
-%    \end{macrocode}
-% The command |\@@_test_if_to_tag:| (which is protected and, thus, will not be
-% expanded during the construction of the preamble) will test, at each row,
-% whether the current row must be tagged (and the tag will be put in the very
-% last column).
-%    \begin{macrocode}
-                    \@@_test_if_to_tag:
-%    \end{macrocode}
-% The command |\@@_set_qedhere:| will do a redefinition of |\qedhere| in each
-% cell of the last column.
-%    \begin{macrocode}
-                    \bool_if:NT \c_@@_amsthm_loaded_bool \@@_set_qedhere:
-                  }
-              }
-            \str_if_eq:VnT \l_@@_type_col_str { c } \hfil
-            \str_if_eq:VnT \l_@@_type_col_str { r } \hfill
-            \int_gincr:N \g_@@_col_int
-            \int_gset:Nn \g_@@_static_col_int { \int_use:N \g_@@_col_int }
-            \c_math_toggle_token
-              {
-                { }
-                \bool_if:NT \l_@@_displaystyle_bool \displaystyle
-                ####
-              }
-            \c_math_toggle_token
-            \int_compare:nNnTF \g_@@_col_int = \l_@@_nb_cols_int
-              { \@@_construct_nodes: }
-              {
-%    \end{macrocode}
-% The following glue (|\hfil|) will be added only if we are not in the last cell
-% because, in the last cell, a glue (=skip) is added between the nodes (in
-% |\@@_construct_nodes:|). 
-%    \begin{macrocode}
-                \str_if_eq:VnT \l_@@_type_col_str { l } \hfil
-                \str_if_eq:VnT \l_@@_type_col_str { c } \hfil
-                \bool_if:NT \l_@@_in_DispWithArrows_bool { \tabskip = \c_zero_skip }
-                &
-              }
-          } 
-      }
-%    \end{macrocode}
-% Now the tokens that will be inserted after the analyze of all the tokens of
-% the format: here is the token |\halign|.
-%    \begin{macrocode}
-      { 
-        \bool_if:NTF \l_@@_in_WithArrows_bool
-          {
-            \ialign
-            \bgroup
-          }
-          {
-            \halign to \l_@@_linewidth_dim
-            \bgroup
-            \bool_if:NT \l_@@_fleqn_bool
-              { \skip_horizontal:N \l_@@_mathindent_dim }
-          }
-        \int_gincr:N \g_@@_line_int 
-        \int_gzero:N \g_@@_col_int
-        \tl_if_eq:NNF \l_@@_left_brace_tl \c_novalue_tl
-          {
-            \skip_horizontal:n 
-              { \box_wd:N \l_@@_left_brace_box + \l_@@_delim_wd_dim } 
-          }
-        \strut
-      }
-  }
-%    \end{macrocode}
-% 
-%
-% \bigskip
-% The command |\@@_construct_nodes:| is only for the lisibility of the code
-% because, in fact, it is used only once. It constructs the ``left node'' and
-% the ``right node'' at the end of each row of the arrow.
-%    \begin{macrocode}
-\cs_new_protected:Npn \@@_construct_nodes:
-  { 
-%    \end{macrocode}
-% We create the ``left node'' of the line (when using macros in Tikz node names,
-% the macros have to be fully expandable: here, |\int_use:N| is fully
-% expandable).
-%    \begin{macrocode}
-    \tikz [ remember~picture , overlay ] 
-      \node 
-        [ 
-          node~contents = { } ,
-          @@_node_style ,
-          name = wa - \l_@@_prefix_str - \int_use:N \g_@@_line_int - l ,
-          alias = 
-            { 
-              \str_if_empty:NF \l_@@_name_str
-                { \l_@@_name_str - \int_use:N \g_@@_line_int - l }
-            } 
-        ] 
-        ;
-    \hfil
-%    \end{macrocode}
-%
-% \bigskip
-% Now, after the |\hfil|, we create the ``right node'' and, if the option
-% |show-node-names| is raised, the name of the node is written in the document
-% (useful for debugging).
-%    \begin{macrocode}
-    \tikz [ remember~picture , overlay ] 
-      \node 
-        [ 
-          node~contents = { } ,
-          @@_node_style ,
-          name = wa - \l_@@_prefix_str - \int_use:N \g_@@_line_int - r ,
-          alias = 
-            {
-              \str_if_empty:NF \l_@@_name_str
-                { \l_@@_name_str - \int_use:N \g_@@_line_int - r }
-            } 
-        ] 
-        ;
-    \bool_if:NT \l_@@_show_node_names_bool
-      { 
-        \hbox_overlap_right:n 
-          { \small wa - \l_@@_prefix_str - \int_use:N \g_@@_line_int - r }
-      }
-  }
-%    \end{macrocode}
-%
-%
-%
-% \bigskip
-% \subsubsection{The environment \{WithArrows\}}
-%
-% 
-%    \begin{macrocode}
-\NewDocumentEnvironment { WithArrows } { ! O { } }
-  { 
-    \bool_set_true:N \l_@@_in_WithArrows_bool
-    \bool_set_false:N \l_@@_in_DispWithArrows_bool
-    \@@_pre_halign:n { #1 } 
-    \if_mode_math: \else:
-      \@@_error:n { WithArrows~outside~math~mode }
-    \fi:
-%    \end{macrocode}
-%
-% \bigskip 
-% The environment begins with a |\vtop|, a |\vcenter| or a
-% |\vbox|\footnote{Notice that the use of |\vtop| seems color-safe here...}
-% depending of the value of |\l_@@_pos_env_int| (fixed by the options |t|, |c|
-% or |b|). The environment |{WithArrows}| must be used in math mode\footnote{An
-% error is raised if the environment is used outside math mode.} and therefore,
-% we can use |\vcenter|.
-%    \begin{macrocode}
-    \int_case:nn \l_@@_pos_env_int { 0 \vtop 1 \vcenter 2 \vbox }
-    \bgroup
-%    \end{macrocode}
-%
-% \bigskip
-% We begin the |\halign| and the preamble. During the construction of the
-% preamble, |\l_tmpa_int| will be incremented during each column constructed.
-%    \begin{macrocode}
-    \@@_construct_halign: 
-%    \end{macrocode}
-% 
-% 
-% \medskip
-% In fact, the construction of the preamble is not finished. We add a little more.
-% 
-% \medskip
-% An environmemnt |{WithArrows}| should have a number of columns equal to the
-% length of its format (by default, 2 since the default format is |rl|).
-% Nevertheless, if the user wants to use more columns (without arrows)
-% it's possible with the option |more-columns|.
-%    \begin{macrocode}
-    && 
-    \@@_error:n { Too~much~columns~in~WithArrows }
-    \c_math_toggle_token
-    \bool_if:NT \l_@@_displaystyle_bool \displaystyle 
-    { ## } 
-    \c_math_toggle_token
-    \cr
-  }
-%    \end{macrocode}
-%
-%
-% \bigskip 
-% We begin the second part of the environment |{WithArrows}|. We have two
-% |\egroup|\,: one for the |\halign| and one for the |\vtop| (or |\vcenter| or
-% |\vbox|).
-%    \begin{macrocode}
-  {
-    \\
-    \egroup 
-    \egroup
-    \@@_post_halign:
-%    \end{macrocode}
-%
-% \bigskip
-% If the option |footnote| or the option |footnotehyper| is used, then we
-% extract the footnotes with an environment |{footnote}| (of the package
-% \pkg{footnote} or the package \pkg{footnotehyper}).
-%    \begin{macrocode}
-    \bool_if:NT \g_@@_footnote_bool { \end { savenotes } }
-  }
-%    \end{macrocode}
-% This is the end of the environment |{WithArrows}|.
-% 
-%
-% \bigskip
-% \subsubsection{After the construction of the \textbackslash halign}
-%
-% The command |\@@_post_halign:| is a code common to the second part of the
-% environment |{WithArrows}| and the environment |{DispWithArrows}|.
-%    \begin{macrocode}
-\cs_new_protected:Npn \@@_post_halign:
-%    \end{macrocode}
-%
-% \bigskip
-% The command |\WithArrowsRightX| is not used by \pkg{witharrows}. It's only a
-% convenience given to the user.
-%    \begin{macrocode}
-  { 
-    \cs_set:Npn \WithArrowsRightX { \g_@@_right_x_dim }  
-%    \end{macrocode}
-%
-% \bigskip 
-% It there is really arrows in the environment, we draw the arrows.
-%    \begin{macrocode}
-    \int_compare:nNnT \g_@@_arrow_int > 0 \@@_scan_arrows:
-%    \end{macrocode}
-%
-% \bigskip
-% We will execute the code specified in the option |code-after|, after some
-% settings. 
-%    \begin{macrocode}
-    \group_begin:
-      \tikzset { every~picture / .style = @@_standard }
-%    \end{macrocode}
-% The command |\WithArrowsNbLines| is not used by \pkg{witharrows}. It's only a
-% convenience given to the user.  
-%    \begin{macrocode}
-      \cs_set:Npn \WithArrowsNbLines { \int_use:N \g_@@_line_int }
-%    \end{macrocode}
-% The command |\MultiArrow| is available in |code-after|, and we have a special
-% version of |\Arrow|, called ``|\Arrow| in |code-after|'' in the
-% documentation.\footnote{As for now, |\MultiArrow| has no option, and that's
-% why its internal name is a name of \pkg{expl3} with the signature |:nn|
-% whereas |\Arrow| in |code-after| provides options and has the name of a
-% function defined with |\NewDocumentCommand|.}
-%    \begin{macrocode}
-      \cs_set_eq:NN \MultiArrow \@@_MultiArrow:nn
-      \cs_set_eq:cN \l_@@_command_name_str \@@_Arrow_code_after
-      \bool_set_true:N \l_@@_in_code_after_bool
-      \l_@@_code_after_tl
-    \group_end:
-%    \end{macrocode}
-%
-% \bigskip
-% We update the position-in-the-tree. First, we drop the last component and then
-% we increment the last element.
-%    \begin{macrocode}
-    \seq_gpop_right:NN \g_@@_position_in_the_tree_seq \l_tmpa_tl
-    \seq_gpop_right:NN \g_@@_position_in_the_tree_seq \l_tmpa_tl
-    \seq_gput_right:Nx \g_@@_position_in_the_tree_seq 
-      { \int_eval:n { \l_tmpa_tl + 1 } }
-%    \end{macrocode}
-%
-% \bigskip
-% We update the value of the counter |\g_@@_last_env_int|. This counter is used
-% only by the user function |\WithArrowsLastEnv|.
-%    \begin{macrocode}
-    \int_compare:nNnT { \seq_count:N \g_@@_position_in_the_tree_seq } = 1
-      { \int_gincr:N \g_@@_last_env_int }
-%    \end{macrocode}
-%
-% \bigskip
-% Finally, we restore the previous values of the counters |\g_@@_arrow_int|,
-% |\g_@@_line_int| and |\g_@@_col_int|. It is recalled that we manage three
-% stacks in order to be able to do such a restoration.
-%    \begin{macrocode}
-    \seq_gpop_right:NN \g_@@_arrow_int_seq \l_tmpa_tl 
-    \int_gset:Nn \g_@@_arrow_int \l_tmpa_tl 
-    \seq_gpop_right:NN \g_@@_line_int_seq \l_tmpa_tl
-    \int_gset:Nn \g_@@_line_int \l_tmpa_tl
-    \seq_gpop_right:NN \g_@@_col_int_seq \l_tmpa_tl
-    \int_gset:Nn \g_@@_col_int \l_tmpa_tl
-  }
-%    \end{macrocode}
-% That's the end of the command |\@@_post_halign:|.
-%
-% \bigskip
-% \subsubsection{The command of end of row}
-%
-% We give now the definition of |\@@_cr:| which is the definition of |\\| in an
-% environment |{WithArrows}|. The two \pkg{expl3} commands
-% |\group_align_safe_begin:| and |\group_align_safe_end:| are specifically
-% designed for this purpose: test the token that follows in an |\halign|
-% structure.
-%
-% First, we remove an eventual token |*| (just after the |\\|: there should not
-% be space between the two) since the commands |\\| and |\\*| are equivalent in
-% an environment |{WithArrows}| (an environment |{WithArrows}|, like an
-% environment |{aligned}| of \pkg{amsmath}, is always unbreakable). 
-%    \begin{macrocode}
-\cs_new_protected:Npn \@@_cr:
-  { 
-    \scan_stop:
-%    \end{macrocode}
-% We try to detect some |\omit| (as of now, an |\omit| in the last column is
-% not detected).
-%    \begin{macrocode}
-    \int_compare:nNnF \g_@@_col_int = \g_@@_static_col_int
-      { \@@_error:n { omit~probably~used } }
-    \prg_replicate:nn { \l_@@_nb_cols_int - \g_@@_static_col_int } { & { } } 
-    \group_align_safe_begin:
-    \peek_meaning_remove:NTF * \@@_cr_i: \@@_cr_i:
-  }
-%    \end{macrocode}
-%
-% \medskip
-% Then, we peek the next token to see if it's a |[|. In this case, the command
-% |\\| has an optional argument which is the vertical skip (=glue) to put.
-%    \begin{macrocode}
-\cs_new_protected:Npn \@@_cr_i:
-  { \peek_meaning:NTF [ \@@_cr_ii: { \@@_cr_ii: [ \c_zero_dim ] } }
-%    \end{macrocode}
-% 
-% \bigskip
-% Now, we test if the next token is the token |\end|. Indeed, we want to test if
-% the following tokens are |\end{WithArrows}| (or |\end{DispWithArrows}|, etc).
-% In this case, we raise an error because the user must not put "\\" at the end
-% of its alignment.
-%    \begin{macrocode}
-\cs_new_protected:Npn \@@_cr_ii: [ #1 ]
-  { 
-    \peek_meaning_ignore_spaces:NTF \end 
-      { 
-        \@@_cr_iii:n { #1 } 
-%    \end{macrocode}
-% The analyse of the argument of the token |\end| must be after the
-% |\group_align_safe_end:| which is the beginning of |\@@_cr_iii:n|.
-%    \begin{macrocode}
-        \@@_analyze_end:Nn 
-      }
-      { \@@_cr_iii:n { #1 } }
-  }
-%    \end{macrocode}
-%
-%    \begin{macrocode}
-\cs_new_protected:Npn \@@_cr_iii:n #1 
-  {
-    \group_align_safe_end:
-%    \end{macrocode}
-% For the environment |{DispWithArrows}|, the behaviour of |\\| is different
-% because we add the last column which is the column for the tag (number of the
-% equation). Even if there is no tag, this column is used for the
-% |v|-nodes.\footnote{The |v|-nodes are used to compute the abscissa of the
-% right margin, used by the option |wrap-lines|.}
-%    \begin{macrocode}
-    \bool_if:NT \l_@@_in_DispWithArrows_bool
-%    \end{macrocode}
-% At this stage, we know that we have a tag to put if (and only if) the value of
-% |\l_@@_tags_clist| is the comma list |all| (only one element). Maybe,
-% previously, the value of |\l_@@_tags_clist| was, for example, |1,last| (which
-% means that only the first line and the last line must be tagged). However, in
-% this case, the comparison with the number of line has be done before and, now,
-% if we are in a line to tag, the value of |\l_@@_tags_clist| is |all|.
-%    \begin{macrocode}
-      { 
-        \clist_if_in:NnTF \l_@@_tags_clist { all }
-          {
-%    \end{macrocode}
-% Here, we can't use |\refstepcounter{equation}| because if the user has issued
-% a |\tag| command, we have to use |\l_@@_tag_tl| and not |\theequation|. That's
-% why we have to do the job done by |\refstepcounter| manually.
-% 
-% First, the incrementation of the counter (potentially).
-%    \begin{macrocode}
-            \tl_if_empty:NT \l_@@_tag_tl { \int_gincr:N \c@equation }
-%    \end{macrocode}
-% 
-% We store in |\g_tmpa_tl| the tag we will have to compose at the end of the
-% line. We use a global variable because we will use it in the \emph{next} cell
-% (after the |&|).
-%    \begin{macrocode}
-            \cs_gset:Npx \g_tmpa_tl
-              { \tl_if_empty:NTF \l_@@_tag_tl \theequation \l_@@_tag_tl }
-%    \end{macrocode}
-% It's possible to put several labels for the same line (it's not possible in
-% the environments of \pkg{amsmath}). That's why the differents labels of a same
-% line are stored in a sequence |\l_@@_labels_seq|.
-%    \begin{macrocode}
-            \seq_if_empty:NF \l_@@_labels_seq
-              {
-%    \end{macrocode}
-% Now, we do the job done by |\refstepcounter| and by the redefinitions of
-% |\refstepcounter| done by some packages (the incrementation of the counter has
-% been done yet).
-%
-% First an action which is in the definition of |\refstepcounter|. The command
-% |\p@equation| is redefined by some extensions like \pkg{fncylab}.
-%    \begin{macrocode}
-                \cs_set:Npx \@currentlabel { \p@equation \g_tmpa_tl }
-%    \end{macrocode}
-% Then, an action done by \pkg{hyperref} in its redefinition of
-% |\refstepcounter|.
-%    \begin{macrocode}
-                \bool_if:NT \c_@@_hyperref_loaded_bool
-                  { 
-                    \str_set:Nn \This@name { equation }
-                    \hyper@refstepcounter { equation }
-                  }
-%    \end{macrocode}
-% Then, an action done by \pkg{cleveref} in its redefinition of
-% |\refstepcounter|. The package \pkg{cleveref} creates in the |aux| file a
-% command |\cref@currentlabel| similar to |\@currentlabel| but with more
-% informations.
-%    \begin{macrocode}        
-                \bool_if:NT \c_@@_cleveref_loaded_bool
-                  {
-                    \cref@constructprefix { equation } \cref@result
-                    \protected@edef \cref@currentlabel
-                      { 
-                        [ 
-                          \cs_if_exist:NTF \cref@equation@alias 
-                            \cref@equation@alias 
-                            { equation } 
-                        ] 
-                        [ \arabic { equation } ] [ \cref@result ]
-                        \p@equation \g_tmpa_tl
-                      }
-                  }
-%    \end{macrocode}
-% Now, we can issue the command |\label| (some packages may have redefined
-% |\label|, for example \pkg{typedref}) for each item in the sequence of the
-% labels (it's possible with \pkg{witharrows} to put several labels to the same
-% line and that's why the labels are in the sequence |\l_@@_labels_seq|).
-%    \begin{macrocode}
-                \seq_map_function:NN \l_@@_labels_seq \@@_old_label
-              }
-%    \end{macrocode}
-% We save the booleans |\l_@@_tag_star_bool| and |\l_@@_qedhere_bool| because
-% they will be used in the \emph{next} cell (after the |&|). We recall that the
-% cells of a |\halign| are TeX groups.
-%    \begin{macrocode}
-            \@@_save:N \l_@@_tag_star_bool
-            \@@_save:N \l_@@_qedhere_bool
-            \bool_if:NT \l_@@_tag_next_line_bool 
-              { 
-                \openup -\jot 
-                \bool_set_false:N \l_@@_tag_next_line_bool 
-                \notag \\ & 
-              }
-            & 
-            \@@_restore:N \l_@@_tag_star_bool
-            \@@_restore:N \l_@@_qedhere_bool
-            \bool_if:NT \l_@@_qedhere_bool 
-               { \hbox_overlap_left:n \@@_qedhere_i: }
-            \cs_set_eq:NN \theequation \g_tmpa_tl
-            \bool_if:NT \l_@@_tag_star_bool 
-              { \cs_set_eq:NN \tagform@ \prg_do_nothing: }
-%    \end{macrocode}
-% We use |\@eqnnum| (we recall that there are two definitions of |\@eqnnum|, a
-% standard definition and another, loaded if the class option |leqno| is used).
-% However, of course, the position of the |v|-node is not the same whether the
-% option |leqno| is used or not. That's here that we use the flag
-% |\c_@@_leqno_bool|.
-%    \begin{macrocode}
-            \hbox_overlap_left:n 
-              { 
-                \bool_if:NF \c_@@_leqno_bool
-                  { 
-                    \tikz [ @@_standard ] 
-                      \coordinate ( \int_use:N \g_@@_line_int - v ) ; 
-                  }
-                \quad
-                \@eqnnum 
-              }
-            \bool_if:NT \c_@@_leqno_bool
-              { 
-                \tikz [ @@_standard ] 
-                  \coordinate ( \int_use:N \g_@@_line_int - v ) ; 
-              } 
-          }
-          { 
-            \@@_save:N \l_@@_qedhere_bool 
-            & 
-            \@@_restore:N \l_@@_qedhere_bool
-            \bool_if:NT \l_@@_qedhere_bool 
-               { \hbox_overlap_left:n \@@_qedhere_i: }
-            \tikz [ @@_standard ] 
-               \coordinate ( \int_use:N \g_@@_line_int - v ) ; 
-          }
-      }
-    \dim_compare:nNnT { #1 } < \c_zero_dim
-       { \@@_error:n { option~of~cr~negative } }
-    \dim_set:Nn \l_tmpa_dim { \dim_max:nn { #1 } \c_zero_dim }
-    \cr 
-    \noalign 
-      { 
-        \skip_vertical:n { \l_tmpa_dim + \l_@@_interline_skip }
-        \scan_stop: 
-      }  
-  }
-%    \end{macrocode}
-% According to the documentation of \pkg{expl3}, the previous addition in 
-% ``|#1 + \l_@@_interline_skip|'' is really an addition of skips (=glues).
-%
-%
-% The following command will be used when, after a |\\| (and its optional
-% arguments) there is a |\end|. You want to known if this is the end of the
-% environment |{WithArrows}| (or |{DispWithArrows}|, etc.) because, in this
-% case, we will explain that the environment must not be ended by |\\|. If it is
-% not the case, that means it's a classical situation of LaTeX environments not
-% correctly imbricated and there will be a LaTeX error.
-%    \begin{macrocode}
-\cs_new_protected:Npn \@@_analyze_end:Nn #1 #2
-  {
-    \exp_args:NV \str_if_eq:nnT \l_@@_type_env_str { #2 }
-      { \@@_warning:n { newline~at~the~end~of~env } }
-%    \end{macrocode}
-% We reput in the stream the |\end{...}| we have extracted.
-%    \begin{macrocode}
-    \end { #2 }
-  }
-%    \end{macrocode}
-%
-% \bigskip
-% \subsubsection{The environment \{DispWithArrows\}}
-%
-% For the environment |{DispWithArrows}|, the general form of the construction
-% is of the type:
-%
-% |\[\vtop{\halign to \displaywidth {...}}\]|
-% 
-% The purpose of the |\vtop| is to have an environment unbreakable.
-%
-% However, if we are juste after an item of a LaTeX list or at the beginning of
-% a |{minipage}|, the construction is slightly different:
-%
-% |\[\vtop{\halign to \linewidth {...}}\]|
-% 
-% 
-% \bigskip
-% The boolean |\l_@@_in_label_or_minipage_bool| will be raised if we are just after a |\item|
-% of a list of LaTeX or at the beginning of a |{minipage}|.
-%    \begin{macrocode}
-\bool_new:N \l_@@_in_label_or_minipage_bool
-%    \end{macrocode}
-%
-% 
-%    \begin{macrocode}
-\NewDocumentEnvironment { DispWithArrows } { ! d < > ! O { } }
-  { 
-    \bool_set_true:N \l_@@_in_DispWithArrows_bool
-%    \end{macrocode}
-% If \pkg{mathtools} has been loaded with the option |showonlyrefs|, we disable
-% the code of \pkg{mathtools} for the option |showonlyrefs| with the command
-% |\MT_showonlyrefs_false:| (it will be reactivated at the end of the
-% environment). 
-%    \begin{macrocode}
-    \bool_if:nT \c_@@_mathtools_loaded_bool 
-      { 
-        \MH_if_boolean:nT { show_only_refs } 
-          {
-            \MT_showonlyrefs_false:
-%    \end{macrocode}
-% However, we have to re-raise the flag |{show_only_refs}| of \pkg{mhsetup}
-% because it has been switched off by |\MT_showonlyrefs_false:| and we will use
-% it in the code of the new version of |\label|.
-%    \begin{macrocode}
-            \MH_set_boolean_T:n { show_only_refs } 
-          }
-      }
-%    \end{macrocode}
-%
-% An action done by \pkg{typedref} in its redefinition of |\refstepcounter|. The
-% command |\sr@name| is a prefix added to the name of the label by the
-% redefinition of |\label| done by \pkg{typedref}.
-%    \begin{macrocode}
-    \bool_if:NT \c_@@_typedref_loaded_bool { \str_set:Nn \sr@name { equation } }
-%    \end{macrocode}
-%
-% The command |\intertext@| is a command of \pkg{amsmath} which loads the
-% definition of |\intertext|.
-%    \begin{macrocode}
-    \bool_if:NT \c_@@_amsmath_loaded_bool \intertext@
-    \IfValueT { #1 } { \tl_set:Nn \l_@@_left_brace_tl { #1 } }
-    \@@_pre_halign:n { #2 }
-%    \end{macrocode}
-%
-% If |subequations| is used, we encapsulate the environment in an
-% environment |{subequations}| of \pkg{amsmath}.
-%    \begin{macrocode}
-    \bool_if:NT \l_@@_subequations_bool { \begin { subequations } }
-%    \end{macrocode}
-% Since the version 1.16 of \pkg{witharrows}, no space is added between an
-% |\item| of a LaTeX list and an environment |{DispWithArrows}| except with the
-% option |standard-behaviour-with-items| stored in the boolean
-% |\l_@@_sbwi_bool|. We have to know if we are just after an |\item| and this
-% information will be stored in |\l_@@_in_label_or_minipage_bool|.
-%    \begin{macrocode}
-    \bool_if:NF \l_@@_sbwi_bool
-      {  
-        \if@inlabel
-        \bool_set_true:N \l_@@_in_label_or_minipage_bool
-        \fi
-        \if@minipage
-        \bool_set_true:N \l_@@_in_label_or_minipage_bool
-        \fi
-      }
-%    \end{macrocode}
-%
-%
-%    \begin{macrocode}
-    \tl_if_eq:NNF \l_@@_left_brace_tl \c_novalue_tl
-      {
-        \hbox_set:Nn \l_tmpa_box 
-          { 
-            \c_math_toggle_token
-            \left \l_@@_replace_left_brace_by_tl \vcenter to 1 cm { } \right.
-            \c_math_toggle_token
-          }
-        \dim_zero_new:N \l_@@_delim_wd_dim
-        \dim_set:Nn \l_@@_delim_wd_dim { \box_wd:N \l_tmpa_box }
-        \box_clear_new:N \l_@@_left_brace_box
-        \hbox_set:Nn \l_@@_left_brace_box 
-          { 
-            \group_begin:
-              \cs_set_eq:NN \label \@@_old_label
-              \c_math_toggle_token
-              \bool_if:NT \l_@@_displaystyle_bool \displaystyle 
-              \l_@@_left_brace_tl
-              { } 
-              \c_math_toggle_token
-            \group_end:
-          }  
-      }
-%    \end{macrocode}
-% 
-% \bigskip
-% The token list |\l_@@_tag_tl| will contain the argument of the command |\tag|.
-%    \begin{macrocode}
-    \tl_clear_new:N \l_@@_tag_tl
-%    \end{macrocode}
-% 
-% \bigskip
-%    \begin{macrocode}
-    \bool_set_false:N \l_@@_qedhere_bool
-%    \end{macrocode}
-%
-% \bigskip
-% The boolean |\l_@@_tag_star_bool| will be raised if the user uses the command
-% |\tag| with a star.
-%    \begin{macrocode}
-    \bool_set_false:N \l_@@_tag_star_bool
-%    \end{macrocode}
-% 
-%    \begin{macrocode}
-    \if_mode_math:
-      \@@_fatal:n { DispWithArrows~in~math~mode }
-    \fi:
-%    \end{macrocode}
-%
-% \bigskip
-% The construction is not exactly the same whether we are just after an |\item|
-% of a LaTeX list or not. We know if we are after an |\item| thanks to the
-% boolean |\l_@@_in_label_or_minipage_bool|.
-%    \begin{macrocode}
-    \bool_if:NTF \l_@@_in_label_or_minipage_bool
-      { \c_math_toggle_token } 
-      {  
-%    \end{macrocode}
-% We don't use |\[| of LaTeX because some extensions, like \pkg{autonum}, do a
-% redefinition of |\[|. However, we put the following lines which are in the
-% definition of |\[| even though they are in case of misuse.
-%    \begin{macrocode}
-        \if_mode_vertical:
-        \nointerlineskip
-        \hbox_to_wd:nn { .6 \linewidth } { }
-        \fi:
-        \c_math_toggle_token \c_math_toggle_token
-      }
-%    \end{macrocode}
-%
-%    \begin{macrocode}
-    \dim_zero_new:N \l_@@_linewidth_dim
-    \bool_if:NTF \l_@@_in_label_or_minipage_bool 
-       { \dim_set_eq:NN \l_@@_linewidth_dim \linewidth }
-       { \dim_set_eq:NN \l_@@_linewidth_dim \displaywidth }
-%    \end{macrocode}
-%
-% 
-%    \begin{macrocode}
-    \box_clear_new:N \l_@@_halign_box
-    \setbox \l_@@_halign_box \vtop \bgroup
-    \tabskip =
-      \bool_if:NTF \l_@@_fleqn_bool
-        \c_zero_skip 
-        { 0 pt plus 1000 pt minus 1000 pt }
-%    \end{macrocode}
-%
-%
-%    \begin{macrocode}
-    \@@_construct_halign:
-    \tabskip = 0 pt plus 1000 pt minus 1000 pt
-    & 
-%    \end{macrocode}
-%
-% If the user tries to use more columns than the length of the format, we have to
-% raise an error. However, the error won't be in the next column which is the
-% columns for the labels of the equations. The error will be after... and it
-% must be after. That means that we must not have an error in the next column
-% simply because we are not in math mode. That's why this column, even if it is
-% for the labels, is in math mode.
-%    \begin{macrocode}
-    $ ## $
-    \tabskip = \c_zero_skip
-    && 
-    \@@_fatal:n { Too~much~columns~in~DispWithArrows } 
-    \bool_if:nT \c_false_bool { ## }
-    \cr
-  }
-%    \end{macrocode}
-% 
-% \bigskip
-% We begin the second part of the environment |{DispWithArrows}|.
-%    \begin{macrocode}
-  { 
-    \clist_if_in:NnT \l_@@_tags_clist { last }
-      { \clist_set:Nn \l_@@_tags_clist { all } }
-    \\
-%    \end{macrocode}
-% The following |\egroup| is for the |\halign|.
-%    \begin{macrocode}
-    \egroup 
-    \unskip \unpenalty \unskip \unpenalty 
-    \box_set_to_last:N \l_tmpa_box
-    \nointerlineskip 
-    \box_use:N \l_tmpa_box 
-    \dim_gzero_new:N \g_@@_alignment_dim
-    \dim_gset:Nn \g_@@_alignment_dim { \box_wd:N \l_tmpa_box }
-    \box_clear_new:N \l_@@_new_box
-    \hbox_set:Nn \l_@@_new_box { \hbox_unpack_clear:N \l_tmpa_box } 
-    \dim_compare:nNnT 
-      { \box_wd:N \l_@@_new_box } < \g_@@_alignment_dim
-      { \dim_gset:Nn \g_@@_alignment_dim { \box_wd:N \l_@@_new_box } }
-%    \end{macrocode}
-% The |\egroup| is for the box |\l_@@_halign_box|.
-%    \begin{macrocode}
-    \egroup
-%    \end{macrocode}
-%
-%    \begin{macrocode}
-     \tl_if_eq:NNTF \l_@@_left_brace_tl \c_novalue_tl
-       { \box_use_drop:N \l_@@_halign_box }
-       { 
-         \hbox_to_wd:nn \l_@@_linewidth_dim
-           {
-            \bool_if:NTF \l_@@_fleqn_bool
-              { \skip_horizontal:n \l_@@_mathindent_dim }
-              \hfil
-            \hbox_to_wd:nn \g_@@_alignment_dim 
-              { 
-                \box_use_drop:N \l_@@_left_brace_box
-                \dim_set:Nn \l_tmpa_dim 
-                  { 
-                    \box_ht:N \l_@@_halign_box
-                    + \box_dp:N \l_@@_halign_box
-                  }
-                \c_math_toggle_token
-                  \left \l_@@_replace_left_brace_by_tl 
-                    \vcenter to \l_tmpa_dim { \vfil } 
-                  \right. 
-                \c_math_toggle_token
-                \hfil
-              }
-            \hfil
-           } 
-         \skip_horizontal:n { - \l_@@_linewidth_dim } 
-         \vcenter { \box_use_drop:N \l_@@_halign_box }
-       }
-%    \end{macrocode}
-% 
-% We compute the dimension |\g_@@_right_x_dim|. As a first approximation,
-% |\g_@@_right_x_dim| is the $x$-value of the right side of the current
-% composition box. In fact, we must take into account the potential labels of
-% the equations. That's why we compute |\g_@@_right_x_dim| with the |v|-nodes of
-% each row specifically built in this goal. |\g_@@_right_x_dim| is the minimal
-% value of the $x$-value of these nodes.
-%    \begin{macrocode}
-    \dim_gzero_new:N \g_@@_right_x_dim 
-    \dim_gset_eq:NN \g_@@_right_x_dim \c_max_dim
-    \begin { tikzpicture } [ @@_standard ]
-      \int_step_variable:nNn \g_@@_line_int \l_tmpa_int
-        { 
-          \cs_if_free:cTF 
-            { pgf@sh@ns@wa - \l_@@_prefix_str - \l_tmpa_int - v }
-            { \@@_fatal:n { Inexistent~v-node } }
-            { 
-              \tikz@parse@node\pgfutil@firstofone ( \l_tmpa_int - v )
-              \dim_set:Nn \l_tmpa_dim \pgf@x
-              \dim_compare:nNnT \l_tmpa_dim < \g_@@_right_x_dim
-                { \dim_gset:Nn \g_@@_right_x_dim \l_tmpa_dim } 
-            } 
-        }
-    \end { tikzpicture } 
-%    \end{macrocode}
-% 
-%
-% \bigskip
-% The code in |\@@_post_halign:| is common to |{WithArrows}| and
-% |{DispWithArrows}|.
-%    \begin{macrocode}
-    \@@_post_halign:
-%    \end{macrocode}
-% If \pkg{mathtools} has been loaded with the option |showonlyrefs|, we
-% reactivate the code of \pkg{mathtools} for the option |showonlyrefs| with the
-% command |\MT_showonlyrefs_true:| (it has been deactivated in the beginning of
-% the environment).
-%    \begin{macrocode}
-    \bool_if:nT \c_@@_mathtools_loaded_bool
-      { \MH_if_boolean:nT { show_only_refs } \MT_showonlyrefs_true: }
-    \bool_if:NTF \l_@@_in_label_or_minipage_bool
-      { 
-        \c_math_toggle_token
-        \skip_vertical:N \belowdisplayskip
-      }
-      { \c_math_toggle_token \c_math_toggle_token }
-%    \end{macrocode}
-%
-%    \begin{macrocode}
-    \bool_if:NT \l_@@_subequations_bool { \end { subequations } }
-%    \end{macrocode}
-%
-% \bigskip 
-% If the option |footnote| or the option |footnotehyper| is used, then we
-% extract the footnotes with an environment |{savenotes}| (of the package
-% \pkg{footnote} or the package \pkg{footnotehyper}).
-%    \begin{macrocode}
-    \bool_if:NT \g_@@_footnote_bool { \end { savenotes } }
-    \ignorespacesafterend
-  }
-%    \end{macrocode}
-%
-% \bigskip
-% With the environment |{DispWithArrows*}|, the equations are not numbered. We
-% don't put |\begin{DispWithArrows}| and |\end{DispWithArrows}| because there is
-% a |\@currenvir| in some error messages.
-%    \begin{macrocode}
-\NewDocumentEnvironment { DispWithArrows* } { }
-  { 
-    \WithArrowsOptions { notag }
-    \DispWithArrows
-  }
-  \endDispWithArrows
-%    \end{macrocode}
-%
-% 
-% \bigskip
-% \subsection{The commands \textbackslash tag, \textbackslash notag,
-% \textbackslash label, \textbackslash tagnextline and \textbackslash qedhere for
-% \{DispWithArrows\}} 
-%
-% Some commands are allowed only in the last column of the environment
-% |{DispWithArrows}|. We write a command |\@@_if_in_last_col_of_disp:Nn| to
-% execute this command only if we are in the last column. If we are in 
-% another column, an error is raised. The first argument of
-% |\@@_if_in_last_col_of_disp:Nn| is the name of the command used in the error
-% message and the second is the code to execute.
-%    \begin{macrocode}
-\cs_new_protected:Npn \@@_if_in_last_col_of_disp:Nn #1 #2
-  { 
-    \bool_if:NTF \l_@@_in_WithArrows_bool
-      { \@@_error:nn { Not~allowed~in~WithArrows } { #1 } }
-      { 
-        \int_compare:nNnTF \g_@@_col_int < \l_@@_nb_cols_int
-          { \@@_error:nn { Not~allowed~in~DispWithArrows } { #1 } }
-          { #2 }
-      }
-  }
-%    \end{macrocode}
-% 
-% \bigskip
-% The command |\@@_notag:| will be linked to the command |\notag| and also to
-% in the environments |{WithArrows}| and |{DispWithArrows}|. 
-%    \begin{macrocode}
-\cs_new_protected:Npn \@@_notag: 
-  { \@@_if_in_last_col_of_disp:Nn \notag { \clist_clear:N \l_@@_tags_clist } }
-%    \end{macrocode}
-% 
-% \bigskip
-% The command |\@@_nonumber:| will be linked to the command |\nonumber| and also to
-% in the environments |{WithArrows}| and |{DispWithArrows}|. 
-%    \begin{macrocode}
-\cs_new_protected:Npn \@@_nonumber: 
-  { \@@_if_in_last_col_of_disp:Nn \nonumber { \clist_clear:N \l_@@_tags_clist } }
-%    \end{macrocode}
-%
-% \bigskip 
-% The command |\@@_tag| will be linked to |\tag| in |{WithArrows}| and
-% |{DispWithArrows}|. We do the definition with |\NewDocumentCommand| because this
-% command has a starred version.
-%    \begin{macrocode}
-\NewDocumentCommand \@@_tag { s m } 
-  { 
-    \@@_if_in_last_col_of_disp:Nn \tag
-      { 
-        \tl_if_empty:NF \l_@@_tag_tl
-          { \@@_error:nn  { Multiple~tags } { #2 } }
-        \clist_set:Nn \l_@@_tags_clist { all }
-        \bool_if:nT \c_@@_mathtools_loaded_bool
-          {
-            \MH_if_boolean:nT { show_only_refs }
-              {
-                \MH_if_boolean:nF { show_manual_tags }
-                  { \clist_clear:N \l_@@_tags_clist }
-              }
-          }
-        \tl_set:Nn \l_@@_tag_tl { #2 }
-        \bool_set:Nn \l_@@_tag_star_bool { #1 }
-%    \end{macrocode}
-% The starred version |\tag*| can't be used if \pkg{amsmath} has not been loaded
-% because this version does the job by deactivating the command |\tagform@|
-% inserted by \pkg{amsmath} in the (two versions of the) command
-% |\@eqnnum|.\footnote{There are two versions of |@eqnnum|, a standard version
-% and a version for the option |leqno|.}
-%    \begin{macrocode}
-        \bool_if:nT { #1 && ! \bool_if_p:N \c_@@_amsmath_loaded_bool }
-          { \@@_error:n { tag*~without~amsmath } } 
-      }
-  }
-%    \end{macrocode}
-%
-% \bigskip
-% The command |\@@_label:n| will be linked to |\label| in the environments
-% |{WithArrows}| and |{DispWithArrows}|. In these environments, it's possible to
-% put several labels for the same line (it's not possible in the environments of
-% \pkg{amsmath}). That's why we store the differents labels of a same line in a
-% sequence |\l_@@_labels_seq|.
-%    \begin{macrocode}
-\cs_new_protected:Npn \@@_label:n #1
-  {  
-    \@@_if_in_last_col_of_disp:Nn \label
-      { 
-        \seq_if_empty:NF \l_@@_labels_seq 
-          { 
-            \bool_if:NTF \c_@@_cleveref_loaded_bool
-              { \@@_error:n { Multiple~labels~with~cleveref } }
-              { \@@_error:n { Multiple~labels } } 
-          }
-        \seq_put_right:Nn \l_@@_labels_seq { #1 }
-        \bool_if:nT \c_@@_mathtools_loaded_bool
-          {
-            \MH_if_boolean:nT { show_only_refs } 
-              { 
-                \cs_if_exist:cTF { MT_r_#1 }
-                  { \clist_set:Nn \l_@@_tags_clist { all } }
-                  { \clist_clear:N \l_@@_tags_clist } 
-              }
-          }
-        \bool_if:nT \c_@@_autonum_loaded_bool
-          { 
-            \cs_if_exist:cTF { autonum@#1Referenced }
-              { \clist_set:Nn \l_@@_tags_clist { all } }
-              { \clist_clear:N \l_@@_tags_clist } 
-          } 
-      } 
-  }
-%    \end{macrocode}
-%
-% \bigskip
-% The command |\@@_tagnextline:| will be linked to |\tagnextline| in 
-% |{DispWithArrows}|.
-%    \begin{macrocode}
-\cs_new_protected:Npn \@@_tagnextline:
-  { 
-    \@@_if_in_last_col_of_disp:Nn \tagnextline
-      { \bool_set_true:N \l_@@_tag_next_line_bool }
-  }
-%    \end{macrocode}
-%
-%
-% \bigskip
-% The environments |{DispWithArrows}| and |{DispWithArrows*}| are compliant with
-% the command |\qedhere| of \pkg{amsthm}. However, this compatibility requires a
-% special version of |\qedhere|.
-% 
-% This special version is called |\@@_qedhere:| and will be linked with
-% |\qedhere| in the last column of the environment |{DispWithArrows}| (only if
-% the package \pkg{amsthm} has been loaded). |\@@_qedhere:| raises the boolean
-% |\l_@@_qedhere_bool|.
-%    \begin{macrocode}
-\cs_new_protected:Npn \@@_qedhere: { \bool_set_true:N \l_@@_qedhere_bool }
-\cs_new_protected:Npn \@@_set_qedhere: { \cs_set_eq:NN \qedhere \@@_qedhere: }  
-%    \end{macrocode}
-%
-% In the last column of the |\halign| of |{DispWithArrows}| (column of the
-% labels, that is to say the numbers of the equations), a command
-% |\@@_qedhere_i:| will be issued if the flag |\l_@@_qedhere_bool| has been
-% raised. The code of this command is an adaptation of the code of |\qedhere| in
-% \pkg{amsthm}.
-%    \begin{macrocode}
-\cs_new_protected:Npn \@@_qedhere_i: 
-  {
-    \group_begin:
-      \cs_set_eq:NN \qed \qedsymbol
-%    \end{macrocode}
-% The line |\cs_set_eq:NN \qed@elt \setQED@elt| is a preparation for an action
-% on the \textsc{qed} stack. Despite its form, the instruction |\QED@stack|
-% executes an operation on the stack. This operation prints the \textsc{qed}
-% symbol and nullify the top of the stack.
-%    \begin{macrocode}
-      \cs_set_eq:NN \qed@elt \setQED@elt 
-      \QED@stack \relax \relax 
-    \group_end: 
-  }
-%    \end{macrocode}
-% 
-% 
-%
-%
-% \subsection{We draw the arrows}
-%
-% \bigskip
-% The arrows are divided in groups. There is two reasons for this division.
-% \begin{itemize}
-% \item If the option |group| or the option |groups| is used, all the arrows of
-% a group are drawn on a same vertical at an abscissa of |\l_@@_x_dim|.
-% \item For aesthetic reasons, the starting point of all the starting arrows of
-% a group is raised upwards by the value |\l_@@_start_adjust_dim|. Idem for the
-% ending arrows.
-% \end{itemize}
-% 
-% \medskip
-% If the option |group| is used (|\l_@@_pos_arrow_int| = 7), we scan the arrows
-% twice: in the first step we only compute the value of |\l_@@_x_dim| for the
-% whole group, and, in the second step (|\l_@@_pos_arrow_int| is set to 8), we
-% divide the arrows in groups (for the vertical adjustement) and we actually
-% draw the arrows.
-%    \begin{macrocode}
-\cs_new_protected:Npn \@@_scan_arrows:
-  { 
-    \group_begin:
-    \int_compare:nNnT \l_@@_pos_arrow_int = 7
-      { 
-        \@@_scan_arrows_i:
-        \int_set:Nn \l_@@_pos_arrow_int 8 
-      }
-    \@@_scan_arrows_i:
-    \group_end:
-  }
-%    \end{macrocode}
-% 
-% \bigskip
-%    \begin{macrocode}
-\cs_new_protected:Npn \@@_scan_arrows_i:
-  { 
-%    \end{macrocode}
-%
-% \bigskip 
-% |\l_@@_first_arrow_of_group_int| will be the first arrow of the current group.
-%
-% |\l_@@_first_line_of_group_int| will be the first line involved in the group
-% of arrows (equal to the initial line of the first arrow of the group because
-% the option |jump| is always positive).
-%
-% |\l_@@_first_arrows_seq| will be the list the arrows of the group starting at
-% the first line of the group (we may have several arrows starting from the same
-% line). We have to know all these arrows because of the adjustement by
-% |\l_@@_start_adjust_dim|.
-%
-% |\l_@@_last_line_of_group_int| will be the last line involved in the group
-% (impossible to guess in advance).
-%
-% |\l_@@_last_arrows_seq| will be the list of all the arrows of the group
-% ending at the last line of the group (impossible to guess in advance).
-%    \begin{macrocode}
-    \int_zero_new:N \l_@@_first_arrow_of_group_int 
-    \int_zero_new:N \l_@@_first_line_of_group_int
-    \int_zero_new:N \l_@@_last_line_of_group_int
-    \seq_clear_new:N \l_@@_first_arrows_seq
-    \seq_clear_new:N \l_@@_last_arrows_seq
-%    \end{macrocode}
-%
-% \medskip
-% The boolean |\l_@@_new_group_bool| is a switch that we will use the indicate
-% that a group is finished (and the lines of that group have to be drawn). This
-% boolean is not directed connected to the option |new-group| of an individual
-% arrow.
-%    \begin{macrocode}
-    \bool_set_true:N \l_@@_new_group_bool
-%    \end{macrocode}
-%
-% \bigskip
-% We begin a loop over all the arrows of the environment. Inside this loop, if a
-% group is finished, we will draw the arrows of that group.
-%    \begin{macrocode}
-    \int_set:Nn \l_@@_arrow_int \c_one_int
-    \int_until_do:nNnn \l_@@_arrow_int > \g_@@_arrow_int
-      { 
-%    \end{macrocode}
-%
-% \bigskip 
-% We extract from the property list of the current arrow the fields ``initial'',
-% ``final'', ``status'' and ``input-line''. For the two former, we have to do
-% conversions to integers.
-%    \begin{macrocode}
-        \prop_get:cnN 
-          { g_@@_arrow _ \l_@@_prefix_str _ \int_use:N \l_@@_arrow_int _ prop }
-          { initial } \l_tmpa_tl
-        \int_set:Nn \l_@@_initial_int \l_tmpa_tl
-        \prop_get:cnN 
-          { g_@@_arrow _ \l_@@_prefix_str _ \int_use:N \l_@@_arrow_int _ prop }
-          { final } \l_tmpa_tl
-        \int_set:Nn \l_@@_final_int \l_tmpa_tl
-        \prop_get:cnN 
-          { g_@@_arrow _ \l_@@_prefix_str _ \int_use:N \l_@@_arrow_int _ prop }
-          { status } \l_@@_status_arrow_str
-        \prop_get:cnN 
-          { g_@@_arrow _ \l_@@_prefix_str _ \int_use:N \l_@@_arrow_int _ prop }
-          { input-line } \l_@@_input_line_str
-%    \end{macrocode}
-%
-% \bigskip
-% We recall that, after the construction of the |\halign|, |\g_@@_line_int| is
-% the total number of lines of the environment. Therefore, the conditionnal
-% |\l_@@_final_int > \g_@@_line_int| tests whether an arrow arrives after the
-% last line of the environment. In this case, we raise an error (except in the
-% second step of treatment for the option |group|). The arrow will be completely
-% ignored, even for the computation of |\l_@@_x_dim|.
-%    \begin{macrocode}
-        \int_compare:nNnTF \l_@@_final_int > \g_@@_line_int
-          { 
-            \int_compare:nNnF \l_@@_pos_arrow_int = 8
-              { \@@_error:n { Too~few~lines~for~an~arrow } }
-          }
-          \@@_code_for_possible_arrow:
-%    \end{macrocode}
-%
-% \bigskip
-% Incrementation of the index of the loop (and end of the loop).
-%    \begin{macrocode}
-        \int_incr:N \l_@@_arrow_int
-      }
-%    \end{macrocode}
-%
-% \bigskip
-% After the last arrow of the environment, we have to draw the last group of
-% arrows. If we are in option |group| and in the first step of treatment
-% (|\l_@@_pos_arrow_int| = 7), we don't draw because, in the first step, we
-% don't draw anything. If there is no arrow in the group, we don't draw (this
-% situation occurs when all the arrows of the potential group arrive after the
-% last line of the environment).
-%    \begin{macrocode}
-    \bool_if:nT
-      { 
-        \int_compare_p:n { \l_@@_pos_arrow_int != 7 } 
-          &&
-        \int_compare_p:nNn \l_@@_first_arrow_of_group_int > 0 
-      }
-      { \@@_draw_arrows:nn \l_@@_first_arrow_of_group_int \g_@@_arrow_int }
-  }
-%    \end{macrocode}
-%
-% \bigskip
-%    \begin{macrocode}
-\cs_new_protected:Npn \@@_code_for_possible_arrow:
-  { 
-%    \end{macrocode}
-% We test whether the previous arrow was in fact the last arrow of a group. In
-% this case, we have to draw all the arrows of that group, except if we are with
-% the option |group| and in the first step of treatment (|\l_@@_pos_arrow_int| =
-% 7). 
-%    \begin{macrocode}
-    \bool_if:nT 
-      { 
-        \int_compare_p:nNn \l_@@_arrow_int > \c_one_int
-        && 
-       ( \int_compare_p:n { \l_@@_initial_int > \l_@@_last_line_of_group_int }
-           &&
-         \int_compare_p:n { \l_@@_pos_arrow_int != 7 }
-           ||
-         \str_if_eq_p:Vn \l_@@_status_arrow_str { new-group }
-       ) 
-      }
-      { 
-        \int_compare:nNnF \l_@@_first_arrow_of_group_int = \c_zero_int
-          { 
-            \@@_draw_arrows:nn 
-              \l_@@_first_arrow_of_group_int 
-              { \l_@@_arrow_int - 1 } 
-          }
-        \bool_set_true:N \l_@@_new_group_bool
-      }
-%    \end{macrocode}
-%
-% \bigskip 
-% The flag |\l_@@_new_group_bool| indicates if we have to begin a new group of
-% arrows. In fact, we have to begin a new group in three circonstancies: if we
-% are at the first arrow of the environment (that's why the flag is raised
-% before the beginning of the loop), if we have just finished a group (that's
-% why the flag is raised in the previous conditionnal, for topological reasons
-% or if the previous arrows had the status ``new-group''). At the beginning of a
-% group, we have to initialize the following variables: |\l_@@_first_arrow_int|,
-% |\l_@@_first_line_of_group_int|, |\l_@@_last_line_of_group|,
-% |\l_@@_first_arrows_seq|, |\l_@@_last_arrows_seq|.
-%
-%    \begin{macrocode}
-    \bool_if:nTF \l_@@_new_group_bool
-      { 
-        \bool_set_false:N \l_@@_new_group_bool
-        \int_set_eq:NN \l_@@_first_arrow_of_group_int \l_@@_arrow_int
-        \int_set_eq:NN \l_@@_first_line_of_group_int \l_@@_initial_int
-        \int_set_eq:NN \l_@@_last_line_of_group_int \l_@@_final_int
-        \seq_clear:N \l_@@_first_arrows_seq 
-        \seq_put_left:NV \l_@@_first_arrows_seq \l_@@_arrow_int
-        \seq_clear:N \l_@@_last_arrows_seq 
-        \seq_put_left:NV \l_@@_last_arrows_seq \l_@@_arrow_int
-%    \end{macrocode}
-%
-% If we are in option |group| and in the second step of treatment
-% (|\l_@@_pos_arrow_int| = 8), we don't initialize |\l_@@_x_dim| because we want
-% to use the same value of |\l_@@_x_dim| (computed during the first step) for
-% all the groups.
-%    \begin{macrocode}
-        \int_compare:nT { \l_@@_pos_arrow_int != 8 }
-          { \dim_set:Nn \l_@@_x_dim { - \c_max_dim } }
-      }
-%    \end{macrocode}
-%
-% \bigskip
-% If we are not at the beginning of a new group.
-%    \begin{macrocode}
-      { 
-%    \end{macrocode}
-% 
-% If the arrow is independent, we don't take into account this arrow for the
-% detection of the end of the group.
-%    \begin{macrocode}
-        \bool_if:nF 
-          { \str_if_eq_p:Vn \l_@@_status_arrow_str { independent } }
-          { 
-%    \end{macrocode}
-% If the arrow is not independant, the arrow belongs to the current group and we
-% have to take it into account in some variables.
-%    \begin{macrocode}
-            \int_compare:nT 
-              { \l_@@_initial_int = \l_@@_first_line_of_group_int }
-              { \seq_put_left:NV \l_@@_first_arrows_seq \l_@@_arrow_int }
-            \int_compare:nNnTF \l_@@_final_int > \l_@@_last_line_of_group_int
-              { 
-                \int_set_eq:NN \l_@@_last_line_of_group_int \l_@@_final_int
-                \seq_clear:N \l_@@_last_arrows_seq
-                \seq_put_left:NV \l_@@_last_arrows_seq \l_@@_arrow_int
-              }
-              { 
-                \int_compare:nNnT \l_@@_final_int = \l_@@_last_line_of_group_int
-                  { \seq_put_left:NV \l_@@_last_arrows_seq \l_@@_arrow_int }
-              }
-          }
-      }
-%    \end{macrocode}
-%
-% \bigskip 
-% If the arrow is not independent, we update the current $x$-value (in 
-% |\l_@@_x_dim|) with the dedicated command |\@@_update_x:nn|. If we are
-% in option |group| and in the second step of treatment (|\l_@@_pos_arrow_int| =
-% 8), we don't initialize |\l_@@_x_dim| because we want to use the same value of
-% |\l_@@_x_dim| (computed during the first step) for all the groups.
-%    \begin{macrocode}
-    \bool_if:nF { \str_if_eq_p:Vn \l_@@_status_arrow_str { independent } }
-      { 
-        \int_compare:nT { \l_@@_pos_arrow_int != 8 }
-          { \@@_update_x:nn \l_@@_initial_int \l_@@_final_int }
-      } 
-  }
-%    \end{macrocode}
-%
-%
-% \bigskip
-% The following code is necessary because we will have to expand an argument
-% exactly 3 times.
-%    \begin{macrocode}
-\cs_generate_variant:Nn \keys_set:nn { n o }
-\cs_new_protected:Npn \@@_keys_set: 
-  { \keys_set_known:no { WithArrows / Arrow / SecondPass } }
-%    \end{macrocode}
-%
-% \bigskip
-% The macro |\@@_draw_arrows:nn| draws all the arrows whose numbers are between
-% |#1| and |#2|. |#1| and |#2| must be expressions that expands to an integer
-% (they are expanded in the beginning of the macro). This macro is nullified by
-% the option |no-arrows|.
-%    \begin{macrocode}
-\cs_new_protected:Npn \@@_draw_arrows:nn #1 #2
-  {
-    \group_begin:
-    \int_zero_new:N \l_@@_first_arrow_int
-    \int_set:Nn \l_@@_first_arrow_int { #1 }
-    \int_zero_new:N \l_@@_last_arrow_int
-    \int_set:Nn \l_@@_last_arrow_int { #2 }
-%    \end{macrocode}
-%
-% \bigskip
-% We begin a loop over the arrows we have to draw. The variable
-% |\l_@@_arrow_int| (local in the environment |{WithArrows}|) will be used as
-% index for the loop.
-%    \begin{macrocode}
-    \int_set:Nn \l_@@_arrow_int \l_@@_first_arrow_int
-    \int_until_do:nNnn \l_@@_arrow_int > \l_@@_last_arrow_int
-      {
-%    \end{macrocode}
-%
-% \bigskip 
-% We extract from the property list of the current arrow the fields ``initial''
-% and ``final'' and we store these values in |\l_@@_initial_int| and
-% |\l_@@_final_int|. However, we have to do a conversion because the components
-% of a property list are token lists.
-%    \begin{macrocode}
-        \prop_get:cnN 
-          { g_@@_arrow _ \l_@@_prefix_str _ \int_use:N \l_@@_arrow_int _ prop }
-          { initial } \l_tmpa_tl
-        \int_set:Nn \l_@@_initial_int \l_tmpa_tl
-        \prop_get:cnN 
-          { g_@@_arrow _ \l_@@_prefix_str _ \int_use:N \l_@@_arrow_int _ prop }
-          { final } \l_tmpa_tl
-        \int_set:Nn \l_@@_final_int \l_tmpa_tl
-%    \end{macrocode}
-%
-% \bigskip
-% If the arrow ends after the last line of the environment, we don't draw the
-% arrow (an error has already been raised in |\@@_scan_arrows:|). We recall
-% that, after the construction of the |\halign|, |\g_@@_line_int| is the total
-% number of lines of the environment).
-%    \begin{macrocode}
-        \int_compare:nT { \l_@@_final_int <= \g_@@_line_int } \@@_draw_arrows_i:
-        \int_incr:N \l_@@_arrow_int
-      } 
-    \group_end:
-  }
-%    \end{macrocode}
-%
-% \bigskip
-% The macro |\@@_draw_arrows_i:| is only for the lisibility of the code. The
-% first |\group_begin:| is for the options of the arrows (but we remind that the
-% options |ll|, |rr|, |rl|, |lr|, |i| and |jump| have already been extracted and
-% are not present in the field |options| of the property list of the arrow).
-%    \begin{macrocode}
-\cs_new_protected:Npn \@@_draw_arrows_i:
-  { 
-    \group_begin:
-%    \end{macrocode}
-%
-% \bigskip
-% We process the options of the current arrow. The second argument of
-% |\keys_set:nn| must be expanded exactly three times. An x-expansion is not
-% possible because there can be tokens like |\bfseries| in the option |font| of
-% the option |tikz|. This expansion is a bit tricky.
-%    \begin{macrocode}
-    \prop_get:cnN 
-      { g_@@_arrow _\l_@@_prefix_str _ \int_use:N \l_@@_arrow_int _ prop } 
-      { options } \l_tmpa_tl
-    \str_clear_new:N \l_@@_previous_key_str
-    \exp_args:NNo \exp_args:No 
-    \@@_keys_set: { \l_tmpa_tl , tikz = { xshift = \l_@@_xoffset_dim } }
-%    \end{macrocode}
-%
-% We create two booleans to indicate the position of the initial node and final
-% node of the arrow in cases of options |rr|, |rl|, |lr| or |ll|:
-%    \begin{macrocode}
-    \bool_set_false:N \l_@@_initial_r_bool
-    \bool_set_false:N \l_@@_final_r_bool
-    \int_case:nn \l_@@_pos_arrow_int 
-      {
-        0 { \bool_set_true:N \l_@@_final_r_bool }
-        2 { \bool_set_true:N \l_@@_initial_r_bool }
-        3 
-          { 
-            \bool_set_true:N \l_@@_initial_r_bool
-            \bool_set_true:N \l_@@_final_r_bool 
-          }
-      }
-%    \end{macrocode}
-%
-% \bigskip
-% \begin{center}
-% \begin{tabular}{l}
-% \begin{tabular}{@{}l*8c@{}}
-% \toprule
-% option & |lr| & |ll| & |rl| & |rr| & |v| & |i| & |groups| & |group| \\
-% \midrule
-% |\l_@@_pos_arrow_int| & $0$  & $1$  & $2$  & $3$  & $4$ & $5$  & $6$  & $7$ \\
-% \bottomrule
-% \end{tabular} \\
-% \footnotesize The option |v| can be used only in |\Arrow| in |code-after| (see
-% below). 
-% \end{tabular}
-% \end{center}
-% 
-% \bigskip
-% In case of option |i| at a local or global level (|\l_@@_pos_arrow_int| = 5),
-% we have to compute the $x$-value of the arrow (which is vertical). The
-% computed $x$-value is stored in |\l_@@_x_dim| (the same variable used when the
-% option |group| or the option |groups| is used).
-%    \begin{macrocode}
-    \int_compare:nNnT \l_@@_pos_arrow_int = 5
-      { 
-        \dim_set:Nn \l_@@_x_dim { - \c_max_dim }
-        \@@_update_x:nn \l_@@_initial_int \l_@@_final_int 
-      }
-%    \end{macrocode}
-%
-% \bigskip
-% |\l_@@_initial_tl| contains the name of the Tikz node from which the arrow
-% starts (in normal cases... because with the option |i|, |group| and |groups|,
-% the point will perhaps have another
-% $x$-value --- but always the same $y$-value). Idem for |\l_@@_final_tl|.
-%    \begin{macrocode}
-    \tl_set:Nx \l_@@_initial_tl 
-      { 
-        \int_use:N \l_@@_initial_int - \bool_if:NTF \l_@@_initial_r_bool rl 
-        .south 
-      } 
-    \tl_set:Nx \l_@@_final_tl 
-      { \int_use:N \l_@@_final_int - \bool_if:NTF \l_@@_final_r_bool rl .north }
-%    \end{macrocode}
-% We use ``|.south|'' and ``|.north|'' because we want a small gap between two
-% consecutive arrows (and the Tikz nodes created have the shape of small
-% vertical segments: use option |show-nodes| to visualize the nodes).
-%
-% \bigskip
-% The label of the arrow will be stored in |\l_tmpa_tl|.
-%    \begin{macrocode}
-    \prop_get:cnN 
-      { g_@@_arrow _ \l_@@_prefix_str _ \int_use:N \l_@@_arrow_int _ prop } 
-      { label } 
-      \l_tmpa_tl 
-%    \end{macrocode}
-%
-% \bigskip
-% Now, we have to know if the arrow starts at the first line of the group and/or
-% ends at the last line of the group. That's the reason why we have stored in
-% |\l_@@_first_arrows_seq| the list of all the arrows starting at the
-% first line of the group and in |\l_@@_last_arrows_seq| the list of
-% all the arrows ending at the last line of the group. We compute these values
-% in the booleans |\l_tmpa_bool| and |\l_tmpb_bool|. These computations can't be
-% done in the following |{tikzpicture}| because the command |\seq_if_in:NnTF|
-% which is \emph{not} expandable.
-%    \begin{macrocode}
-    \seq_if_in:NxTF \l_@@_first_arrows_seq 
-      { \int_use:N \l_@@_arrow_int }
-      { \bool_set_true:N \l_tmpa_bool }
-      { \bool_set_false:N \l_tmpa_bool }
-    \seq_if_in:NxTF \l_@@_last_arrows_seq 
-      { \int_use:N \l_@@_arrow_int } 
-      { \bool_set_true:N \l_tmpb_bool }
-      { \bool_set_false:N \l_tmpb_bool }
-    \int_compare:nNnT \l_@@_pos_arrow_int = 5
-      { 
-        \bool_set_true:N \l_tmpa_bool
-        \bool_set_true:N \l_tmpb_bool 
-      }
-%    \end{macrocode}
-%
-% \bigskip 
-% We compute and store in |\g_tmpa_tl| and |\g_tmpb_tl| the exact coordinates of
-% the extremities of the arrow.
-% \begin{itemize}
-% \item Concerning the
-% $x$-values, the abscissa computed in |\l_@@_x_dim| will be used if the option
-% of position is |i|, |group| or |groups|.
-% \item Concerning the
-% $y$-values, an adjustement is done for each arrow starting at the first line
-% of the group and each arrow ending at the last line of the group (with the
-% values of |\l_@@_start_adjust_dim| and |\l_@@_end_adjust_dim|).
-% \end{itemize}
-% 
-%    \begin{macrocode}
-    \begin { tikzpicture } [ @@_standard ]
-      \tikz@scan@one@point \pgfutil@firstofone ( \l_@@_initial_tl )
-      \tl_gset:Nx \g_tmpa_tl 
-        {
-          \int_compare:nNnTF \l_@@_pos_arrow_int < 5
-            { \dim_use:N \pgf@x }
-            { \dim_use:N \l_@@_x_dim } , 
-          \bool_if:NTF \l_tmpa_bool
-            { \dim_eval:n { \pgf@y + \l_@@_start_adjust_dim } }
-            { \dim_use:N \pgf@y } 
-        }
-      \tikz@scan@one@point \pgfutil@firstofone ( \l_@@_final_tl )
-      \tl_gset:Nx \g_tmpb_tl 
-        {
-          \int_compare:nNnTF \l_@@_pos_arrow_int < 5 
-            { \dim_use:N \pgf@x }
-            { \dim_use:N \l_@@_x_dim } , 
-          \bool_if:NTF \l_tmpb_bool
-            { \dim_eval:n { \pgf@y - \l_@@_end_adjust_dim } }
-            { \dim_use:N \pgf@y } 
-        } 
-    \end { tikzpicture } 
-%    \end{macrocode}
-%
-% \bigskip
-% Eventually, we can draw the arrow with the code in |\l_@@_tikz_code_tl|. We
-% recall that the value by default for this token list is :\enskip
-% ``\verb|\draw (#1) to node {#3} (#2) ;|''. This value can be modified with the
-% option |tikz-code|. We use the variant |\@@_draw_arrow:nno| of the macro
-% |\@@_draw_arrow:nnn| because of the characters \emph{underscore} in the name
-% |\l_tmpa_tl|: if the user uses the Tikz library |babel|, the third argument of
-% the command |\@@_draw_arrow:nno| will be rescanned because this third argument
-% will be in the argument of a command |node| of an instruction |\draw| of
-% Tikz... and we will have an error because of the characters
-% \emph{underscore}.\footnote{There were other solutions: use another name
-% without \emph{underscore} (like \Verb|\ltmpatl|) or use the package
-% \pkg{underscore} (with this package, the characters \emph{underscore} will be
-% rescanned without errors, even in text mode).}
-%    \begin{macrocode}
-    \@@_draw_arrow:nno \g_tmpa_tl \g_tmpb_tl \l_tmpa_tl
-%    \end{macrocode}
-%
-% \smallskip
-% We close the TeX group opened for the options given to |\Arrow[...]| (local
-% level of the options).
-%    \begin{macrocode}
-    \group_end: 
-  }
-%    \end{macrocode}
-%
-%
-% \bigskip
-% The function |@@_tmpa:nnn| will draw the arrow. It's merely an environment
-% |{tikzpicture}|. However, the Tikz instruction in this environment must be
-% inserted from |\l_@@_tikz_code_tl| with the markers |#1|, |#2| and |#3|.
-% That's why we create a function |\@@_def_function_tmpa:n| which will create
-% the function |\@@_tmpa:nnn|.
-%    \begin{macrocode}
-\cs_new_protected:Npn \@@_def_function_tmpa:n #1
-  { 
-    \cs_set:Npn \@@_tmpa:nnn ##1 ##2 ##3
-      { 
-        \begin{tikzpicture} 
-          [ 
-            @@_standard , 
-            every~path / .style = WithArrows / arrow 
-          ] 
-          #1 
-        \end{tikzpicture}
-      }
-  }
-%    \end{macrocode}
-%
-% \medskip
-% When we draw the arrow (with |\@@_draw_arrow:nnn|), we first create the
-% function |\@@_tmpa:nnn| and, then, we use the function |\@@_tmpa:nnn| :
-%    \begin{macrocode}
-\cs_new_protected:Npn \@@_draw_arrow:nnn #1 #2 #3
-  {
-%    \end{macrocode}
-%
-% \medskip
-% If the option |wrap-lines| is used, we have to use a special version of
-% |\l_@@_tikz_code_tl| (which corresponds to the option |tikz-code|).
-%    \begin{macrocode}
-    \bool_if:nT { \l_@@_wrap_lines_bool && \l_@@_in_DispWithArrows_bool }
-       { \tl_set_eq:NN \l_@@_tikz_code_tl \c_@@_tikz_code_wrap_lines_tl }
-%    \end{macrocode}
-% 
-% \medskip
-% Now, the main lines of this function |\@@_draw_arrow:nnn|.
-%    \begin{macrocode}
-    \exp_args:NV \@@_def_function_tmpa:n \l_@@_tikz_code_tl
-    \@@_tmpa:nnn { #1 } { #2 } { #3 } 
-  }
-\cs_generate_variant:Nn \@@_draw_arrow:nnn { n n o }
-%    \end{macrocode}
-% 
-% \bigskip
-% If the option |wrap-lines| is used, we have to use a special version of
-% |\l_@@_tikz_code_tl| (which corresponds to the option |tikz-code|).
-%    \begin{macrocode}
-\tl_const:Nn \c_@@_tikz_code_wrap_lines_tl
-  { 
-%    \end{macrocode}
-% First, we draw the arrow without the label.
-%    \begin{macrocode}
-    \draw ( #1 ) to node ( @@_label ) { } ( #2 ) ;
-%    \end{macrocode}
-% We retrieve in |\pgf@x| the abscissa of the left-side of the label we will
-% put.
-%    \begin{macrocode}
-    \tikz@parse@node \pgfutil@firstofone ( @@_label.west )
-%    \end{macrocode}
-% We compute in |\l_tmpa_dim| the maximal width possible for the label. 
-% Here is the use of |\g_@@_right_x_dim| which has been computed previously with
-% the |v|-nodes. 
-%    \begin{macrocode}
-    \dim_set:Nn \l_tmpa_dim 
-      { \g_@@_right_x_dim - \pgf@x - \pgfkeysvalueof { / pgf / inner~xsep } } 
-%    \end{macrocode}
-% We retrieve in |\g_tmpa_tl| the current value of the Tikz parameter 
-% ``|text width|''.\footnote{In fact, it's not the current value of 
-% ``|text width|'': it's the value of ``|text width|'' set in the option |tikz|
-% provided by \pkg{witharrows}. These options are given to Tikz in a 
-% ``|every path|''. That's why we have to retrieve it in a path.}
-%    \begin{macrocode}
-    \path \pgfextra { \tl_gset:Nx \g_tmpa_tl \tikz@text@width } ;
-%    \end{macrocode}
-% Maybe the current value of the parameter ``|text width|'' is shorter than
-% |\l_tmpa_dim|. In this case, we must use ``|text width|'' (we update
-% |\l_tmpa_dim|).
-%    \begin{macrocode}
-    \tl_if_empty:NF \g_tmpa_tl
-      {
-        \dim_set:Nn \l_tmpb_dim \g_tmpa_tl
-        \dim_compare:nNnT \l_tmpb_dim < \l_tmpa_dim
-          { \dim_set_eq:NN \l_tmpa_dim \l_tmpb_dim }
-      }
-%    \end{macrocode}
-% Now, we can put the label with the right value for ``|text width|''.
-%    \begin{macrocode}
-    \dim_compare:nNnT \l_tmpa_dim > \c_zero_dim
-      { 
-        \path ( @@_label.west ) 
-           node [ anchor = west , text~width = \dim_use:N \l_tmpa_dim ] 
-                { #3 } ; 
-      } 
-  }
-%    \end{macrocode}
-% 
-% \bigskip
-% The command |\@@_update_x:nn| will analyze the lines between |#1| and
-% |#2| in order to modify |\l_@@_x_dim| in consequence. More precisely,
-% |\l_@@_x_dim| is increased if a line longer than the current value of
-% |\l_@@_x_dim| is found. |\@@_update_x:nn| is used in |\@@_scan_arrows:|
-% (for options |group| and |groups|) and in |\@@_draw_arrows:nn| (for option
-% |i|).
-%    \begin{macrocode}
-\cs_new_protected:Npn \@@_update_x:nn #1 #2
-  { 
-    \int_step_inline:nnn { #1 } { #2 } 
-      { 
-        \begin { tikzpicture } [ @@_standard ]
-          \tikz@scan@one@point \pgfutil@firstofone ( ##1 - l )
-          \dim_gset:Nn \g_tmpa_dim { \dim_max:nn \l_@@_x_dim \pgf@x }
-        \end { tikzpicture }
-        \dim_set_eq:NN \l_@@_x_dim \g_tmpa_dim 
-      } 
-  } 
-%    \end{macrocode}
-%
-%
-% \bigskip
-% The command |\WithArrowsLastEnv| is not used by the package \pkg{witharrows}.
-% It's only a facility given to the final user. It gives the number of the last
-% environment |{WithArrows}| at
-% level~$0$ (to the sense of the nested environments). This macro is fully
-% expandable and, thus, can be used directly in the name of a Tikz node.
-%    \begin{macrocode}
-\cs_new:Npn \WithArrowsLastEnv { \int_use:N \g_@@_last_env_int }
-%    \end{macrocode}
-%
-% \bigskip
-% \subsection{The command \textbackslash Arrow in code-after}
-%
-% The option |code-after| is an option of the environment |{WithArrows}| (this
-% option is only available at the environment level). In the option |code-after|,
-% one can use the command |Arrow| but it's a special version of the command
-% |Arrow|. For this special version (internally called |\@@_Arrow_code_after|),
-% we define a special set of keys called |WithArrows/Arrow/code-after|.
-%
-%    \begin{macrocode}
-\keys_define:nn { WithArrows / Arrow / code-after }
-  {
-    tikz     .code:n = 
-      \tikzset { WithArrows / arrow / .append~style = { #1 } } ,
-    tikz     .value_required:n  = true ,
-    rr       .value_forbidden:n = true ,
-    rr       .code:n            = \@@_fix_pos_option:n 0 ,
-    ll       .value_forbidden:n = true,
-    ll       .code:n            = \@@_fix_pos_option:n 1 ,
-    rl       .value_forbidden:n = true ,
-    rl       .code:n            = \@@_fix_pos_option:n 2 ,
-    lr       .value_forbidden:n = true ,
-    lr       .code:n            = \@@_fix_pos_option:n 3 ,
-    v        .value_forbidden:n = true ,
-    v        .code:n            = \@@_fix_pos_option:n 4 ,
-    tikz-code .tl_set:N          = \l_@@_tikz_code_tl ,
-    tikz-code .value_required:n  = true ,
-    xoffset  .dim_set:N         = \l_@@_xoffset_dim ,
-    xoffset  .value_required:n  = true ,
-    unknown .code:n  = 
-      \@@_sort_seq:N \l_@@_options_Arrow_code_after_seq
-      \@@_error:n { Unknown~option~Arrow~in~code-after } 
-  }
-%    \end{macrocode}
-%
-% \bigskip
-% A sequence of the options available in |\Arrow| in |code-after|. This sequence
-% will be used in the error messages and can be modified dynamically.
-%    \begin{macrocode}
-\seq_new:N \l_@@_options_Arrow_code_after_seq
-\@@_set_seq_of_str_from_clist:Nn \l_@@_options_Arrow_code_after_seq
-  { ll, lr, rl, rr, tikz, tikz-code, v, x, offset }
-%    \end{macrocode}
-% 
-% \bigskip
-%    \begin{macrocode}
-\NewDocumentCommand \@@_Arrow_code_after { O { } m m m ! O { } }
-  {
-    \int_set:Nn \l_@@_pos_arrow_int 1
-    \str_clear_new:N \l_@@_previous_key_str
-    \group_begin:
-      \keys_set:nn { WithArrows / Arrow / code-after } 
-        { #1, #5, tikz = { xshift = \l_@@_xoffset_dim } }
-      \bool_set_false:N \l_@@_initial_r_bool
-      \bool_set_false:N \l_@@_final_r_bool
-      \int_case:nn \l_@@_pos_arrow_int
-        { 
-          0
-            { 
-              \bool_set_true:N \l_@@_initial_r_bool
-              \bool_set_true:N \l_@@_final_r_bool
-            }
-          2 { \bool_set_true:N \l_@@_initial_r_bool }
-          3 { \bool_set_true:N \l_@@_final_r_bool } 
-        }
-%    \end{macrocode}
-% We prevent drawing a arrow from a line to itself.
-%    \begin{macrocode}
-      \tl_if_eq:nnTF { #2 } { #3 }
-        { \@@_error:nn { Both~lines~are~equal } { #2 } }
-%    \end{macrocode}
-% We test whether the two Tikz nodes |(#2-l)| and |(#3-l)| really exist. If not, 
-% the arrow won't be drawn.
-%    \begin{macrocode}
-        {
-          \cs_if_free:cTF { pgf@sh@ns@wa - \l_@@_prefix_str - #2 - l }
-            { \@@_error:nx { Wrong~line~in~Arrow } { #2 } }
-            { 
-              \cs_if_free:cTF { pgf@sh@ns@wa - \l_@@_prefix_str - #3 - l }
-                { \@@_error:nx { Wrong~line~in~Arrow } { #3 }  }
-                { 
-                  \int_compare:nNnTF \l_@@_pos_arrow_int = 4
-                    {
-                      \begin { tikzpicture } [ @@_standard ]
-                        \tikz@scan@one@point \pgfutil@firstofone (#2-l.south)
-                        \dim_set_eq:NN \l_tmpa_dim \pgf@x
-                        \dim_set_eq:NN \l_tmpb_dim \pgf@y
-                        \tikz@scan@one@point \pgfutil@firstofone (#3-l.north)
-                        \dim_set:Nn \l_tmpa_dim 
-                          { \dim_max:nn \l_tmpa_dim \pgf@x }
-                        \tl_gset:Nx \g_tmpa_tl 
-                          { \dim_use:N \l_tmpa_dim , \dim_use:N \l_tmpb_dim } 
-                        \tl_gset:Nx \g_tmpb_tl 
-                          { \dim_use:N \l_tmpa_dim , \dim_use:N \pgf@y } 
-                      \end { tikzpicture } 
-                    }
-                    { 
-                      \begin { tikzpicture } [ @@_standard ]
-                        \tikz@scan@one@point \pgfutil@firstofone
-                           ( #2-\bool_if:NTF\l_@@_initial_r_bool rl .south )
-                        \tl_gset:Nx \g_tmpa_tl 
-                           { \dim_use:N \pgf@x , \dim_use:N \pgf@y }
-                        \tikz@scan@one@point \pgfutil@firstofone
-                           ( #3-\bool_if:NTF\l_@@_final_r_bool rl .north )
-                        \tl_gset:Nx \g_tmpb_tl 
-                           { \dim_use:N \pgf@x , \dim_use:N \pgf@y }
-                      \end { tikzpicture } 
-                    }
-                  \@@_draw_arrow:nnn \g_tmpa_tl \g_tmpb_tl { #4 } 
-                } 
-            }
-        }
-    \group_end:
-  }
-%    \end{macrocode}
-%
-%                               
-% \bigskip
-% \subsection{The command \textbackslash MultiArrow in code-after}
-% The command |\@@_MultiArrow:nn| will be linked to |\MultiArrow| when the
-% |code-after| is executed.
-%    
-%    \begin{macrocode}
-\cs_new_protected:Npn \@@_MultiArrow:nn #1 #2
-  {  
-%    \end{macrocode}
-% The user of the command |\MultiArrow| (in |code-after|) will be able to specify
-% the list of lines with the same syntax as the loop |\foreach| of \pkg{pgffor}.
-% That's why we construct a ``clist'' of \pkg{expl3} from the specification of
-% list given by the user. The construction of the ``clist'' must be global in
-% order to exit the |\foreach| and that's why we construct the list in
-% |\g_tmpa_clist|.
-%    \begin{macrocode}
-    \foreach \x in { #1 } 
-      { 
-        \cs_if_free:cTF { pgf@sh@ns@wa - \l_@@_prefix_str - \x - l }
-           { \@@_error:nx { Wrong~line~specification~in~MultiArrow } \x }
-           { \clist_gput_right:Nx \g_tmpa_clist \x } 
-      } 
-%    \end{macrocode}
-% We sort the list |\g_tmpa_clist| because we want to extract the minimum and
-% the maximum.
-%    \begin{macrocode}
-    \int_compare:nTF { \clist_count:N \g_tmpa_clist < 2 }
-      { \@@_error:n { Too~small~specification~for~MultiArrow } }
-      {
-        \clist_sort:Nn \g_tmpa_clist 
-          {
-            \int_compare:nTF { ##1 > ##2 }
-              \sort_return_swapped: 
-              \sort_return_same:
-          }
-%    \end{macrocode}
-% We extract the minimum in |\l_tmpa_tl| (it must be an integer but we store it
-% in a token list of \pkg{expl3}).
-%    \begin{macrocode}
-        \clist_pop:NN \g_tmpa_clist \l_tmpa_tl
-%    \end{macrocode}
-%
-% We extract the maximum in |\l_tmpb_tl|. The remaining list (in
-% |\g_tmpa_clist|) will be sorted in decreasing order but never mind...
-%    \begin{macrocode}
-        \clist_reverse:N \g_tmpa_clist
-        \clist_pop:NN \g_tmpa_clist \l_tmpb_tl
-%    \end{macrocode}
-%
-% We draw the teeth of the rak (except the first one and the last one) with the
-% auxiliary function |\@@_MultiArrow_i:n|. This auxiliary fonction is necessary
-% to expand the specification of the list in the |\foreach| loop. The first and
-% the last teeth of the rak can't be drawn the same way as the others (think,
-% for example, to the case of the option ``|rounded corners|'' is used).
-%    \begin{macrocode}
-        \exp_args:NV \@@_MultiArrow_i:n \g_tmpa_clist
-%    \end{macrocode}
-%
-% Now, we draw the rest of the structure.
-%    \begin{macrocode}
-        \begin { tikzpicture }
-          [ 
-            @@_standard , 
-            every~path / .style = { WithArrows / arrow } 
-          ] 
-          \draw [<->] ([xshift = \l_@@_xoffset_dim]\l_tmpa_tl-r.south)
-                      -- ++(5mm,0)
-                      -- node (@@_label) {} 
-                         ([xshift = \l_@@_xoffset_dim+5mm]\l_tmpb_tl-r.south)
-                      -- ([xshift = \l_@@_xoffset_dim]\l_tmpb_tl-r.south)  ;
-          \tikz@parse@node \pgfutil@firstofone (@@_label.west)
-          \dim_set:Nn \l_tmpa_dim { 20 cm }
-          \path \pgfextra { \tl_gset:Nx \g_tmpa_tl \tikz@text@width } ;
-          \tl_if_empty:NF \g_tmpa_tl { \dim_set:Nn \l_tmpa_dim \g_tmpa_tl }
-          \bool_if:nT { \l_@@_wrap_lines_bool && \l_@@_in_DispWithArrows_bool }
-            { 
-              \dim_set:Nn \l_tmpb_dim 
-                { \g_@@_right_x_dim - \pgf@x - 0.3333 em }
-              \dim_compare:nNnT \l_tmpb_dim < \l_tmpa_dim
-                { \dim_set_eq:NN \l_tmpa_dim \l_tmpb_dim } 
-            }
-          \path (@@_label.west) 
-           node [ anchor = west, text~width = \dim_use:N \l_tmpa_dim ] { #2 } ;
-        \end{tikzpicture} 
-      } 
-  }
-%    \end{macrocode}
-%
-%    \begin{macrocode}
-\cs_new_protected:Npn \@@_MultiArrow_i:n #1
-  { 
-    \begin {tikzpicture }
-      [ 
-        @@_standard , 
-        every~path / .style = { WithArrows / arrow } 
-      ] 
-      \foreach \k in { #1 }
-        { 
-          \draw [ <- ] 
-            ( [xshift = \l_@@_xoffset_dim]\k-r.south ) -- ++(5mm,0) ; 
-        } ;
-    \end { tikzpicture } 
-  }
-%    \end{macrocode}
-%
-%
-% \bigskip
-% \subsection{The error messages of the package}
-%
-%    \begin{macrocode}
-\str_const:Nn \c_@@_option_ignored_str
-  { If~you~go~on,~this~option~will~be~ignored. }
-\str_const:Nn \c_@@_command_ignored_str
-  { If~you~go~on,~this~command~will~be~ignored. }
-%    \end{macrocode}
-%
-%    \begin{macrocode}
-\@@_msg_new:nn { amsmath~not~loaded }
-  {
-    You~can't~use~the~option~'\l_keys_key_tl'~because~the~
-    package~'amsmath'~has~not~been~loaded.\\
-    If~you~go~on,~this~option~will~be~ignored~in~the~rest~
-    of~the~document.
-  }
-%    \end{macrocode}
-%
-%    \begin{macrocode}
-\@@_msg_new:nn { Bad~value~for~replace~brace~by }
-  {
-    Bad~value~for~the~option~'\l_keys_key_tl'.~The~value~must~be~
-    an~extensible~left~delimiter.~The~possible~values~are:~
-    \token_to_str:N \{,~(,~[,~\token_to_str:N \lbrace,~
-    \token_to_str:N \lbrack,~\token_to_str:N \lgroup,~
-    \token_to_str:N \langle,~\token_to_str:N \lmoustache,~
-    \token_to_str:N \lfloor\ and~\token_to_str:N \lceil\ 
-    (and~\token_to_str:N \lvert\ and~\token_to_str:N \lVert\
-    if~amsmath~or~unicode-math~is~loaded).\\
-    \c_@@_option_ignored_str 
-  }
-%    \end{macrocode}
-%
-%    \begin{macrocode}
-\@@_msg_new:nn { option~of~cr~negative }
-  {
-    The~argument~of~the~command~\token_to_str:N\\~
-    should~be~positive~in~the~row~\int_use:N \g_@@_line_int\
-    of~your~environment~\{\l_@@_type_env_str\}.\\
-    \c_@@_option_ignored_str
-  }
-%    \end{macrocode}
-% 
-%    \begin{macrocode}
-\@@_msg_new:nn { omit~probably~used } 
-  {
-    There~is~a~problem.~Maybe~you~have~used~a~command~
-    \token_to_str:N\omit\ in~the~line~\int_use:N \g_@@_line_int\
-    (or~another~line)~of~your~environment~\{\l_@@_type_env_str\}.\\ 
-    You~can~go~on~but~you~may~have~others~errors.
-  }
-%    \end{macrocode}
-%
-%    \begin{macrocode}
-\@@_msg_new:nn { newline~at~the~end~of~env }
-  { 
-    Your~environment~\{\l_@@_type_env_str\}~should~not~end~with~
-    a~\token_to_str:N \\.\\
-    This~warning~might~become~an~error~in~a~future~version.
-  }
-%    \end{macrocode}    
-%
-%    \begin{macrocode}
-\@@_msg_new:nn { Invalid~option~format }
-  {
-    The~key~'format'~should~contain~only~letters~r,~c~and~l~and~
-    must~not~be~empty.\\  
-    \c_@@_option_ignored_str
-  }
-%    \end{macrocode}
-%
-%    \begin{macrocode}
-\@@_msg_new:nn { Value~for~a~key }
-  {
-    The~key~'\l_keys_key_tl'~should~be~used~without~value. \\
-    However,~you~can~go~on~for~this~time.
-  }
-%    \end{macrocode}
-%
-%    \begin{macrocode}          
-\@@_msg_new:nnn { Unknown~option~in~Arrow }
-  { 
-    The~key~'\l_keys_key_tl'~is~unknown~for~the~command~
-    \l_@@_string_Arrow_for_msg_str\ in~the~row~
-    \int_use:N \g_@@_line_int\ of~your~environment~
-    \{\l_@@_type_env_str\}. \l_tmpa_str \\
-    \c_@@_option_ignored_str \\
-    For~a~list~of~the~available~keys,~type~H~<return>.
-  }
-  { 
-    The~available~keys~are~(in~alphabetic~order):~
-    \seq_use:Nnnn \l_@@_options_Arrow_seq {~and~} {,~} {~and~}.
-  }
-%    \end{macrocode}
-%
-%
-%    \begin{macrocode}          
-\@@_msg_new:nnn { Unknown~option~WithArrows }
-  {
-    The~key~'\l_keys_key_tl'~is~unknown~in~\{\l_@@_type_env_str\}. \\
-    \c_@@_option_ignored_str \\
-    For~a~list~of~the~available~keys,~type~H~<return>.
-  }
-  {
-    The~available~keys~are~(in~alphabetic~order):~
-    \seq_use:Nnnn \l_@@_options_WithArrows_seq {~and~} {,~} {~and~}.
-  }
-%    \end{macrocode}
-%
-%    \begin{macrocode}          
-\@@_msg_new:nnn { Unknown~option~DispWithArrows }
-  { 
-    The~key~'\l_keys_key_tl'~is~unknown~in~\{\l_@@_type_env_str\}. \\
-    \c_@@_option_ignored_str \\
-    For~a~list~of~the~available~keys,~type~H~<return>.
-  }
-  {
-    The~available~keys~are~(in~alphabetic~order):~
-    \seq_use:Nnnn \l_@@_options_DispWithArrows_seq {~and~} {,~} {~and~}.
-  }
-%    \end{macrocode}
-%
-%    \begin{macrocode}          
-\@@_msg_new:nnn { Unknown~option~WithArrowsOptions }
-  { 
-    The~key~'\l_keys_key_tl'~is~unknown~in~
-    \token_to_str:N \WithArrowsOptions. \\
-    \c_@@_option_ignored_str \\
-    For~a~list~of~the~available~keys,~type~H~<return>. 
-  }
-  {
-    The~available~keys~are~(in~alphabetic~order):~
-    \seq_use:Nnnn \l_@@_options_WithArrowsOptions_seq {~and~} {,~} {~and~}.
-  }
-%    \end{macrocode}
-%
-%    \begin{macrocode}
-\@@_msg_new:nnn { Unknown~option~Arrow~in~code-after }
-  { 
-    The~key~'\l_keys_key_tl'~is~unknown~in~
-    \token_to_str:N \Arrow\ in~code-after. \\
-    \c_@@_option_ignored_str \\
-    For~a~list~of~the~available~keys,~type~H~<return>.
-  }
-  { 
-    The~available~keys~are~(in~alphabetic~order):~
-    \seq_use:Nnnn \l_@@_options_Arrow_code_after_seq {~and~} {,~} {~and~}.
-  }
-%    \end{macrocode}
-%
-%
-%    \begin{macrocode}          
-\@@_msg_new:nn { Too~much~columns~in~WithArrows }
-  { 
-    Your~environment~\{\l_@@_type_env_str\}~has~\int_use:N 
-    \l_@@_nb_cols_int\ columns~and~you~try~to~use~one~more.~
-    Maybe~you~have~forgotten~a~\c_backslash_str\c_backslash_str.~
-    If~you~really~want~to~use~more~columns~(after~the~arrows)~you~should~use~ 
-    the~option~'more-columns'~at~a~global~level~or~for~an~environment. \\
-    However,~you~can~go~one~for~this~time.
-  }
-%    \end{macrocode}
-%
-%    \begin{macrocode}          
-\@@_msg_new:nn { Too~much~columns~in~DispWithArrows }
-  { 
-    Your~environment~\{\l_@@_type_env_str\}~has~\int_use:N 
-    \l_@@_nb_cols_int\ columns~and~you~try~to~use~one~more.~
-    Maybe~you~have~forgotten~a~\c_backslash_str\c_backslash_str\ 
-    at~the~end~of~row~\int_use:N \g_@@_line_int. \\
-    This~error~is~fatal.
-  }
-%    \end{macrocode}
-%
-%    \begin{macrocode}          
-\@@_msg_new:nn { Negative~jump }
-  { 
-    You~can't~use~a~negative~value~for~the~option~'jump'~of~command~
-    \l_@@_string_Arrow_for_msg_str\
-    in~the~row~\int_use:N \g_@@_line_int\
-    of~your~environment~\{\l_@@_type_env_str\}.~
-    You~can~create~an~arrow~going~backwards~with~the~option~'<-'~of~Tikz. \\
-    \c_@@_option_ignored_str
-  }
-%    \end{macrocode}
-%
-%    \begin{macrocode}
-\@@_msg_new:nn { new-group~without~groups }
-  { 
-    You~can't~use~the~option~'new-group'~for~the~command~
-    \l_@@_string_Arrow_for_msg_str\
-    because~you~are~not~in~'groups'~mode.~Try~to~use~the~option~
-    'groups'~in~your~environment~\{\l_@@_type_env_str\}. \\
-    \c_@@_option_ignored_str
-  }
-%    \end{macrocode}
-%
-%
-%    \begin{macrocode}          
-\@@_msg_new:nn          
-  { Too~few~lines~for~an~arrow }
-  { 
-    Line~\l_@@_input_line_str\
-    :~an~arrow~specified~in~the~row~\int_use:N \l_@@_initial_int\
-    of~your~environment~\{\l_@@_type_env_str\}~can't~be~drawn~
-    because~it~arrives~after~the~last~row~of~the~environment. \\
-    If~you~go~on,~this~arrow~will~be~ignored.
-  }
-%    \end{macrocode}
-%
-%    \begin{macrocode}          
-\@@_msg_new:nn { WithArrows~outside~math~mode }
-  { 
-    The~environment~\{\l_@@_type_env_str\}~should~be~used~only~in~math~mode~
-    like~the~environment~\{aligned\}~of~amsmath. \\
-    Nevertheless,~you~can~go~on.
-  }
-%    \end{macrocode}
-%
-%    \begin{macrocode}          
-\@@_msg_new:nn { DispWithArrows~in~math~mode }
-  { 
-    The~environment~\{\l_@@_type_env_str\}~should~be~used~only~outside~math~
-    mode~like~the~environment~\{align\}~of~amsmath. \\ 
-    This~error~is~fatal.
-  }
-%    \end{macrocode}
-%
-%    \begin{macrocode}
-\@@_msg_new:nn { Incompatible~options~in~Arrow }
-  { 
-    You~try~to~use~the~option~'\l_keys_key_tl'~but~
-    this~option~is~incompatible~or~redundant~with~the~option~
-    '\l_@@_previous_key_str'~set~in~the~same~command~
-    \l_@@_string_Arrow_for_msg_str. \\
-    \c_@@_option_ignored_str
-  }
-%    \end{macrocode}
-% 
-%
-%    \begin{macrocode}          
-\@@_msg_new:nn { Incompatible~options }
-  { You~try~to~use~the~option~'\l_keys_key_tl'~but~
-    this~option~is~incompatible~or~redundant~with~the~option~
-    '\l_@@_previous_key_str'~set~in~the~same~command~
-    \bool_if:NT \l_@@_in_code_after_bool
-      { 
-        \l_@@_string_Arrow_for_msg_str\
-        in~the~code-after~of~your~environment~\{\l_@@_type_env_str\}
-      }. \\
-    \c_@@_option_ignored_str
-  }
-%    \end{macrocode}
-%
-%    \begin{macrocode}
-\@@_msg_new:nn { Arrow~not~in~last~column }
-  { 
-    You~should~use~the~command~\l_@@_string_Arrow_for_msg_str\
-    only~in~the~last~column~(column~\int_use:N\l_@@_nb_cols_int)~
-    of~your~environment~\{\l_@@_type_env_str\}.\\
-    However~you~can~go~on~for~this~time.
-  }
-%    \end{macrocode}
-%
-%    \begin{macrocode}
-\@@_msg_new:nn { Wrong~line~in~Arrow }
-  { 
-    The~specification~of~line~'#1'~you~use~in~the~command~
-    \l_@@_string_Arrow_for_msg_str\
-    in~the~'code-after'~of~\{\l_@@_type_env_str\}~doesn't~exist. \\
-    \c_@@_option_ignored_str
-  }
-%    \end{macrocode}
-%
-%    \begin{macrocode}
-\@@_msg_new:nn { Both~lines~are~equal }
-  {
-    In~the~'code-after'~of~\{\l_@@_type_env_str\}~you~try~to~
-    draw~an~arrow~going~to~it~self~from~the~line~'#1'.~This~is~not~possible. \\
-    \c_@@_option_ignored_str
-  }
-%    \end{macrocode}
-% 
-%    \begin{macrocode}
-\@@_msg_new:nn { Wrong~line~specification~in~MultiArrow }
-  { 
-    The~specification~of~line~'#1'~doesn't~exist. \\
-    If~you~go~on,~it~will~be~ignored~for~\token_to_str:N \MultiArrow.
-  }
-%    \end{macrocode}
-%
-%    \begin{macrocode}
-\@@_msg_new:nn { Too~small~specification~for~MultiArrow }
-  { 
-    The~specification~of~lines~you~gave~to~\token_to_str:N \MultiArrow\ 
-    is~too~small:~you~need~at~least~two~lines. \\
-    \c_@@_option_ignored_str
-  }
-%    \end{macrocode}
-%
-%    \begin{macrocode}
-\@@_msg_new:nn { tag*~without~amsmath }
-  { 
-    We~can't~use~\token_to_str:N\tag*~because~you~haven't~loaded~amsmath~
-    (or~mathtools). \\
-    If~you~go~on,~the~command~\token_to_str:N\tag\ 
-    will~be~used~instead.
-  }
-%    \end{macrocode}
-%
-%    \begin{macrocode}
-\@@_msg_new:nn { Not~allowed~in~DispWithArrows }
-  { 
-    The~command~\token_to_str:N #1
-    is~allowed~only~in~the~last~column~
-    (column~\int_use:N\l_@@_nb_cols_int)~of~\{\l_@@_type_env_str\}. \\ 
-    \c_@@_option_ignored_str
-  }
-%    \end{macrocode}
-% 
-%    \begin{macrocode}
-\@@_msg_new:nn { Not~allowed~in~WithArrows }
-  { 
-    The~command~\token_to_str:N #1 is~not~allowed~in~\{\l_@@_type_env_str\}~
-    (it's~allowed~in~the~last~column~of~\{DispWithArrows\}). \\
-    \c_@@_option_ignored_str
-  }
-%    \end{macrocode}
-%
-%    \begin{macrocode}
-\@@_msg_new:nn { Multiple~tags }
-  {
-    You~can't~use~twice~the~command~\token_to_str:N\tag\ 
-    in~a~line~of~the~environment~\{\l_@@_type_env_str\}. \\
-    If~you~go~on,~the~tag~'#1'~will~be~used.
-  }
-%    \end{macrocode}
-%
-%
-%    \begin{macrocode}
-\@@_msg_new:nn { Multiple~labels }
-  { 
-    Normally,~we~can't~use~the~command~\token_to_str:N\label\ 
-    twice~in~a~line~of~the~environment~\{\l_@@_type_env_str\}. \\
-    However,~you~can~go~on.~
-    \bool_if:NT \c_@@_showlabels_loaded_bool
-      { However,~only~the~last~label~will~be~shown~by~showlabels.~ }
-    If~you~don't~want~to~see~this~message~again,~you~can~use~the~option~
-    'allow-multiple-labels'~at~the~global~or~environment~level.
-  }
-%    \end{macrocode}
-%
-%    \begin{macrocode}
-\@@_msg_new:nn { Multiple~labels~with~cleveref }
-  {
-    Since~you~use~cleveref,~you~can't~use~the~command~\token_to_str:N\label\ 
-    twice~in~a~line~of~the~environment~\{\l_@@_type_env_str\}. \\
-    If~you~go~on,~you~may~have~undefined~references.
-  }
-%    \end{macrocode}
-%
-% 
-%    \begin{macrocode}
-\@@_msg_new:nn { Inexistent~v-node }
-  {
-    There~is~a~problem.~Maybe~you~have~put~a~command~\token_to_str:N\cr\
-    instead~of~a~command~\token_to_str:N\\~at~the~end~of~
-    the~row~\l_tmpa_int\
-    of~your~environment~\{\l_@@_type_env_str\}. \\
-    This~error~is~fatal.
-  }
-%    \end{macrocode}
-%
-%    \begin{macrocode}          
-\@@_msg_new:nn { Option~xoffset~forbidden }
-  { 
-    You~can't~use~the~option~'xoffset'~in~the~command~
-    \l_@@_string_Arrow_for_msg_str\
-    while~you~are~using~the~option~
-    ' \int_compare:nNnTF \l_@@_pos_arrow_int = 7
-        { group } 
-        { groups } '. \\
-    \c_@@_option_ignored_str
-  }
-%    \end{macrocode}
-%
-%    \begin{macrocode}
-\@@_msg_new:nnn { Duplicate~name }
-  { 
-    The~name~'\l_keys_value_tl'~is~already~used~and~you~shouldn't~use~
-    the~same~environment~name~twice.~You~can~go~on,~but,~
-    maybe,~you~will~have~incorrect~results. \\
-    For~a~list~of~the~names~already~used,~type~H~<return>. \\ 
-    If~you~don't~want~to~see~this~message~again,~use~the~option~
-    'allow-duplicate-names'. 
-  }
-  {
-    The~names~already~defined~in~this~document~are:~
-    \seq_use:Nnnn \g_@@_names_seq { ,~ } { ,~ } { ~and~ }.
-  }
-%    \end{macrocode}
-%
-% 
-%
-% \subsection{The command \textbackslash WithArrowsNewStyle}
-%
-% A new key defined with |\WithArrowsNewStyle| will not be available at the
-% local level.
-%    \begin{macrocode}
-\NewDocumentCommand \WithArrowsNewStyle { m m }
-  { 
-    \keys_if_exist:nnTF { WithArrows / Global } { #1 }
-      { \@@_error:nn { Key~already~defined } { #1 } }
-      { 
-        \keys_define:nn { WithArrows / Global }
-          { 
-            #1 .code:n = 
-             { \keys_set_known:nn { WithArrows / WithArrowsOptions } { #2 } }
-          } 
-        \seq_put_right:Nx \l_@@_options_WithArrows_seq { \tl_to_str:n { #1 } }
-        \seq_put_right:Nx \l_@@_options_DispWithArrows_seq 
-          { \tl_to_str:n { #1 } }
-        \seq_put_right:Nx \l_@@_options_WithArrowsOptions_seq 
-          { \tl_to_str:N { #1 } }
-%    \end{macrocode}
-% We now set the options in a TeX group in order to detect if some keys in |#2|
-% are unknown. If a key is unknown, an error will be raised. However, the key
-% will, even so, be stored in the definition of key~|#1|. 
-%    \begin{macrocode}
-        \group_begin:
-          \msg_set:nnn { witharrows } { Unknown~option~WithArrowsOptions }
-            {
-              The~key~'\l_keys_key_tl'~can't~be~set~in~the~
-              definition~of~a~style.~You~can~go~on~for~this~time~
-              but~you~should~suppress~this~key. 
-            }
-          \WithArrowsOptions { #2 }
-        \group_end:
-      } 
-  }
-%    \end{macrocode}
-% 
-%    \begin{macrocode}
-\@@_msg_new:nn { Key~already~defined }
-  {
-    The~key~'#1'~is~already~defined. \\
-    If~you~go~on,~your~instruction~\token_to_str:N\WithArrowsNewStyle\ 
-    will~be~ignored.
-  }
-%    \end{macrocode}
-%
-%
-% \subsection{The options up and down}
-%
-% The options |up| and |down| are available for individual arrows. The
-% corresponding code is given here. It is independent of the main code of the
-% extension \pkg{witharrows}.
-% 
-% This code is the only part of the code of \pkg{witharrows} which uses the
-% package \pkg{varwidth} and also the Tikz library |calc|. That's why we have
-% decided not to load this package and this library. If they are not loaded, the
-% user will have an error only when using the option |up| or the option |down|.
-% 
-% \medskip
-% The token list |\c_@@_tikz_code_up_tl| is the value of |tikz-code| which will
-% be used for an option |up|.
-%    \begin{macrocode}
-\tl_const:Nn \c_@@_tikz_code_up_tl
-  {
-    \draw [ rounded~corners ]
-       let \p1 = (#1) ,
-           \p2 = (#2)
-       in (\p1) -- node { 
-                          \dim_set:Nn \l_tmpa_dim { \x2 - \x1 }
-                          \begin { varwidth } \l_tmpa_dim
-                            \raggedright
-                            #3
-                          \end { varwidth } 
-                        } 
-          (\x2,\y1) -- (\p2) ;
-  }
-%    \end{macrocode}
-% 
-% \medskip
-% Idem for the option |down|.
-%    \begin{macrocode}
-\tl_const:Nn \c_@@_tikz_code_down_tl
-  {
-    \draw [ rounded~corners ]
-      let \p1 = (#1) ,
-          \p2 = (#2)
-      in (\p1) -- (\x1,\y2) --
-               node {
-                      \dim_set:Nn \l_tmpa_dim { \x1 - \x2 }
-                      \begin { varwidth } \l_tmpa_dim
-                        \raggedright
-                        #3
-                      \end { varwidth }
-                    } 
-               (\p2) ;
-  }
-%    \end{macrocode}
-% 
-%    \begin{macrocode}
-\keys_define:nn { WithArrows / Arrow / FirstPass }
-  {
-    up   .code:n = \@@_set_independent: ,
-    down .code:n = \@@_set_independent: ,
-    up   .default:n = NoValue ,
-    down .default:n = NoValue 
-  }
-%    \end{macrocode}
-% 
-% \bigskip
-%    \begin{macrocode}
-\keys_define:nn { WithArrows / Arrow / SecondPass }
-  { 
-    up .code:n =  
-      \str_if_empty:NT \l_@@_previous_key_str
-        { 
-          \str_set:Nn \l_@@_previous_key_str { up }
-          \bool_if:NTF \c_@@_varwidth_loaded_bool
-            { 
-              \cs_if_exist:cTF { tikz@library@calc@loaded }
-                { 
-                  \int_set:Nn \l_@@_pos_arrow_int \c_one_int
-%    \end{macrocode}
-% We have to set |\l_@@_wrap_lines_bool| to |false| because, otherwise, if the
-% option |wrap_lines| is used at a higher level (global or environment), we will
-% have a special affectation to |tikz-code| that will overwrite our affectation.
-%    \begin{macrocode}
-                  \bool_set_false:N \l_@@_wrap_lines_bool
-                  \tl_set_eq:NN \l_@@_tikz_code_tl 
-                    \c_@@_tikz_code_up_tl
-                }
-                { \@@_error:n { calc~not~loaded } }
-            }
-            { \@@_error:n { varwidth~not~loaded } } 
-        } ,
-    down .code:n = 
-      \str_if_empty:NT \l_@@_previous_key_str
-        { 
-          \str_set:Nn \l_@@_previous_key_str { down }
-          \bool_if:NTF \c_@@_varwidth_loaded_bool
-            { 
-              \cs_if_exist:cTF { tikz@library@calc@loaded }
-                { 
-                  \int_set:Nn \l_@@_pos_arrow_int \c_one_int
-                  \bool_set_false:N \l_@@_wrap_lines_bool
-                  \tl_set_eq:NN \l_@@_tikz_code_tl 
-                    \c_@@_tikz_code_down_tl
-                }
-                { \@@_error:n { calc~not~loaded } }
-            }
-            { \@@_error:n { varwidth~not~loaded } } 
-        }
-  }
-%    \end{macrocode}
-%
-%    
-% 
-%    \begin{macrocode}
-\seq_put_right:Nn \l_@@_options_Arrow_seq { down }
-\seq_put_right:Nn \l_@@_options_Arrow_seq { up }
-%    \end{macrocode}
-%
-%
-%    \begin{macrocode}
-\@@_msg_new:nn { varwidth~not~loaded } 
-  {
-    You~can't~use~the~option~'\l_keys_key_tl'~because~
-    you~don't~have~loaded~the~package~'varwidth'. \\
-    \c_@@_option_ignored_str
-  }
-%    \end{macrocode}
-% 
-%    \begin{macrocode}
-\@@_msg_new:nn { calc~not~loaded }
-  { 
-    You~can't~use~the~option~'\l_keys_key_tl'~because~you~don't~have~loaded~the~
-    Tikz~library~'calc'.You~should~add~'\token_to_str:N\usetikzlibrary{calc}'
-    ~in~the~preamble~of~your~document. \\
-    \c_@@_option_ignored_str
-  }
-%    \end{macrocode}
-%
-% 
-% \section{History}
-%
-% \subsection*{Changes between versions 1.0 and 1.1}
-% 
-% Option for the command |\\| and option |interline|
-% 
-% Compatibility with |\usetikzlibrary{babel}|
-%
-% Possibility of nested environments |{WithArrows}|
-% 
-%
-% \subsection*{Changes between versions 1.1 and 1.2}
-%
-% The package \pkg{witharrows} can now be loaded without having loaded
-% previously \pkg{tikz} and the libraries |arrow.meta| and |bending| (this
-% extension and these libraries are loaded silently by \pkg{witharrows}).
-%
-% New option |groups| (with a \emph{s})
-%
-% 
-% \subsection*{Changes between versions 1.2 and 1.3}
-% 
-% New options |ygap| and |ystart| for fine tuning.
-%
-% \subsection*{Changes between versions 1.3 and 1.4}
-% 
-% The package \pkg{footnote} is no longer loaded by default. Instead, two
-% options |footnote| and |footnotehyper| have been added. In particular,
-% \pkg{witharrows} becomes compatible with \cls{beamer}.
-% 
-% \subsection*{Changes between versions 1.4 and 1.5}
-% 
-% The Tikz code used to draw the arrows can be changed with the option
-% |tikz-code|.
-%
-% Two new options |code-before| and |code-after| have been added at the
-% environment level.
-%
-% A special version of |\Arrow| is available in |code-after| in order to draw
-% arrows in nested environments.
-% 
-% A command |\MultiArrow| is available in |code-after| to draw arrows of other
-% shapes.
-% 
-% \subsection*{Changes between versions 1.5 and 1.6}
-% 
-% The code has been improved to be faster and the Tikz library |calc| is no
-% longer required.
-%
-% A new option |name| is available for the environments |{WithArrows}|.
-%
-% \subsection*{Changes between 1.6 and 1.7}
-%
-% New environments |{DispWithArrows}| and |{DispWithArrows*}|.
-%
-% \subsection*{Changes between 1.7 and 1.8}
-%
-% The numbers and tags of the environment |{DispWithArrows}| are now compatible
-% with all the major LaTeX packages concerning references (\pkg{autonum},
-% \pkg{cleveref}, \pkg{fancyref}, \pkg{hyperref}, \pkg{prettyref},
-% \pkg{refstyle}, \pkg{typedref} and \pkg{varioref}) and with the options
-% |showonlyrefs| and |showmanualtags| of \pkg{mathtools}.
-%
-% \subsection*{Changes between 1.8 and 1.9}
-% 
-% New option |wrap-lines| for the environments |{DispWithArrows}| and
-% |{DispWithArrows*}|.
-%
-% \subsection*{Changes between 1.9 and 1.10}
-%
-% If the option |wrap-lines| is used, the option ``|text width|'' of Tikz is
-% still active: if the value given to ``|text width|'' is lower than the width
-% computed by |wrap-lines|, this value is used to wrap the lines.
-%
-% The option |wrap-lines| is now fully compatible with the class option |leqno|.
-%
-% Correction of a bug: |\nointerlineskip| and |\makebox[.6\linewidth]{}| should
-% be inserted in |{DispWithArrows}| only in vertical mode.
-%
-% \subsection*{Changes between 1.10 and 1.11}
-%
-% New commands |\WithArrowsNewStyle| and |\WithArrowsRightX|.
-%
-% \subsection*{Changes between 1.11 and 1.12}
-%
-% New command |\tagnextline|.
-%
-% New option |tagged-lines|.
-%
-% An option of position (|ll|, |lr|, |rl|, |rr| or |i|) is now allowed at the
-% local level even if the option |group| or the option |groups| is used at the
-% global or environment level.
-%
-% Compatibility of |{DispWithArrows}| with |\qedhere| of \pkg{amsthm}.
-%
-% Compatibility with the packages \pkg{refcheck}, \pkg{showlabels} and
-% \pkg{listlbls}.
-%
-% The option |\AllowLineWithoutAmpersand| is deprecated because lines without
-% ampersands are now always allowed.
-%
-% \subsection*{Changes between 1.12 and 1.13}
-%
-% Options |start-adjust|, |end-adjust| and |adjust|.
-% 
-% This version is not stricty compatible with previous ones. To restore the
-% behaviour of the previous versions, one has to use the option |adjust| with
-% the value $0$~pt:
-% 
-% \begin{Verbatim}
-% \WithArrowsOptions{adjust = 0pt}
-% \end{Verbatim}
-%
-% \subsection*{Changes between 1.13 and 1.14}
-%
-% New options |up| and |down| for the arrows.
-%
-% \smallskip
-% Replacement of some options |O { }| in commands and environments defined with
-% \pkg{xparse} by |! O { }| (a recent version of \pkg{xparse} introduced
-% the specifier |!| and modified the default behaviour of the last optional
-% arguments:
-% |//www.texdev.net/2018/04/21/xparse-optional-arguments-at-the-end|).
-%
-% \smallskip
-% Modification of the code of |\WithArrowsNewStyle| following a correction of a
-% bug in \pkg{l3keys} in the version of \pkg{l3kernel} of 2019/01/28.
-% 
-% New error message |Inexistent~v-node| to avoid a \pkg{pgf} error.
-%
-% The error |Option incompatible with 'group(s)'| was suppressed in the version
-% 1.12 but this was a mistake since this error is used with the option |xoffset|
-% at the local level. The error is put back.
-% 
-% \subsection*{Changes between 1.14 and 1.15}
-%
-% Option |new-group| to start a new group of arrows (only available when the
-% environment is composed with the option |groups|).
-%
-% Tikz externalization is now deactivated in the environments of the
-% extension \pkg{witharrows}.\footnote{Before this version, there was an error
-% when using \pkg{witharrows} with Tikz externalization. In any case, it's not
-% possible to externalize the Tikz elements constructed by \pkg{witharrows}
-% because they use the options |overlay| and |remember picture|.} 
-%
-% \subsection*{Changes between 1.15 and 1.16}
-%
-% Option |no-arrows| 
-%
-% The behaviour of |{DispWithArrows}| after an |\item| of a LaTeX list has been
-% changed : no vertical is added. The previous behaviour can be restored with
-% the option |standard-behaviour-with-items|.
-% 
-% A given name can no longer be used for two distinct environments. However,
-% it's possible to deactivate this control with the option
-% |allow-duplicate-names|.
-% 
-%
-% \subsection*{Changes between 1.16 and 1.17}
-% 
-% Option |format|
-%
-% \subsection*{Changes between 1.17 and 1.18}
-%
-% New option |<...>| for |{DispWithArrows}|.
-%
-% Option |subequations|.
-%
-% Warning when |{WithArrows}| or |{DispWithArrows}| ends by "\\".
-% 
-% No space before an environnement |{DispWithArrows}| if we are at the beginning
-% of a |{minipage}|.
-% \PrintIndex
-%
-% \tableofcontents
-%
-% \endinput
-% Local Variables:
-% TeX-fold-mode: nil
-% fill-column: 80
-% End:
diff --git a/Master/texmf-dist/source/latex/witharrows/witharrows.ins b/Master/texmf-dist/source/latex/witharrows/witharrows.ins
deleted file mode 100644
index 6aad8b87f3e..00000000000
--- a/Master/texmf-dist/source/latex/witharrows/witharrows.ins
+++ /dev/null
@@ -1,47 +0,0 @@
-%%
-%% Copyright (C) 2017-2019 by F. Pantigny
-%%
-%%
-%% This file may be distributed and/or modified under the
-%% conditions of the LaTeX Project Public License, either
-%% version 1.3 of this license or (at your option) any later
-%% version.  The latest version of this license is in:
-%%
-%%      http://www.latex-project.org/lppl.txt
-%%
-%% and version 1.3 or later is part of all distributions of
-%% LaTeX version 2005/12/01 or later.
-%%
-\input l3docstrip.tex
-\keepsilent
-\usedir{tex/latex/witharrows}
-\preamble
-
-Copyright (C) 2017-2019 by F. Pantigny
-
-This file may be distributed and/or modified under the
-conditions of the LaTeX Project Public License, either
-version 1.3 of this license or (at your option) any later
-version.  The latest version of this license is in:
-
-     http://www.latex-project.org/lppl.txt
-
-and version 1.3 or later is part of all distributions of
-LaTeX version 2005/12/01 or later.
-
-\endpreamble
-\generate{\file{witharrows.sty}{\from{witharrows.dtx}{package}}}
-\Msg{*********************************************************}
-\Msg{*}
-\Msg{* To finish the installation you have to move the}
-\Msg{* following file into a directory searched by TeX:}
-\Msg{*}
-\Msg{* \space\space witharrows.sty}
-\Msg{*}
-\Msg{* To produce the documentation run the file witharrows.dtx}
-\Msg{* through XeLaTeX.}
-\Msg{*}
-\Msg{* Happy TeXing!}
-\Msg{*********************************************************}
-\endbatchfile
-
diff --git a/Master/texmf-dist/tex/latex/witharrows/witharrows.sty b/Master/texmf-dist/tex/latex/witharrows/witharrows.sty
deleted file mode 100644
index 563c6e8b260..00000000000
--- a/Master/texmf-dist/tex/latex/witharrows/witharrows.sty
+++ /dev/null
@@ -1,2037 +0,0 @@
-%%
-%% This is file `witharrows.sty',
-%% generated with the docstrip utility.
-%%
-%% The original source files were:
-%%
-%% witharrows.dtx  (with options: `package')
-%% 
-%% Copyright (C) 2017-2019 by F. Pantigny
-%% 
-%% This file may be distributed and/or modified under the
-%% conditions of the LaTeX Project Public License, either
-%% version 1.3 of this license or (at your option) any later
-%% version.  The latest version of this license is in:
-%% 
-%%      http://www.latex-project.org/lppl.txt
-%% 
-%% and version 1.3 or later is part of all distributions of
-%% LaTeX version 2005/12/01 or later.
-%% 
-\def\myfileversion{1.18}
-\def\myfiledate{2019/07/24}
-\RequirePackage{tikz}
-\usetikzlibrary{arrows.meta,bending}
-\RequirePackage{expl3}[2019/02/15]
-\RequirePackage{l3keys2e}
-\ProvidesExplPackage
-  {witharrows}
-  {\myfiledate}
-  {\myfileversion}
-  {Draws arrows for explanations on the right}
-\RequirePackage { xparse } [ 2018-10-17 ]
-\bool_new:N \g__wi_footnotehyper_bool
-\bool_new:N \g__wi_footnote_bool
-\cs_new_protected:Npn \__wi_msg_new:nn { \msg_new:nnn { witharrows } }
-\cs_new_protected:Npn \__wi_msg_new:nnn { \msg_new:nnnn { witharrows } }
-\cs_new_protected:Npn \__wi_msg_redirect_name:nn
-  { \msg_redirect_name:nnn { witharrows } }
-\cs_new_protected:Npn \__wi_error:n { \msg_error:nn { witharrows } }
-\cs_new_protected:Npn \__wi_warning:n { \msg_error:nn { witharrows } }
-\cs_new_protected:Npn \__wi_fatal:n { \msg_fatal:nn { witharrows } }
-\cs_new_protected:Npn \__wi_error:nn  { \msg_error:nnn { witharrows } }
-\cs_generate_variant:Nn \__wi_error:nn { n x }
-\keys_define:nn { WithArrows / package }
-  {
-    footnote .bool_gset:N = \g__wi_footnote_bool ,
-    footnotehyper .bool_gset:N = \g__wi_footnotehyper_bool ,
-    unknown .code:n =
-      \__wi_fatal:n { Option~unknown~for~package }
-  }
-\__wi_msg_new:nn { Option~unknown~for~package }
-  {
-    You~can't~use~the~option~'\l_keys_key_tl'~when~loading~the~
-    package~witharrows.~Try~to~use~the~command~
-    \token_to_str:N\WithArrowsOptions.
-  }
-\ProcessKeysOptions { WithArrows / package }
-\__wi_msg_new:nn { Option~incompatible~with~Beamer }
-  {
-    The~option~'\l_keys_key_tl'\ is~incompatible~
-    with~Beamer~because~Beamer~has~its~own~system~to~extract~footnotes.
-  }
-\__wi_msg_new:nn { footnote~with~footnotehyper~package }
-  {
-    You~can't~use~the~option~'footnote'~because~the~package~
-    footnotehyper~has~already~been~loaded.~
-    If~you~want,~you~can~use~the~option~'footnotehyper'~and~the~footnotes~
-    within~the~environments~of~witharrows~will~be~extracted~with~the~tools~
-    of~the~package~footnotehyper.\\
-    If~you~go~on,~the~package~footnote~won't~be~loaded.
-  }
-\__wi_msg_new:nn { footnotehyper~with~footnote~package }
-  {
-    You~can't~use~the~option~'footnotehyper'~because~the~package~
-    footnote~has~already~been~loaded.~
-    If~you~want,~you~can~use~the~option~'footnote'~and~the~footnotes~
-    within~the~environments~of~witharrows~will~be~extracted~with~the~tools~
-    of~the~package~footnote.\\
-    If~you~go~on,~the~package~footnotehyper~won't~be~loaded.
-  }
-\bool_if:NT \g__wi_footnote_bool
-  {
-    \@ifclassloaded { beamer }
-      { \msg_info:nn { witharrows } { Option~incompatible~with~Beamer } }
-      {
-        \@ifpackageloaded { footnotehyper }
-          { \__wi_error:n { footnote~with~footnotehyper~package } }
-          { \usepackage { footnote } }
-      }
-  }
-\bool_if:NT \g__wi_footnotehyper_bool
-  {
-    \@ifclassloaded { beamer }
-      { \__wi_info:n  { Option~incompatible~with~Beamer } }
-      {
-        \@ifpackageloaded { footnote }
-          { \__wi_error:n { footnotehyper~with~footnote~package } }
-          { \usepackage { footnotehyper } }
-      }
-    \bool_gset_true:N \g__wi_footnote_bool
-  }
-\bool_new:N \c__wi_leqno_bool
-\DeclareOption { leqno } { \bool_set_true:N \c__wi_leqno_bool }
-\DeclareOption* { }
-\ProcessOptions*
-\cs_generate_variant:Nn \tl_put_right:Nn { N v }
-\cs_generate_variant:Nn \seq_set_split:Nnn { N x x }
-\AtBeginDocument
-  {
-    \clist_map_inline:nn
-      {
-        amsmath, amsthm, autonum, cleveref, hyperref, mathtools, showlabels,
-        typedref, unicode-math, varwidth
-      }
-      {
-        \bool_new:c { c__wi_#1_loaded_bool }
-        \@ifpackageloaded { #1 }
-          { \bool_set_true:c { c__wi_#1_loaded_bool } }
-          { }
-      }
-  }
-\sys_if_engine_luatex:TF
-  {
-    \cs_new_protected:Npn \__wi_strcmp:nn  #1 #2
-      { \lua_now:e { l3kernel.strcmp('#1','#2') } }
-  }
-  {
-    \cs_new_protected:Npn \__wi_strcmp:nn #1 #2
-      { \pdftex_strcmp:D { #1 } { #2 } }
-  }
-\cs_new_protected:Npn \__wi_sort_seq:N #1
-  {
-    \seq_sort:Nn #1
-      {
-        \int_compare:nNnTF
-          {
-            \__wi_strcmp:nn
-              { \str_lower_case:n { ##1 } }
-              { \str_lower_case:n { ##2 } }
-          }
-          > 0
-          \sort_return_swapped:
-          \sort_return_same:
-      }
-  }
-\cs_new_protected:Npn \__wi_convert_to_str_seq:N #1
-  {
-    \seq_clear:N \l_tmpa_seq
-    \seq_map_inline:Nn #1
-      {
-        \seq_put_left:Nx \l_tmpa_seq { \tl_to_str:n { ##1 } }
-      }
-    \seq_set_eq:NN #1 \l_tmpa_seq
-  }
-\cs_new_protected:Npn \__wi_set_seq_of_str_from_clist:Nn #1 #2
-  {
-    \seq_set_from_clist:Nn #1 { #2 }
-    \__wi_convert_to_str_seq:N #1
-  }
-\cs_new_protected:Npn \__wi_save:N #1
-  {
-    \seq_set_split:Nxx \l_tmpa_seq
-       { \char_generate:nn { `_ } { 12 } }
-       { \cs_to_str:N #1 }
-    \seq_pop_left:NN \l_tmpa_seq \l_tmpa_tl
-    \str_set:Nx \l_tmpa_str { \seq_item:Nn \l_tmpa_seq { -1 } }
-    \use:c { \l_tmpa_str _if_exist:cF }
-      { g _\seq_use:Nnnn \l_tmpa_seq _ _ _ }
-      {
-        \use:c { \l_tmpa_str _new:c }
-          { g _\seq_use:Nnnn \l_tmpa_seq _ _ _ }
-      }
-    \use:c { \l_tmpa_str _gset_eq:cN }
-      { g _\seq_use:Nnnn \l_tmpa_seq _ _ _ } #1
-  }
-\cs_new_protected:Npn \__wi_restore:N #1
-  {
-    \seq_set_split:Nxx \l_tmpa_seq
-      { \char_generate:nn { `_ } { 12 } }
-      { \cs_to_str:N #1 }
-    \seq_pop_left:NN \l_tmpa_seq \l_tmpa_tl
-    \str_set:Nx \l_tmpa_str { \seq_item:Nn \l_tmpa_seq { -1 } }
-    \use:c { \l_tmpa_str _set_eq:Nc }
-      #1 { g_\seq_use:Nnnn \l_tmpa_seq _ _ _ }
-  }
-\tikzset
-  {
-    __wi_node_style / .style =
-      {
-        above = \l__wi_ystart_dim ,
-        inner~sep = \c_zero_dim ,
-        minimum~width = \c_zero_dim ,
-        minimum~height = \l__wi_ygap_dim
-      }
-  }
-\tikzset
-  {
-    __wi_standard / .style =
-      {
-        remember~picture ,
-        overlay ,
-        name~prefix = wa - \l__wi_prefix_str -
-      }
-  }
-\tikzset
-  {
-    WithArrows / arrow / tips / .style =
-      { > = { Straight~Barb [ scale = 1.2 , bend ] } }
-  }
-\tikzset
- {
-   WithArrows / arrow / .style  =
-     {
-       align = left ,
-       auto = left ,
-       font = \small \itshape ,
-       WithArrows / arrow / tips ,
-       bend~left = 45 ,
-       ->
-     }
- }
-\AtBeginDocument
-  {
-    \bool_if:NTF \c__wi_amsmath_loaded_bool
-      {
-        \seq_put_right:Nn \l__wi_options_WithArrowsOptions_seq { subequations }
-        \seq_put_right:Nn \l__wi_options_DispWithArrows_seq { subequations }
-      }
-      {
-        \cs_new_protected:Npn \spread@equation
-          {
-            \openup \jot
-            \cs_set_eq:NN \spread@equation \prg_do_nothing:
-          }
-      }
-  }
-\tl_new:N \l__wi_left_brace_tl
-\tl_set_eq:NN \l__wi_left_brace_tl \c_novalue_tl
-\bool_new:N \l__wi_in_WithArrows_bool
-\bool_new:N \l__wi_in_DispWithArrows_bool
-\bool_new:N \l__wi_in_code_after_bool
-\seq_new:N \g__wi_position_in_the_tree_seq
-\seq_gput_right:Nn \g__wi_position_in_the_tree_seq 1
-\int_new:N \g__wi_last_env_int
-\int_new:N \l__wi_pos_env_int
-\int_new:N \l__wi_pos_arrow_int
-\int_set:Nn \l__wi_pos_arrow_int 3
-\seq_new:N \g__wi_arrow_int_seq
-\int_new:N \g__wi_arrow_int
-\seq_new:N \g__wi_line_int_seq
-\int_new:N \g__wi_line_int
-\seq_new:N \g__wi_col_int_seq
-\int_new:N \g__wi_col_int
-\clist_new:N \l__wi_tags_clist
-\clist_set:Nn \l__wi_tags_clist { all }
-\cs_new_protected:Npn \__wi_test_if_to_tag:
-  {
-    \clist_if_in:NVT \l__wi_tags_clist \g__wi_line_int
-      { \clist_set:Nn \l__wi_tags_clist { all } }
-  }
-\str_new:N \l__wi_command_name_str
-\str_set:Nn \l__wi_command_name_str { Arrow }
-\str_new:N \l__wi_string_Arrow_for_msg_str
-\str_set:Nx \l__wi_string_Arrow_for_msg_str { \token_to_str:N \Arrow }
-\seq_new:N \g__wi_names_seq
-\bool_new:N \l__wi_sbwi_bool
-\bool_new:N \l__wi_in_first_columns_bool
-\bool_new:N \l__wi_tag_star_bool
-\bool_new:N \l__wi_tag_next_line_bool
-\bool_new:N \l__wi_qedhere_bool
-\bool_new:N \l__wi_new_group_bool
-\bool_new:N \l__wi_initial_r_bool
-\bool_new:N \l__wi_final_r_bool
-\tl_new:N \l__wi_initial_tl
-\tl_new:N \l__wi_final_tl
-\int_new:N \l__wi_nb_cols_int
-\str_new:N \l__wi_format_str
-\bool_new:N \l__wi_subequations_bool
-\cs_new_protected:Npn \__wi_eval_if_allowed:n #1
-  {
-    \str_if_empty:NTF \l__wi_previous_key_str
-      {
-        \str_set_eq:NN \l__wi_previous_key_str \l_keys_key_tl
-        #1
-      }
-      { \__wi_error:n { Incompatible~options } }
-  }
-\cs_new_protected:Npn \__wi_fix_pos_option:n #1
-  { \__wi_eval_if_allowed:n { \int_set:Nn \l__wi_pos_arrow_int { #1 } } }
-\keys_define:nn { WithArrows / Global }
-  {
-    ygap .dim_set:N = \l__wi_ygap_dim ,
-    ygap .value_required:n = true ,
-    ygap .initial:n = 0.4 ex ,
-    ystart .dim_set:N = \l__wi_ystart_dim ,
-    ystart .value_required:n = true ,
-    ystart .initial:n = 0.4 ex ,
-    more-columns .code:n =
-      \__wi_msg_redirect_name:nn { Too~much~columns~in~WithArrows } { none } ,
-    more-columns .value_forbidden:n = true,
-    command-name .code:n =
-      \str_set:Nn \l__wi_command_name_str { #1 }
-      \str_set:Nx \l__wi_string_Arrow_for_msg_str
-        { \c_backslash_str Arrow~alias~\c_backslash_str #1 } ,
-    command-name .value_required:n = true ,
-    tikz-code .tl_set:N = \l__wi_tikz_code_tl,
-    tikz-code .initial:n = \draw~(#1)~to~node{#3}~(#2)~; ,
-    tikz-code .value_required:n = true ,
-    TikzCode .meta:n = { tikz-code = #1 } ,
-    displaystyle .bool_set:N = \l__wi_displaystyle_bool ,
-    displaystyle .default:n = true ,
-    show-nodes .code:n =
-      \tikzset { __wi_node_style / .append~style = { draw , red } } ,
-    show-nodes .value_forbidden:n = true,
-    show-node-names .bool_set:N = \l__wi_show_node_names_bool ,
-    show-node-names .default:n = true ,
-    group .code:n =
-      \str_if_empty:NTF \l__wi_previous_key_str
-        {
-          \str_set:Nn \l__wi_previous_key_str { group }
-          \seq_remove_all:Nn \l__wi_options_Arrow_seq { xoffset }
-          \int_set:Nn \l__wi_pos_arrow_int 7
-        }
-        { \__wi_error:n { Incompatible~options } } ,
-    group .value_forbidden:n = true ,
-    groups .code:n =
-      \str_if_empty:NTF \l__wi_previous_key_str
-        {
-          \str_set:Nn \l__wi_previous_key_str { groups }
-          \seq_if_in:NnF \l__wi_options_Arrow_seq { new-group }
-            { \seq_put_right:Nn \l__wi_options_Arrow_seq { new-group } }
-          \seq_remove_all:Nn \l__wi_options_Arrow_seq { xoffset }
-          \int_set:Nn \l__wi_pos_arrow_int 6
-        }
-        { \__wi_error:n { Incompatible~options } } ,
-    groups .value_forbidden:n = true ,
-    tikz   .code:n = \tikzset { WithArrows / arrow / .append~style = { #1 } } ,
-    tikz   .initial:n         = \c_empty_tl ,
-    tikz   .value_required:n  = true ,
-    rr     .value_forbidden:n = true ,
-    rr     .code:n            = \__wi_fix_pos_option:n 3 ,
-    ll     .value_forbidden:n = true ,
-    ll     .code:n            = \__wi_fix_pos_option:n 1 ,
-    rl     .value_forbidden:n = true ,
-    rl     .code:n            = \__wi_fix_pos_option:n 2 ,
-    lr     .value_forbidden:n = true ,
-    lr     .code:n            = \__wi_fix_pos_option:n 0 ,
-    i      .value_forbidden:n = true ,
-    i      .code:n            = \__wi_fix_pos_option:n 5 ,
-    xoffset .dim_set:N  = \l__wi_xoffset_dim ,
-    xoffset .value_required:n  = true ,
-    xoffset .initial:n = 3 mm ,
-    jot .dim_set:N = \jot ,
-    jot .value_required:n = true ,
-    interline .skip_set:N = \l__wi_interline_skip ,
-    interline .value_required:n = true ,
-    start-adjust .dim_set:N = \l__wi_start_adjust_dim ,
-    start-adjust .value_required:n = true ,
-    start-adjust .initial:n = 0.4 ex ,
-    end-adjust .dim_set:N = \l__wi_end_adjust_dim ,
-    end-adjust .value_required:n = true ,
-    end-adjust .initial:n = 0.4 ex ,
-    adjust .meta:n  = { start-adjust = #1 , end-adjust = #1 } ,
-    adjust .value_required:n = true ,
-    no-arrows .code:n =
-      \cs_set_eq:NN \__wi_draw_arrows:nn \use_none:nn
-      \cs_set_eq:NN \__wi_draw_arrow:nnn \use_none:nnn  ,
-    no-arrows .value_forbidden:n = true ,
-  }
-\keys_define:nn { WithArrows / WithArrowsSpecific }
-  {
-    t   .code:n            = \int_set:Nn \l__wi_pos_env_int O ,
-    t   .value_forbidden:n = true ,
-    c   .code:n            = \int_set:Nn \l__wi_pos_env_int 1 ,
-    c   .value_forbidden:n = true ,
-    b   .code:n            = \int_set:Nn \l__wi_pos_env_int 2 ,
-    b   .value_forbidden:n = true
-  }
-\clist_new:N \c__wi_extensible_delimiters_clist
-\clist_set:Nn \c__wi_extensible_delimiters_clist
-  {
-    \{, (, [, \lbrace, \lbrack, \lgroup, \langle, \lmoustache, \lceil, \lfloor
-  }
-\AtBeginDocument
-  {
-    \bool_if:nT
-      { \c__wi_amsmath_loaded_bool || \use:c { c__wi_unicode-math_loaded_bool } }
-      {
-        \clist_put_right:Nn \c__wi_extensible_delimiters_clist { \lvert, \lVert }
-      }
-  }
-\keys_define:nn { WithArrows / DispWithArrowsSpecific }
-  {
-    fleqn .bool_set:N = \l__wi_fleqn_bool ,
-    fleqn .default:n = true ,
-    mathindent .dim_set:N = \l__wi_mathindent_dim ,
-    mathindent .value_required:n = true ,
-    mathindent .initial:n = 25 pt ,
-    notag .code:n =
-      \str_if_eq:nnTF { #1 } { true }
-        { \clist_clear:N \l__wi_tags_clist }
-        { \clist_set:Nn \l__wi_tags_clist { all } } ,
-    notag .default:n = true ,
-    subequations .code:n =
-      \bool_if:NTF \c__wi_amsmath_loaded_bool
-        { \bool_set_true:N \l__wi_subequations_bool }
-        {
-          \__wi_error:n { amsmath~not~loaded }
-          \group_begin:
-          \globaldefs = 1
-          \__wi_msg_redirect_name:nn { amsmath~not~loaded } { info }
-          \group_end:
-        } ,
-    subequations .default:n = true ,
-    subequations .value_forbidden:n = true ,
-    nonumber .meta:n = notag ,
-    allow-multiple-labels .code:n =
-      \__wi_msg_redirect_name:nn { Multiple~labels } { none } ,
-    allow-multiple-labels .value_forbidden:n = true ,
-    wrap-lines .bool_set:N = \l__wi_wrap_lines_bool ,
-    wrap-lines .default:n = true ,
-    tagged-lines .code:n =
-      \clist_set:Nn \l__wi_tags_clist { #1 }
-      \clist_if_in:NnT \l__wi_tags_clist { first }
-        {
-          \clist_remove_all:Nn \l__wi_tags_clist { first }
-          \clist_put_left:Nn \l__wi_tags_clist \c_one_int
-        } ,
-    tagged-lines .value_required:n = true ,
-    replace-left-brace-by .code:n =
-      {
-        \clist_if_in:NnTF
-          \c__wi_extensible_delimiters_clist
-          { #1 }
-          { \tl_set:Nn \l__wi_replace_left_brace_by_tl { #1 } }
-          { \__wi_error:n { Bad~value~for~replace~brace~by } }
-      } ,
-    replace-left-brace-by .initial:n = \lbrace ,
-    standard-behaviour-with-items .bool_set:N = \l__wi_sbwi_bool ,
-    standard-behaviour-with-items .default:n = true
-  }
-\keys_define:nn { WithArrows / Env }
-  {
-    name .code:n =
-      \str_set:Nn \l_tmpa_str { #1 }
-      \seq_if_in:NVTF \g__wi_names_seq \l_tmpa_str
-        { \__wi_error:n { Duplicate~name } }
-        { \seq_gput_left:NV \g__wi_names_seq \l_tmpa_str }
-      \str_set_eq:NN \l__wi_name_str \l_tmpa_str ,
-    name .value_required:n = true ,
-    code-before .code:n = \tl_put_right:Nn \l__wi_code_before_tl { #1 } ,
-    code-before .value_required:n = true,
-    CodeBefore .meta:n = { code-before = #1 } ,
-    code-after .code:n = \tl_put_right:Nn \l__wi_code_after_tl { #1 } ,
-    code-after .value_required:n = true ,
-    CodeAfter  .meta:n = { code-after = #1 } ,
-    format .code:n =
-      \tl_if_empty:nTF { #1 }
-        { \__wi_error:n { Invalid~option~format } }
-        {
-          \regex_match:nnTF { \A[rcl]*\Z } { #1 }
-            { \tl_set:Nn \l__wi_format_str { #1 } }
-            { \__wi_error:n { Invalid~option~format } }
-        } ,
-    format .value_required:n = true ,
-  }
-\keys_define:nn { WithArrows }
-  {
-    WithArrows .inherit:n =
-      {
-        WithArrows / Global ,
-        WithArrows / WithArrowsSpecific ,
-        WithArrows / Env
-      } ,
-    DispWithArrows .inherit:n =
-      {
-        WithArrows / DispWithArrowsSpecific ,
-        WithArrows / Global ,
-        WithArrows / Env ,
-      } ,
-    WithArrowsOptions .inherit:n =
-      {
-        WithArrows / Global ,
-        WithArrows / WithArrowsSpecific ,
-        WithArrows / DispWithArrowsSpecific
-      }
-  }
-\seq_new:N \l__wi_options_WithArrows_seq
-\__wi_set_seq_of_str_from_clist:Nn \l__wi_options_WithArrows_seq
-  {
-    adjust, b, c, code-after, code-before, command-name,
-    displaystyle, end-adjust,
-    format, group, groups, i,
-    interline, jot, ll,
-    lr, more-columns, name,
-    no-arrows, rl, rr,
-    show-node-names, show-nodes, start-adjust,
-    t, tikz, tikz-code,
-    xoffset, ygap, ystart
-  }
-\__wi_convert_to_str_seq:N \l__wi_options_WithArrows_seq
-\keys_define:nn { WithArrows / WithArrows }
-  {
-    unknown .code:n  =
-      \__wi_sort_seq:N \l__wi_options_WithArrows_seq
-      \__wi_error:n { Unknown~option~WithArrows }
-  }
-\keys_define:nn { WithArrows / DispWithArrows }
-  {
-    left-brace .tl_set:N = \l__wi_left_brace_tl ,
-    unknown .code:n  =
-      \__wi_sort_seq:N \l__wi_options_DispWithArrows_seq
-      \__wi_error:n { Unknown~option~DispWithArrows }
-  }
-\seq_new:N \l__wi_options_DispWithArrows_seq
-\__wi_set_seq_of_str_from_clist:Nn \l__wi_options_DispWithArrows_seq
-  {
-    allow-multiple-labels, code-after, code-before, command-name, tikz-code, adjust,
-    displaystyle, end-adjust, fleqn, group, format, groups, i, interline, jot,
-    left-brace, ll, lr, mathindent, name, no-arrows, nonumber, notag,
-    replace-left-brace-by, rl, rr, show-node-names, show-nodes, start-adjust,
-    tagged-lines, tikz, wrap-lines, xoffset, ygap, ystart
-  }
-\keys_define:nn { WithArrows / WithArrowsOptions }
-  {
-    allow-duplicate-names .code:n =
-      \__wi_msg_redirect_name:nn { Duplicate~name } { none } ,
-    allow-duplicate-names .value_forbidden:n = true ,
-    unknown .code:n  =
-      \__wi_sort_seq:N \l__wi_options_WithArrowsOptions_seq
-      \__wi_error:n { Unknown~option~WithArrowsOptions }
-  }
-\seq_new:N \l__wi_options_WithArrowsOptions_seq
-\__wi_set_seq_of_str_from_clist:Nn \l__wi_options_WithArrowsOptions_seq
-  {
-    allow-duplicate-names, allow-multiple-labels, b, c, command-name,
-    more-columns, tikz-code, adjust, displaystyle, end-adjust, fleqn, group,
-    groups, i, interline, jot, ll, lr, mathindent, no-arrows, nonumber, notag,
-    rl, rr, show-node-names, show-nodes, standard-behaviour-with-items,
-    start-adjust, t, tagged-lines, tikz, wrap-lines, xoffset, ygap, ystart
-  }
-\cs_new_protected:Npn \__wi_set_independent:
-  {
-    \str_if_empty:NTF \l__wi_previous_key_str
-      {
-        \str_set_eq:NN \l__wi_previous_key_str \l_keys_key_tl
-        \str_set:Nn \l__wi_status_arrow_str { independent }
-        \str_if_eq:VnF \l_keys_value_tl { NoValue }
-          { \__wi_error:n { Value~for~a~key } }
-      }
-      { \__wi_error:n { Incompatible~options~in~Arrow } }
-  }
-\keys_define:nn { WithArrows / Arrow / FirstPass }
-  {
-    jump .code:n =
-      \int_compare:nTF { #1 > 0 }
-        { \int_set:Nn \l__wi_jump_int { #1 } }
-        { \__wi_error:n { Negative~jump } } ,
-    jump .value_required:n  = true,
-    rr .code:n = \__wi_set_independent: ,
-    ll .code:n = \__wi_set_independent: ,
-    rl .code:n = \__wi_set_independent: ,
-    lr .code:n = \__wi_set_independent: ,
-    i  .code:n = \__wi_set_independent: ,
-    rr .default:n = NoValue ,
-    ll .default:n = NoValue ,
-    rl .default:n = NoValue ,
-    lr .default:n = NoValue ,
-    i  .default:n = NoValue ,
-    new-group .value_forbidden:n = true,
-    new-group .code:n =
-      \int_compare:nTF { \l__wi_pos_arrow_int = 6 }
-        { \str_set:Nn \l__wi_status_arrow_str { new-group } }
-        { \__wi_error:n { new-group~without~groups } } ,
-    tikz-code .code:n = \prg_do_nothing: ,
-    tikz-code .value_required:n = true ,
-    tikz .code:n = \prg_do_nothing: ,
-    tikz .value_required:n = true ,
-    xoffset .code:n =
-      \int_compare:nNnT \l__wi_pos_arrow_int > 5
-        { \__wi_error:n { Option~xoffset~forbidden } } ,
-    xoffset .value_required:n = true ,
-    start-adjust .code:n = \prg_do_nothing: ,
-    start-adjust .value_required:n = true ,
-    end-adjust .code:n = \prg_do_nothing: ,
-    end-adjust .value_required:n = true ,
-    adjust .code:n  = \prg_do_nothing: ,
-    adjust .value_required:n = true ,
-    unknown .code:n =
-      \__wi_sort_seq:N \l__wi_options_Arrow_seq
-      \seq_if_in:NVTF \l__wi_options_WithArrows_seq \l_keys_key_tl
-        {
-          \str_set:Nn \l_tmpa_str
-           { ~However,~this~key~can~be~used~in~the~options~of~\{WithArrows\}. }
-        }
-        { \str_clear:N \l_tmpa_str }
-      \__wi_error:n { Unknown~option~in~Arrow }
-  }
-\seq_new:N \l__wi_options_Arrow_seq
-\__wi_set_seq_of_str_from_clist:Nn \l__wi_options_Arrow_seq
-  {
-    adjust, end-adjust, i, jump, ll, lr, rl, rr, start-adjust, tikz, tikz-code,
-    xoffset
-  }
-\cs_new_protected:Npn \__wi_fix_pos_arrow:n #1
-  {
-    \str_if_empty:NT \l__wi_previous_key_str
-      {
-        \str_set_eq:NN \l__wi_previous_key_str \l_keys_key_tl
-        \int_set:Nn \l__wi_pos_arrow_int { #1 }
-      }
-  }
-\keys_define:nn {WithArrows / Arrow / SecondPass }
-  {
-    tikz-code .tl_set:N = \l__wi_tikz_code_tl ,
-    tikz-code .initial:n = \draw~(#1)~to~node{#3}~(#2)~; ,
-    tikz .code:n = \tikzset { WithArrows / arrow / .append~style = { #1 } } ,
-    tikz .initial:n = \c_empty_tl ,
-    rr .code:n = \__wi_fix_pos_arrow:n 3 ,
-    ll .code:n = \__wi_fix_pos_arrow:n 1 ,
-    rl .code:n = \__wi_fix_pos_arrow:n 2 ,
-    lr .code:n = \__wi_fix_pos_arrow:n 0 ,
-    i  .code:n = \__wi_fix_pos_arrow:n 5 ,
-    xoffset .code:n  =
-      \int_compare:nNnF \l__wi_pos_arrow_int > 5
-        { \dim_set:Nn \l__wi_xoffset_dim { #1 } } ,
-    start-adjust .dim_set:N = \l__wi_start_adjust_dim,
-    end-adjust .dim_set:N = \l__wi_end_adjust_dim,
-    adjust .code:n  =
-      \dim_set:Nn \l__wi_start_adjust_dim { #1 }
-      \dim_set:Nn \l__wi_end_adjust_dim { #1 } ,
-  }
-\NewDocumentCommand \WithArrowsOptions { m }
-  {
-    \str_clear_new:N \l__wi_previous_key_str
-    \keys_set:nn { WithArrows / WithArrowsOptions } { #1 }
-  }
-\NewDocumentCommand \__wi_Arrow { O { } m ! O { } }
-  {
-    \int_gincr:N \g__wi_arrow_int
-    \str_clear_new:N \l__wi_previous_key_str
-    \keys_set:nn { WithArrows / Arrow / FirstPass } { #1 , #3 }
-    \prop_put:NnV \l_tmpa_prop { initial } \g__wi_line_int
-    \int_set:Nn \l_tmpa_int { \g__wi_line_int + \l__wi_jump_int }
-    \prop_put:NnV \l_tmpa_prop { final } \l_tmpa_int
-    \prop_put:NnV \l_tmpa_prop { status } \l__wi_status_arrow_str
-    \prop_put:Nnn \l_tmpa_prop { options } { #1 , #3 }
-    \prop_put:Nnn \l_tmpa_prop { label } { #2 }
-    \prop_put:Nnx \l_tmpa_prop { input-line } \msg_line_number:
-    \prop_gclear_new:c
-      { g__wi_arrow _ \l__wi_prefix_str _ \int_use:N \g__wi_arrow_int _ prop }
-    \prop_gset_eq:cN
-      { g__wi_arrow _ \l__wi_prefix_str _ \int_use:N \g__wi_arrow_int _ prop }
-      \l_tmpa_prop
-  }
-\cs_new_protected:Npn \__wi_Arrow_first_columns:
-  { \__wi_error:n { Arrow~not~in~last~column } \__wi_Arrow }
-\cs_new_protected:Npn \__wi_pre_halign:n #1
-  {
-    \str_clear_new:N \l__wi_type_env_str
-    \str_set:NV \l__wi_type_env_str \@currenvir
-    \cs_if_exist:NT \tikz@library@external@loaded
-      { \tikzset { external / export = false } }
-    \str_clear_new:N \l__wi_name_str
-    \str_clear_new:N \l__wi_status_arrow_str
-    \dim_zero_new:N \l__wi_x_dim
-    \str_clear_new:N \l__wi_input_line_str
-    \seq_gput_right:NV \g__wi_arrow_int_seq \g__wi_arrow_int
-    \int_gzero:N \g__wi_arrow_int
-    \seq_gput_right:NV \g__wi_line_int_seq \g__wi_line_int
-    \int_gzero:N \g__wi_line_int
-    \seq_gput_right:NV \g__wi_col_int_seq \g__wi_col_int
-    \int_gzero:N \g__wi_col_int
-    \int_gzero_new:N \g__wi_static_col_int
-    \seq_gput_right:Nn \g__wi_position_in_the_tree_seq 1
-    \seq_set_eq:NN \l_tmpa_seq \g__wi_position_in_the_tree_seq
-    \seq_pop_right:NN \l_tmpa_seq \l_tmpa_tl
-    \str_clear_new:N \l__wi_prefix_str
-    \str_set:Nx \l__wi_prefix_str { \seq_use:Nnnn \l_tmpa_seq - - - }
-    \cs_set_eq:NN \\ \__wi_cr:
-    \dim_zero:N \mathsurround
-    \int_zero_new:N \l__wi_initial_int
-    \int_zero_new:N \l__wi_final_int
-    \int_zero_new:N \l__wi_arrow_int
-    \int_zero_new:N \l__wi_pos_of_arrow_int
-    \int_zero_new:N \l__wi_jump_int
-    \int_set:Nn \l__wi_jump_int \c_one_int
-    \str_set:Nn \l__wi_format_str { rl }
-    \seq_clear_new:N \l__wi_labels_seq
-    \bool_set_false:N \l__wi_tag_next_line_bool
-    \skip_zero:N \l__wi_interline_skip
-    \tl_clear_new:N \l__wi_code_before_tl
-    \tl_clear_new:N \l__wi_code_after_tl
-    \str_clear_new:N \l__wi_previous_key_str
-    \bool_if:NT \l__wi_in_WithArrows_bool
-      { \keys_set:nn { WithArrows / WithArrows } { #1 } }
-    \bool_if:NT \l__wi_in_DispWithArrows_bool
-      { \keys_set:nn { WithArrows / DispWithArrows } { #1 } }
-    \cs_set_eq:cN \l__wi_command_name_str \__wi_Arrow_first_columns:
-    \int_set:Nn \l__wi_nb_cols_int { \str_count:N \l__wi_format_str }
-    \int_gset_eq:NN \g__wi_col_int \l__wi_nb_cols_int
-    \seq_clear_new:N \l__wi_format_seq
-    \seq_set_split:NnV \l__wi_format_seq { } \l__wi_format_str
-    \bool_if:NT \g__wi_footnote_bool { \begin { savenotes } }
-    \l__wi_code_before_tl
-    \spread@equation
-    \cs_set_eq:NN \notag \__wi_notag:
-    \cs_set_eq:NN \nonumber \__wi_nonumber:
-    \cs_set_eq:NN \tag \__wi_tag
-    \cs_set_eq:NN \__wi_old_label \label
-    \cs_set_eq:NN \label \__wi_label:n
-    \cs_set_eq:NN \tagnextline \__wi_tagnextline:
-  }
-\cs_new_protected:Npn \__wi_construct_halign:
-  {
-    \seq_pop_right:NNTF \l__wi_format_seq \l__wi_type_col_str
-      {
-        \use:x
-          {
-            \int_gdecr:N \g__wi_col_int
-            \__wi_construct_halign:
-            \int_compare:nNnT \g__wi_col_int = \l__wi_nb_cols_int
-              {
-                \cs_set_eq:cN { \l__wi_command_name_str } \__wi_Arrow
-                \bool_if:NT \l__wi_in_DispWithArrows_bool
-                  {
-                    \__wi_test_if_to_tag:
-                    \bool_if:NT \c__wi_amsthm_loaded_bool \__wi_set_qedhere:
-                  }
-              }
-            \str_if_eq:VnT \l__wi_type_col_str { c } \hfil
-            \str_if_eq:VnT \l__wi_type_col_str { r } \hfill
-            \int_gincr:N \g__wi_col_int
-            \int_gset:Nn \g__wi_static_col_int { \int_use:N \g__wi_col_int }
-            \c_math_toggle_token
-              {
-                { }
-                \bool_if:NT \l__wi_displaystyle_bool \displaystyle
-                ####
-              }
-            \c_math_toggle_token
-            \int_compare:nNnTF \g__wi_col_int = \l__wi_nb_cols_int
-              { \__wi_construct_nodes: }
-              {
-                \str_if_eq:VnT \l__wi_type_col_str { l } \hfil
-                \str_if_eq:VnT \l__wi_type_col_str { c } \hfil
-                \bool_if:NT \l__wi_in_DispWithArrows_bool { \tabskip = \c_zero_skip }
-                &
-              }
-          }
-      }
-      {
-        \bool_if:NTF \l__wi_in_WithArrows_bool
-          {
-            \ialign
-            \bgroup
-          }
-          {
-            \halign to \l__wi_linewidth_dim
-            \bgroup
-            \bool_if:NT \l__wi_fleqn_bool
-              { \skip_horizontal:N \l__wi_mathindent_dim }
-          }
-        \int_gincr:N \g__wi_line_int
-        \int_gzero:N \g__wi_col_int
-        \tl_if_eq:NNF \l__wi_left_brace_tl \c_novalue_tl
-          {
-            \skip_horizontal:n
-              { \box_wd:N \l__wi_left_brace_box + \l__wi_delim_wd_dim }
-          }
-        \strut
-      }
-  }
-\cs_new_protected:Npn \__wi_construct_nodes:
-  {
-    \tikz [ remember~picture , overlay ]
-      \node
-        [
-          node~contents = { } ,
-          __wi_node_style ,
-          name = wa - \l__wi_prefix_str - \int_use:N \g__wi_line_int - l ,
-          alias =
-            {
-              \str_if_empty:NF \l__wi_name_str
-                { \l__wi_name_str - \int_use:N \g__wi_line_int - l }
-            }
-        ]
-        ;
-    \hfil
-    \tikz [ remember~picture , overlay ]
-      \node
-        [
-          node~contents = { } ,
-          __wi_node_style ,
-          name = wa - \l__wi_prefix_str - \int_use:N \g__wi_line_int - r ,
-          alias =
-            {
-              \str_if_empty:NF \l__wi_name_str
-                { \l__wi_name_str - \int_use:N \g__wi_line_int - r }
-            }
-        ]
-        ;
-    \bool_if:NT \l__wi_show_node_names_bool
-      {
-        \hbox_overlap_right:n
-          { \small wa - \l__wi_prefix_str - \int_use:N \g__wi_line_int - r }
-      }
-  }
-\NewDocumentEnvironment { WithArrows } { ! O { } }
-  {
-    \bool_set_true:N \l__wi_in_WithArrows_bool
-    \bool_set_false:N \l__wi_in_DispWithArrows_bool
-    \__wi_pre_halign:n { #1 }
-    \if_mode_math: \else:
-      \__wi_error:n { WithArrows~outside~math~mode }
-    \fi:
-    \int_case:nn \l__wi_pos_env_int { 0 \vtop 1 \vcenter 2 \vbox }
-    \bgroup
-    \__wi_construct_halign:
-    &&
-    \__wi_error:n { Too~much~columns~in~WithArrows }
-    \c_math_toggle_token
-    \bool_if:NT \l__wi_displaystyle_bool \displaystyle
-    { ## }
-    \c_math_toggle_token
-    \cr
-  }
-  {
-    \\
-    \egroup
-    \egroup
-    \__wi_post_halign:
-    \bool_if:NT \g__wi_footnote_bool { \end { savenotes } }
-  }
-\cs_new_protected:Npn \__wi_post_halign:
-  {
-    \cs_set:Npn \WithArrowsRightX { \g__wi_right_x_dim }
-    \int_compare:nNnT \g__wi_arrow_int > 0 \__wi_scan_arrows:
-    \group_begin:
-      \tikzset { every~picture / .style = __wi_standard }
-      \cs_set:Npn \WithArrowsNbLines { \int_use:N \g__wi_line_int }
-      \cs_set_eq:NN \MultiArrow \__wi_MultiArrow:nn
-      \cs_set_eq:cN \l__wi_command_name_str \__wi_Arrow_code_after
-      \bool_set_true:N \l__wi_in_code_after_bool
-      \l__wi_code_after_tl
-    \group_end:
-    \seq_gpop_right:NN \g__wi_position_in_the_tree_seq \l_tmpa_tl
-    \seq_gpop_right:NN \g__wi_position_in_the_tree_seq \l_tmpa_tl
-    \seq_gput_right:Nx \g__wi_position_in_the_tree_seq
-      { \int_eval:n { \l_tmpa_tl + 1 } }
-    \int_compare:nNnT { \seq_count:N \g__wi_position_in_the_tree_seq } = 1
-      { \int_gincr:N \g__wi_last_env_int }
-    \seq_gpop_right:NN \g__wi_arrow_int_seq \l_tmpa_tl
-    \int_gset:Nn \g__wi_arrow_int \l_tmpa_tl
-    \seq_gpop_right:NN \g__wi_line_int_seq \l_tmpa_tl
-    \int_gset:Nn \g__wi_line_int \l_tmpa_tl
-    \seq_gpop_right:NN \g__wi_col_int_seq \l_tmpa_tl
-    \int_gset:Nn \g__wi_col_int \l_tmpa_tl
-  }
-\cs_new_protected:Npn \__wi_cr:
-  {
-    \scan_stop:
-    \int_compare:nNnF \g__wi_col_int = \g__wi_static_col_int
-      { \__wi_error:n { omit~probably~used } }
-    \prg_replicate:nn { \l__wi_nb_cols_int - \g__wi_static_col_int } { & { } }
-    \group_align_safe_begin:
-    \peek_meaning_remove:NTF * \__wi_cr_i: \__wi_cr_i:
-  }
-\cs_new_protected:Npn \__wi_cr_i:
-  { \peek_meaning:NTF [ \__wi_cr_ii: { \__wi_cr_ii: [ \c_zero_dim ] } }
-\cs_new_protected:Npn \__wi_cr_ii: [ #1 ]
-  {
-    \peek_meaning_ignore_spaces:NTF \end
-      {
-        \__wi_cr_iii:n { #1 }
-        \__wi_analyze_end:Nn
-      }
-      { \__wi_cr_iii:n { #1 } }
-  }
-\cs_new_protected:Npn \__wi_cr_iii:n #1
-  {
-    \group_align_safe_end:
-    \bool_if:NT \l__wi_in_DispWithArrows_bool
-      {
-        \clist_if_in:NnTF \l__wi_tags_clist { all }
-          {
-            \tl_if_empty:NT \l__wi_tag_tl { \int_gincr:N \c@equation }
-            \cs_gset:Npx \g_tmpa_tl
-              { \tl_if_empty:NTF \l__wi_tag_tl \theequation \l__wi_tag_tl }
-            \seq_if_empty:NF \l__wi_labels_seq
-              {
-                \cs_set:Npx \@currentlabel { \p@equation \g_tmpa_tl }
-                \bool_if:NT \c__wi_hyperref_loaded_bool
-                  {
-                    \str_set:Nn \This@name { equation }
-                    \hyper@refstepcounter { equation }
-                  }
-                \bool_if:NT \c__wi_cleveref_loaded_bool
-                  {
-                    \cref@constructprefix { equation } \cref@result
-                    \protected@edef \cref@currentlabel
-                      {
-                        [
-                          \cs_if_exist:NTF \cref@equation@alias
-                            \cref@equation@alias
-                            { equation }
-                        ]
-                        [ \arabic { equation } ] [ \cref@result ]
-                        \p@equation \g_tmpa_tl
-                      }
-                  }
-                \seq_map_function:NN \l__wi_labels_seq \__wi_old_label
-              }
-            \__wi_save:N \l__wi_tag_star_bool
-            \__wi_save:N \l__wi_qedhere_bool
-            \bool_if:NT \l__wi_tag_next_line_bool
-              {
-                \openup -\jot
-                \bool_set_false:N \l__wi_tag_next_line_bool
-                \notag \\ &
-              }
-            &
-            \__wi_restore:N \l__wi_tag_star_bool
-            \__wi_restore:N \l__wi_qedhere_bool
-            \bool_if:NT \l__wi_qedhere_bool
-               { \hbox_overlap_left:n \__wi_qedhere_i: }
-            \cs_set_eq:NN \theequation \g_tmpa_tl
-            \bool_if:NT \l__wi_tag_star_bool
-              { \cs_set_eq:NN \tagform@ \prg_do_nothing: }
-            \hbox_overlap_left:n
-              {
-                \bool_if:NF \c__wi_leqno_bool
-                  {
-                    \tikz [ __wi_standard ]
-                      \coordinate ( \int_use:N \g__wi_line_int - v ) ;
-                  }
-                \quad
-                \@eqnnum
-              }
-            \bool_if:NT \c__wi_leqno_bool
-              {
-                \tikz [ __wi_standard ]
-                  \coordinate ( \int_use:N \g__wi_line_int - v ) ;
-              }
-          }
-          {
-            \__wi_save:N \l__wi_qedhere_bool
-            &
-            \__wi_restore:N \l__wi_qedhere_bool
-            \bool_if:NT \l__wi_qedhere_bool
-               { \hbox_overlap_left:n \__wi_qedhere_i: }
-            \tikz [ __wi_standard ]
-               \coordinate ( \int_use:N \g__wi_line_int - v ) ;
-          }
-      }
-    \dim_compare:nNnT { #1 } < \c_zero_dim
-       { \__wi_error:n { option~of~cr~negative } }
-    \dim_set:Nn \l_tmpa_dim { \dim_max:nn { #1 } \c_zero_dim }
-    \cr
-    \noalign
-      {
-        \skip_vertical:n { \l_tmpa_dim + \l__wi_interline_skip }
-        \scan_stop:
-      }
-  }
-\cs_new_protected:Npn \__wi_analyze_end:Nn #1 #2
-  {
-    \exp_args:NV \str_if_eq:nnT \l__wi_type_env_str { #2 }
-      { \__wi_warning:n { newline~at~the~end~of~env } }
-    \end { #2 }
-  }
-\bool_new:N \l__wi_in_label_or_minipage_bool
-\NewDocumentEnvironment { DispWithArrows } { ! d < > ! O { } }
-  {
-    \bool_set_true:N \l__wi_in_DispWithArrows_bool
-    \bool_if:nT \c__wi_mathtools_loaded_bool
-      {
-        \MH_if_boolean:nT { show_only_refs }
-          {
-            \MT_showonlyrefs_false:
-            \MH_set_boolean_T:n { show_only_refs }
-          }
-      }
-    \bool_if:NT \c__wi_typedref_loaded_bool { \str_set:Nn \sr@name { equation } }
-    \bool_if:NT \c__wi_amsmath_loaded_bool \intertext@
-    \IfValueT { #1 } { \tl_set:Nn \l__wi_left_brace_tl { #1 } }
-    \__wi_pre_halign:n { #2 }
-    \bool_if:NT \l__wi_subequations_bool { \begin { subequations } }
-    \bool_if:NF \l__wi_sbwi_bool
-      {
-        \if@inlabel
-        \bool_set_true:N \l__wi_in_label_or_minipage_bool
-        \fi
-        \if@minipage
-        \bool_set_true:N \l__wi_in_label_or_minipage_bool
-        \fi
-      }
-    \tl_if_eq:NNF \l__wi_left_brace_tl \c_novalue_tl
-      {
-        \hbox_set:Nn \l_tmpa_box
-          {
-            \c_math_toggle_token
-            \left \l__wi_replace_left_brace_by_tl \vcenter to 1 cm { } \right.
-            \c_math_toggle_token
-          }
-        \dim_zero_new:N \l__wi_delim_wd_dim
-        \dim_set:Nn \l__wi_delim_wd_dim { \box_wd:N \l_tmpa_box }
-        \box_clear_new:N \l__wi_left_brace_box
-        \hbox_set:Nn \l__wi_left_brace_box
-          {
-            \group_begin:
-              \cs_set_eq:NN \label \__wi_old_label
-              \c_math_toggle_token
-              \bool_if:NT \l__wi_displaystyle_bool \displaystyle
-              \l__wi_left_brace_tl
-              { }
-              \c_math_toggle_token
-            \group_end:
-          }
-      }
-    \tl_clear_new:N \l__wi_tag_tl
-    \bool_set_false:N \l__wi_qedhere_bool
-    \bool_set_false:N \l__wi_tag_star_bool
-    \if_mode_math:
-      \__wi_fatal:n { DispWithArrows~in~math~mode }
-    \fi:
-    \bool_if:NTF \l__wi_in_label_or_minipage_bool
-      { \c_math_toggle_token }
-      {
-        \if_mode_vertical:
-        \nointerlineskip
-        \hbox_to_wd:nn { .6 \linewidth } { }
-        \fi:
-        \c_math_toggle_token \c_math_toggle_token
-      }
-    \dim_zero_new:N \l__wi_linewidth_dim
-    \bool_if:NTF \l__wi_in_label_or_minipage_bool
-       { \dim_set_eq:NN \l__wi_linewidth_dim \linewidth }
-       { \dim_set_eq:NN \l__wi_linewidth_dim \displaywidth }
-    \box_clear_new:N \l__wi_halign_box
-    \setbox \l__wi_halign_box \vtop \bgroup
-    \tabskip =
-      \bool_if:NTF \l__wi_fleqn_bool
-        \c_zero_skip
-        { 0 pt plus 1000 pt minus 1000 pt }
-    \__wi_construct_halign:
-    \tabskip = 0 pt plus 1000 pt minus 1000 pt
-    &
-    $ ## $
-    \tabskip = \c_zero_skip
-    &&
-    \__wi_fatal:n { Too~much~columns~in~DispWithArrows }
-    \bool_if:nT \c_false_bool { ## }
-    \cr
-  }
-  {
-    \clist_if_in:NnT \l__wi_tags_clist { last }
-      { \clist_set:Nn \l__wi_tags_clist { all } }
-    \\
-    \egroup
-    \unskip \unpenalty \unskip \unpenalty
-    \box_set_to_last:N \l_tmpa_box
-    \nointerlineskip
-    \box_use:N \l_tmpa_box
-    \dim_gzero_new:N \g__wi_alignment_dim
-    \dim_gset:Nn \g__wi_alignment_dim { \box_wd:N \l_tmpa_box }
-    \box_clear_new:N \l__wi_new_box
-    \hbox_set:Nn \l__wi_new_box { \hbox_unpack_clear:N \l_tmpa_box }
-    \dim_compare:nNnT
-      { \box_wd:N \l__wi_new_box } < \g__wi_alignment_dim
-      { \dim_gset:Nn \g__wi_alignment_dim { \box_wd:N \l__wi_new_box } }
-    \egroup
-     \tl_if_eq:NNTF \l__wi_left_brace_tl \c_novalue_tl
-       { \box_use_drop:N \l__wi_halign_box }
-       {
-         \hbox_to_wd:nn \l__wi_linewidth_dim
-           {
-            \bool_if:NTF \l__wi_fleqn_bool
-              { \skip_horizontal:n \l__wi_mathindent_dim }
-              \hfil
-            \hbox_to_wd:nn \g__wi_alignment_dim
-              {
-                \box_use_drop:N \l__wi_left_brace_box
-                \dim_set:Nn \l_tmpa_dim
-                  {
-                    \box_ht:N \l__wi_halign_box
-                    + \box_dp:N \l__wi_halign_box
-                  }
-                \c_math_toggle_token
-                  \left \l__wi_replace_left_brace_by_tl
-                    \vcenter to \l_tmpa_dim { \vfil }
-                  \right.
-                \c_math_toggle_token
-                \hfil
-              }
-            \hfil
-           }
-         \skip_horizontal:n { - \l__wi_linewidth_dim }
-         \vcenter { \box_use_drop:N \l__wi_halign_box }
-       }
-    \dim_gzero_new:N \g__wi_right_x_dim
-    \dim_gset_eq:NN \g__wi_right_x_dim \c_max_dim
-    \begin { tikzpicture } [ __wi_standard ]
-      \int_step_variable:nNn \g__wi_line_int \l_tmpa_int
-        {
-          \cs_if_free:cTF
-            { pgf@sh@ns@wa - \l__wi_prefix_str - \l_tmpa_int - v }
-            { \__wi_fatal:n { Inexistent~v-node } }
-            {
-              \tikz@parse@node\pgfutil@firstofone ( \l_tmpa_int - v )
-              \dim_set:Nn \l_tmpa_dim \pgf@x
-              \dim_compare:nNnT \l_tmpa_dim < \g__wi_right_x_dim
-                { \dim_gset:Nn \g__wi_right_x_dim \l_tmpa_dim }
-            }
-        }
-    \end { tikzpicture }
-    \__wi_post_halign:
-    \bool_if:nT \c__wi_mathtools_loaded_bool
-      { \MH_if_boolean:nT { show_only_refs } \MT_showonlyrefs_true: }
-    \bool_if:NTF \l__wi_in_label_or_minipage_bool
-      {
-        \c_math_toggle_token
-        \skip_vertical:N \belowdisplayskip
-      }
-      { \c_math_toggle_token \c_math_toggle_token }
-    \bool_if:NT \l__wi_subequations_bool { \end { subequations } }
-    \bool_if:NT \g__wi_footnote_bool { \end { savenotes } }
-    \ignorespacesafterend
-  }
-\NewDocumentEnvironment { DispWithArrows* } { }
-  {
-    \WithArrowsOptions { notag }
-    \DispWithArrows
-  }
-  \endDispWithArrows
-\cs_new_protected:Npn \__wi_if_in_last_col_of_disp:Nn #1 #2
-  {
-    \bool_if:NTF \l__wi_in_WithArrows_bool
-      { \__wi_error:nn { Not~allowed~in~WithArrows } { #1 } }
-      {
-        \int_compare:nNnTF \g__wi_col_int < \l__wi_nb_cols_int
-          { \__wi_error:nn { Not~allowed~in~DispWithArrows } { #1 } }
-          { #2 }
-      }
-  }
-\cs_new_protected:Npn \__wi_notag:
-  { \__wi_if_in_last_col_of_disp:Nn \notag { \clist_clear:N \l__wi_tags_clist } }
-\cs_new_protected:Npn \__wi_nonumber:
-  { \__wi_if_in_last_col_of_disp:Nn \nonumber { \clist_clear:N \l__wi_tags_clist } }
-\NewDocumentCommand \__wi_tag { s m }
-  {
-    \__wi_if_in_last_col_of_disp:Nn \tag
-      {
-        \tl_if_empty:NF \l__wi_tag_tl
-          { \__wi_error:nn  { Multiple~tags } { #2 } }
-        \clist_set:Nn \l__wi_tags_clist { all }
-        \bool_if:nT \c__wi_mathtools_loaded_bool
-          {
-            \MH_if_boolean:nT { show_only_refs }
-              {
-                \MH_if_boolean:nF { show_manual_tags }
-                  { \clist_clear:N \l__wi_tags_clist }
-              }
-          }
-        \tl_set:Nn \l__wi_tag_tl { #2 }
-        \bool_set:Nn \l__wi_tag_star_bool { #1 }
-        \bool_if:nT { #1 && ! \bool_if_p:N \c__wi_amsmath_loaded_bool }
-          { \__wi_error:n { tag*~without~amsmath } }
-      }
-  }
-\cs_new_protected:Npn \__wi_label:n #1
-  {
-    \__wi_if_in_last_col_of_disp:Nn \label
-      {
-        \seq_if_empty:NF \l__wi_labels_seq
-          {
-            \bool_if:NTF \c__wi_cleveref_loaded_bool
-              { \__wi_error:n { Multiple~labels~with~cleveref } }
-              { \__wi_error:n { Multiple~labels } }
-          }
-        \seq_put_right:Nn \l__wi_labels_seq { #1 }
-        \bool_if:nT \c__wi_mathtools_loaded_bool
-          {
-            \MH_if_boolean:nT { show_only_refs }
-              {
-                \cs_if_exist:cTF { MT_r_#1 }
-                  { \clist_set:Nn \l__wi_tags_clist { all } }
-                  { \clist_clear:N \l__wi_tags_clist }
-              }
-          }
-        \bool_if:nT \c__wi_autonum_loaded_bool
-          {
-            \cs_if_exist:cTF { autonum@#1Referenced }
-              { \clist_set:Nn \l__wi_tags_clist { all } }
-              { \clist_clear:N \l__wi_tags_clist }
-          }
-      }
-  }
-\cs_new_protected:Npn \__wi_tagnextline:
-  {
-    \__wi_if_in_last_col_of_disp:Nn \tagnextline
-      { \bool_set_true:N \l__wi_tag_next_line_bool }
-  }
-\cs_new_protected:Npn \__wi_qedhere: { \bool_set_true:N \l__wi_qedhere_bool }
-\cs_new_protected:Npn \__wi_set_qedhere: { \cs_set_eq:NN \qedhere \__wi_qedhere: }
-\cs_new_protected:Npn \__wi_qedhere_i:
-  {
-    \group_begin:
-      \cs_set_eq:NN \qed \qedsymbol
-      \cs_set_eq:NN \qed@elt \setQED@elt
-      \QED@stack \relax \relax
-    \group_end:
-  }
-\cs_new_protected:Npn \__wi_scan_arrows:
-  {
-    \group_begin:
-    \int_compare:nNnT \l__wi_pos_arrow_int = 7
-      {
-        \__wi_scan_arrows_i:
-        \int_set:Nn \l__wi_pos_arrow_int 8
-      }
-    \__wi_scan_arrows_i:
-    \group_end:
-  }
-\cs_new_protected:Npn \__wi_scan_arrows_i:
-  {
-    \int_zero_new:N \l__wi_first_arrow_of_group_int
-    \int_zero_new:N \l__wi_first_line_of_group_int
-    \int_zero_new:N \l__wi_last_line_of_group_int
-    \seq_clear_new:N \l__wi_first_arrows_seq
-    \seq_clear_new:N \l__wi_last_arrows_seq
-    \bool_set_true:N \l__wi_new_group_bool
-    \int_set:Nn \l__wi_arrow_int \c_one_int
-    \int_until_do:nNnn \l__wi_arrow_int > \g__wi_arrow_int
-      {
-        \prop_get:cnN
-          { g__wi_arrow _ \l__wi_prefix_str _ \int_use:N \l__wi_arrow_int _ prop }
-          { initial } \l_tmpa_tl
-        \int_set:Nn \l__wi_initial_int \l_tmpa_tl
-        \prop_get:cnN
-          { g__wi_arrow _ \l__wi_prefix_str _ \int_use:N \l__wi_arrow_int _ prop }
-          { final } \l_tmpa_tl
-        \int_set:Nn \l__wi_final_int \l_tmpa_tl
-        \prop_get:cnN
-          { g__wi_arrow _ \l__wi_prefix_str _ \int_use:N \l__wi_arrow_int _ prop }
-          { status } \l__wi_status_arrow_str
-        \prop_get:cnN
-          { g__wi_arrow _ \l__wi_prefix_str _ \int_use:N \l__wi_arrow_int _ prop }
-          { input-line } \l__wi_input_line_str
-        \int_compare:nNnTF \l__wi_final_int > \g__wi_line_int
-          {
-            \int_compare:nNnF \l__wi_pos_arrow_int = 8
-              { \__wi_error:n { Too~few~lines~for~an~arrow } }
-          }
-          \__wi_code_for_possible_arrow:
-        \int_incr:N \l__wi_arrow_int
-      }
-    \bool_if:nT
-      {
-        \int_compare_p:n { \l__wi_pos_arrow_int != 7 }
-          &&
-        \int_compare_p:nNn \l__wi_first_arrow_of_group_int > 0
-      }
-      { \__wi_draw_arrows:nn \l__wi_first_arrow_of_group_int \g__wi_arrow_int }
-  }
-\cs_new_protected:Npn \__wi_code_for_possible_arrow:
-  {
-    \bool_if:nT
-      {
-        \int_compare_p:nNn \l__wi_arrow_int > \c_one_int
-        &&
-       ( \int_compare_p:n { \l__wi_initial_int > \l__wi_last_line_of_group_int }
-           &&
-         \int_compare_p:n { \l__wi_pos_arrow_int != 7 }
-           ||
-         \str_if_eq_p:Vn \l__wi_status_arrow_str { new-group }
-       )
-      }
-      {
-        \int_compare:nNnF \l__wi_first_arrow_of_group_int = \c_zero_int
-          {
-            \__wi_draw_arrows:nn
-              \l__wi_first_arrow_of_group_int
-              { \l__wi_arrow_int - 1 }
-          }
-        \bool_set_true:N \l__wi_new_group_bool
-      }
-    \bool_if:nTF \l__wi_new_group_bool
-      {
-        \bool_set_false:N \l__wi_new_group_bool
-        \int_set_eq:NN \l__wi_first_arrow_of_group_int \l__wi_arrow_int
-        \int_set_eq:NN \l__wi_first_line_of_group_int \l__wi_initial_int
-        \int_set_eq:NN \l__wi_last_line_of_group_int \l__wi_final_int
-        \seq_clear:N \l__wi_first_arrows_seq
-        \seq_put_left:NV \l__wi_first_arrows_seq \l__wi_arrow_int
-        \seq_clear:N \l__wi_last_arrows_seq
-        \seq_put_left:NV \l__wi_last_arrows_seq \l__wi_arrow_int
-        \int_compare:nT { \l__wi_pos_arrow_int != 8 }
-          { \dim_set:Nn \l__wi_x_dim { - \c_max_dim } }
-      }
-      {
-        \bool_if:nF
-          { \str_if_eq_p:Vn \l__wi_status_arrow_str { independent } }
-          {
-            \int_compare:nT
-              { \l__wi_initial_int = \l__wi_first_line_of_group_int }
-              { \seq_put_left:NV \l__wi_first_arrows_seq \l__wi_arrow_int }
-            \int_compare:nNnTF \l__wi_final_int > \l__wi_last_line_of_group_int
-              {
-                \int_set_eq:NN \l__wi_last_line_of_group_int \l__wi_final_int
-                \seq_clear:N \l__wi_last_arrows_seq
-                \seq_put_left:NV \l__wi_last_arrows_seq \l__wi_arrow_int
-              }
-              {
-                \int_compare:nNnT \l__wi_final_int = \l__wi_last_line_of_group_int
-                  { \seq_put_left:NV \l__wi_last_arrows_seq \l__wi_arrow_int }
-              }
-          }
-      }
-    \bool_if:nF { \str_if_eq_p:Vn \l__wi_status_arrow_str { independent } }
-      {
-        \int_compare:nT { \l__wi_pos_arrow_int != 8 }
-          { \__wi_update_x:nn \l__wi_initial_int \l__wi_final_int }
-      }
-  }
-\cs_generate_variant:Nn \keys_set:nn { n o }
-\cs_new_protected:Npn \__wi_keys_set:
-  { \keys_set_known:no { WithArrows / Arrow / SecondPass } }
-\cs_new_protected:Npn \__wi_draw_arrows:nn #1 #2
-  {
-    \group_begin:
-    \int_zero_new:N \l__wi_first_arrow_int
-    \int_set:Nn \l__wi_first_arrow_int { #1 }
-    \int_zero_new:N \l__wi_last_arrow_int
-    \int_set:Nn \l__wi_last_arrow_int { #2 }
-    \int_set:Nn \l__wi_arrow_int \l__wi_first_arrow_int
-    \int_until_do:nNnn \l__wi_arrow_int > \l__wi_last_arrow_int
-      {
-        \prop_get:cnN
-          { g__wi_arrow _ \l__wi_prefix_str _ \int_use:N \l__wi_arrow_int _ prop }
-          { initial } \l_tmpa_tl
-        \int_set:Nn \l__wi_initial_int \l_tmpa_tl
-        \prop_get:cnN
-          { g__wi_arrow _ \l__wi_prefix_str _ \int_use:N \l__wi_arrow_int _ prop }
-          { final } \l_tmpa_tl
-        \int_set:Nn \l__wi_final_int \l_tmpa_tl
-        \int_compare:nT { \l__wi_final_int <= \g__wi_line_int } \__wi_draw_arrows_i:
-        \int_incr:N \l__wi_arrow_int
-      }
-    \group_end:
-  }
-\cs_new_protected:Npn \__wi_draw_arrows_i:
-  {
-    \group_begin:
-    \prop_get:cnN
-      { g__wi_arrow _\l__wi_prefix_str _ \int_use:N \l__wi_arrow_int _ prop }
-      { options } \l_tmpa_tl
-    \str_clear_new:N \l__wi_previous_key_str
-    \exp_args:NNo \exp_args:No
-    \__wi_keys_set: { \l_tmpa_tl , tikz = { xshift = \l__wi_xoffset_dim } }
-    \bool_set_false:N \l__wi_initial_r_bool
-    \bool_set_false:N \l__wi_final_r_bool
-    \int_case:nn \l__wi_pos_arrow_int
-      {
-        0 { \bool_set_true:N \l__wi_final_r_bool }
-        2 { \bool_set_true:N \l__wi_initial_r_bool }
-        3
-          {
-            \bool_set_true:N \l__wi_initial_r_bool
-            \bool_set_true:N \l__wi_final_r_bool
-          }
-      }
-    \int_compare:nNnT \l__wi_pos_arrow_int = 5
-      {
-        \dim_set:Nn \l__wi_x_dim { - \c_max_dim }
-        \__wi_update_x:nn \l__wi_initial_int \l__wi_final_int
-      }
-    \tl_set:Nx \l__wi_initial_tl
-      {
-        \int_use:N \l__wi_initial_int - \bool_if:NTF \l__wi_initial_r_bool rl
-        .south
-      }
-    \tl_set:Nx \l__wi_final_tl
-      { \int_use:N \l__wi_final_int - \bool_if:NTF \l__wi_final_r_bool rl .north }
-    \prop_get:cnN
-      { g__wi_arrow _ \l__wi_prefix_str _ \int_use:N \l__wi_arrow_int _ prop }
-      { label }
-      \l_tmpa_tl
-    \seq_if_in:NxTF \l__wi_first_arrows_seq
-      { \int_use:N \l__wi_arrow_int }
-      { \bool_set_true:N \l_tmpa_bool }
-      { \bool_set_false:N \l_tmpa_bool }
-    \seq_if_in:NxTF \l__wi_last_arrows_seq
-      { \int_use:N \l__wi_arrow_int }
-      { \bool_set_true:N \l_tmpb_bool }
-      { \bool_set_false:N \l_tmpb_bool }
-    \int_compare:nNnT \l__wi_pos_arrow_int = 5
-      {
-        \bool_set_true:N \l_tmpa_bool
-        \bool_set_true:N \l_tmpb_bool
-      }
-    \begin { tikzpicture } [ __wi_standard ]
-      \tikz@scan@one@point \pgfutil@firstofone ( \l__wi_initial_tl )
-      \tl_gset:Nx \g_tmpa_tl
-        {
-          \int_compare:nNnTF \l__wi_pos_arrow_int < 5
-            { \dim_use:N \pgf@x }
-            { \dim_use:N \l__wi_x_dim } ,
-          \bool_if:NTF \l_tmpa_bool
-            { \dim_eval:n { \pgf@y + \l__wi_start_adjust_dim } }
-            { \dim_use:N \pgf@y }
-        }
-      \tikz@scan@one@point \pgfutil@firstofone ( \l__wi_final_tl )
-      \tl_gset:Nx \g_tmpb_tl
-        {
-          \int_compare:nNnTF \l__wi_pos_arrow_int < 5
-            { \dim_use:N \pgf@x }
-            { \dim_use:N \l__wi_x_dim } ,
-          \bool_if:NTF \l_tmpb_bool
-            { \dim_eval:n { \pgf@y - \l__wi_end_adjust_dim } }
-            { \dim_use:N \pgf@y }
-        }
-    \end { tikzpicture }
-    \__wi_draw_arrow:nno \g_tmpa_tl \g_tmpb_tl \l_tmpa_tl
-    \group_end:
-  }
-\cs_new_protected:Npn \__wi_def_function_tmpa:n #1
-  {
-    \cs_set:Npn \__wi_tmpa:nnn ##1 ##2 ##3
-      {
-        \begin{tikzpicture}
-          [
-            __wi_standard ,
-            every~path / .style = WithArrows / arrow
-          ]
-          #1
-        \end{tikzpicture}
-      }
-  }
-\cs_new_protected:Npn \__wi_draw_arrow:nnn #1 #2 #3
-  {
-    \bool_if:nT { \l__wi_wrap_lines_bool && \l__wi_in_DispWithArrows_bool }
-       { \tl_set_eq:NN \l__wi_tikz_code_tl \c__wi_tikz_code_wrap_lines_tl }
-    \exp_args:NV \__wi_def_function_tmpa:n \l__wi_tikz_code_tl
-    \__wi_tmpa:nnn { #1 } { #2 } { #3 }
-  }
-\cs_generate_variant:Nn \__wi_draw_arrow:nnn { n n o }
-\tl_const:Nn \c__wi_tikz_code_wrap_lines_tl
-  {
-    \draw ( #1 ) to node ( __wi_label ) { } ( #2 ) ;
-    \tikz@parse@node \pgfutil@firstofone ( __wi_label.west )
-    \dim_set:Nn \l_tmpa_dim
-      { \g__wi_right_x_dim - \pgf@x - \pgfkeysvalueof { / pgf / inner~xsep } }
-    \path \pgfextra { \tl_gset:Nx \g_tmpa_tl \tikz@text@width } ;
-    \tl_if_empty:NF \g_tmpa_tl
-      {
-        \dim_set:Nn \l_tmpb_dim \g_tmpa_tl
-        \dim_compare:nNnT \l_tmpb_dim < \l_tmpa_dim
-          { \dim_set_eq:NN \l_tmpa_dim \l_tmpb_dim }
-      }
-    \dim_compare:nNnT \l_tmpa_dim > \c_zero_dim
-      {
-        \path ( __wi_label.west )
-           node [ anchor = west , text~width = \dim_use:N \l_tmpa_dim ]
-                { #3 } ;
-      }
-  }
-\cs_new_protected:Npn \__wi_update_x:nn #1 #2
-  {
-    \int_step_inline:nnn { #1 } { #2 }
-      {
-        \begin { tikzpicture } [ __wi_standard ]
-          \tikz@scan@one@point \pgfutil@firstofone ( ##1 - l )
-          \dim_gset:Nn \g_tmpa_dim { \dim_max:nn \l__wi_x_dim \pgf@x }
-        \end { tikzpicture }
-        \dim_set_eq:NN \l__wi_x_dim \g_tmpa_dim
-      }
-  }
-\cs_new:Npn \WithArrowsLastEnv { \int_use:N \g__wi_last_env_int }
-\keys_define:nn { WithArrows / Arrow / code-after }
-  {
-    tikz     .code:n =
-      \tikzset { WithArrows / arrow / .append~style = { #1 } } ,
-    tikz     .value_required:n  = true ,
-    rr       .value_forbidden:n = true ,
-    rr       .code:n            = \__wi_fix_pos_option:n 0 ,
-    ll       .value_forbidden:n = true,
-    ll       .code:n            = \__wi_fix_pos_option:n 1 ,
-    rl       .value_forbidden:n = true ,
-    rl       .code:n            = \__wi_fix_pos_option:n 2 ,
-    lr       .value_forbidden:n = true ,
-    lr       .code:n            = \__wi_fix_pos_option:n 3 ,
-    v        .value_forbidden:n = true ,
-    v        .code:n            = \__wi_fix_pos_option:n 4 ,
-    tikz-code .tl_set:N          = \l__wi_tikz_code_tl ,
-    tikz-code .value_required:n  = true ,
-    xoffset  .dim_set:N         = \l__wi_xoffset_dim ,
-    xoffset  .value_required:n  = true ,
-    unknown .code:n  =
-      \__wi_sort_seq:N \l__wi_options_Arrow_code_after_seq
-      \__wi_error:n { Unknown~option~Arrow~in~code-after }
-  }
-\seq_new:N \l__wi_options_Arrow_code_after_seq
-\__wi_set_seq_of_str_from_clist:Nn \l__wi_options_Arrow_code_after_seq
-  { ll, lr, rl, rr, tikz, tikz-code, v, x, offset }
-\NewDocumentCommand \__wi_Arrow_code_after { O { } m m m ! O { } }
-  {
-    \int_set:Nn \l__wi_pos_arrow_int 1
-    \str_clear_new:N \l__wi_previous_key_str
-    \group_begin:
-      \keys_set:nn { WithArrows / Arrow / code-after }
-        { #1, #5, tikz = { xshift = \l__wi_xoffset_dim } }
-      \bool_set_false:N \l__wi_initial_r_bool
-      \bool_set_false:N \l__wi_final_r_bool
-      \int_case:nn \l__wi_pos_arrow_int
-        {
-          0
-            {
-              \bool_set_true:N \l__wi_initial_r_bool
-              \bool_set_true:N \l__wi_final_r_bool
-            }
-          2 { \bool_set_true:N \l__wi_initial_r_bool }
-          3 { \bool_set_true:N \l__wi_final_r_bool }
-        }
-      \tl_if_eq:nnTF { #2 } { #3 }
-        { \__wi_error:nn { Both~lines~are~equal } { #2 } }
-        {
-          \cs_if_free:cTF { pgf@sh@ns@wa - \l__wi_prefix_str - #2 - l }
-            { \__wi_error:nx { Wrong~line~in~Arrow } { #2 } }
-            {
-              \cs_if_free:cTF { pgf@sh@ns@wa - \l__wi_prefix_str - #3 - l }
-                { \__wi_error:nx { Wrong~line~in~Arrow } { #3 }  }
-                {
-                  \int_compare:nNnTF \l__wi_pos_arrow_int = 4
-                    {
-                      \begin { tikzpicture } [ __wi_standard ]
-                        \tikz@scan@one@point \pgfutil@firstofone (#2-l.south)
-                        \dim_set_eq:NN \l_tmpa_dim \pgf@x
-                        \dim_set_eq:NN \l_tmpb_dim \pgf@y
-                        \tikz@scan@one@point \pgfutil@firstofone (#3-l.north)
-                        \dim_set:Nn \l_tmpa_dim
-                          { \dim_max:nn \l_tmpa_dim \pgf@x }
-                        \tl_gset:Nx \g_tmpa_tl
-                          { \dim_use:N \l_tmpa_dim , \dim_use:N \l_tmpb_dim }
-                        \tl_gset:Nx \g_tmpb_tl
-                          { \dim_use:N \l_tmpa_dim , \dim_use:N \pgf@y }
-                      \end { tikzpicture }
-                    }
-                    {
-                      \begin { tikzpicture } [ __wi_standard ]
-                        \tikz@scan@one@point \pgfutil@firstofone
-                           ( #2-\bool_if:NTF\l__wi_initial_r_bool rl .south )
-                        \tl_gset:Nx \g_tmpa_tl
-                           { \dim_use:N \pgf@x , \dim_use:N \pgf@y }
-                        \tikz@scan@one@point \pgfutil@firstofone
-                           ( #3-\bool_if:NTF\l__wi_final_r_bool rl .north )
-                        \tl_gset:Nx \g_tmpb_tl
-                           { \dim_use:N \pgf@x , \dim_use:N \pgf@y }
-                      \end { tikzpicture }
-                    }
-                  \__wi_draw_arrow:nnn \g_tmpa_tl \g_tmpb_tl { #4 }
-                }
-            }
-        }
-    \group_end:
-  }
-\cs_new_protected:Npn \__wi_MultiArrow:nn #1 #2
-  {
-    \foreach \x in { #1 }
-      {
-        \cs_if_free:cTF { pgf@sh@ns@wa - \l__wi_prefix_str - \x - l }
-           { \__wi_error:nx { Wrong~line~specification~in~MultiArrow } \x }
-           { \clist_gput_right:Nx \g_tmpa_clist \x }
-      }
-    \int_compare:nTF { \clist_count:N \g_tmpa_clist < 2 }
-      { \__wi_error:n { Too~small~specification~for~MultiArrow } }
-      {
-        \clist_sort:Nn \g_tmpa_clist
-          {
-            \int_compare:nTF { ##1 > ##2 }
-              \sort_return_swapped:
-              \sort_return_same:
-          }
-        \clist_pop:NN \g_tmpa_clist \l_tmpa_tl
-        \clist_reverse:N \g_tmpa_clist
-        \clist_pop:NN \g_tmpa_clist \l_tmpb_tl
-        \exp_args:NV \__wi_MultiArrow_i:n \g_tmpa_clist
-        \begin { tikzpicture }
-          [
-            __wi_standard ,
-            every~path / .style = { WithArrows / arrow }
-          ]
-          \draw [<->] ([xshift = \l__wi_xoffset_dim]\l_tmpa_tl-r.south)
-                      -- ++(5mm,0)
-                      -- node (__wi_label) {}
-                         ([xshift = \l__wi_xoffset_dim+5mm]\l_tmpb_tl-r.south)
-                      -- ([xshift = \l__wi_xoffset_dim]\l_tmpb_tl-r.south)  ;
-          \tikz@parse@node \pgfutil@firstofone (__wi_label.west)
-          \dim_set:Nn \l_tmpa_dim { 20 cm }
-          \path \pgfextra { \tl_gset:Nx \g_tmpa_tl \tikz@text@width } ;
-          \tl_if_empty:NF \g_tmpa_tl { \dim_set:Nn \l_tmpa_dim \g_tmpa_tl }
-          \bool_if:nT { \l__wi_wrap_lines_bool && \l__wi_in_DispWithArrows_bool }
-            {
-              \dim_set:Nn \l_tmpb_dim
-                { \g__wi_right_x_dim - \pgf@x - 0.3333 em }
-              \dim_compare:nNnT \l_tmpb_dim < \l_tmpa_dim
-                { \dim_set_eq:NN \l_tmpa_dim \l_tmpb_dim }
-            }
-          \path (__wi_label.west)
-           node [ anchor = west, text~width = \dim_use:N \l_tmpa_dim ] { #2 } ;
-        \end{tikzpicture}
-      }
-  }
-\cs_new_protected:Npn \__wi_MultiArrow_i:n #1
-  {
-    \begin {tikzpicture }
-      [
-        __wi_standard ,
-        every~path / .style = { WithArrows / arrow }
-      ]
-      \foreach \k in { #1 }
-        {
-          \draw [ <- ]
-            ( [xshift = \l__wi_xoffset_dim]\k-r.south ) -- ++(5mm,0) ;
-        } ;
-    \end { tikzpicture }
-  }
-\str_const:Nn \c__wi_option_ignored_str
-  { If~you~go~on,~this~option~will~be~ignored. }
-\str_const:Nn \c__wi_command_ignored_str
-  { If~you~go~on,~this~command~will~be~ignored. }
-\__wi_msg_new:nn { amsmath~not~loaded }
-  {
-    You~can't~use~the~option~'\l_keys_key_tl'~because~the~
-    package~'amsmath'~has~not~been~loaded.\\
-    If~you~go~on,~this~option~will~be~ignored~in~the~rest~
-    of~the~document.
-  }
-\__wi_msg_new:nn { Bad~value~for~replace~brace~by }
-  {
-    Bad~value~for~the~option~'\l_keys_key_tl'.~The~value~must~be~
-    an~extensible~left~delimiter.~The~possible~values~are:~
-    \token_to_str:N \{,~(,~[,~\token_to_str:N \lbrace,~
-    \token_to_str:N \lbrack,~\token_to_str:N \lgroup,~
-    \token_to_str:N \langle,~\token_to_str:N \lmoustache,~
-    \token_to_str:N \lfloor\ and~\token_to_str:N \lceil\
-    (and~\token_to_str:N \lvert\ and~\token_to_str:N \lVert\
-    if~amsmath~or~unicode-math~is~loaded).\\
-    \c__wi_option_ignored_str
-  }
-\__wi_msg_new:nn { option~of~cr~negative }
-  {
-    The~argument~of~the~command~\token_to_str:N\\~
-    should~be~positive~in~the~row~\int_use:N \g__wi_line_int\
-    of~your~environment~\{\l__wi_type_env_str\}.\\
-    \c__wi_option_ignored_str
-  }
-\__wi_msg_new:nn { omit~probably~used }
-  {
-    There~is~a~problem.~Maybe~you~have~used~a~command~
-    \token_to_str:N\omit\ in~the~line~\int_use:N \g__wi_line_int\
-    (or~another~line)~of~your~environment~\{\l__wi_type_env_str\}.\\
-    You~can~go~on~but~you~may~have~others~errors.
-  }
-\__wi_msg_new:nn { newline~at~the~end~of~env }
-  {
-    Your~environment~\{\l__wi_type_env_str\}~should~not~end~with~
-    a~\token_to_str:N \\.\\
-    This~warning~might~become~an~error~in~a~future~version.
-  }
-\__wi_msg_new:nn { Invalid~option~format }
-  {
-    The~key~'format'~should~contain~only~letters~r,~c~and~l~and~
-    must~not~be~empty.\\
-    \c__wi_option_ignored_str
-  }
-\__wi_msg_new:nn { Value~for~a~key }
-  {
-    The~key~'\l_keys_key_tl'~should~be~used~without~value. \\
-    However,~you~can~go~on~for~this~time.
-  }
-\__wi_msg_new:nnn { Unknown~option~in~Arrow }
-  {
-    The~key~'\l_keys_key_tl'~is~unknown~for~the~command~
-    \l__wi_string_Arrow_for_msg_str\ in~the~row~
-    \int_use:N \g__wi_line_int\ of~your~environment~
-    \{\l__wi_type_env_str\}. \l_tmpa_str \\
-    \c__wi_option_ignored_str \\
-    For~a~list~of~the~available~keys,~type~H~<return>.
-  }
-  {
-    The~available~keys~are~(in~alphabetic~order):~
-    \seq_use:Nnnn \l__wi_options_Arrow_seq {~and~} {,~} {~and~}.
-  }
-\__wi_msg_new:nnn { Unknown~option~WithArrows }
-  {
-    The~key~'\l_keys_key_tl'~is~unknown~in~\{\l__wi_type_env_str\}. \\
-    \c__wi_option_ignored_str \\
-    For~a~list~of~the~available~keys,~type~H~<return>.
-  }
-  {
-    The~available~keys~are~(in~alphabetic~order):~
-    \seq_use:Nnnn \l__wi_options_WithArrows_seq {~and~} {,~} {~and~}.
-  }
-\__wi_msg_new:nnn { Unknown~option~DispWithArrows }
-  {
-    The~key~'\l_keys_key_tl'~is~unknown~in~\{\l__wi_type_env_str\}. \\
-    \c__wi_option_ignored_str \\
-    For~a~list~of~the~available~keys,~type~H~<return>.
-  }
-  {
-    The~available~keys~are~(in~alphabetic~order):~
-    \seq_use:Nnnn \l__wi_options_DispWithArrows_seq {~and~} {,~} {~and~}.
-  }
-\__wi_msg_new:nnn { Unknown~option~WithArrowsOptions }
-  {
-    The~key~'\l_keys_key_tl'~is~unknown~in~
-    \token_to_str:N \WithArrowsOptions. \\
-    \c__wi_option_ignored_str \\
-    For~a~list~of~the~available~keys,~type~H~<return>.
-  }
-  {
-    The~available~keys~are~(in~alphabetic~order):~
-    \seq_use:Nnnn \l__wi_options_WithArrowsOptions_seq {~and~} {,~} {~and~}.
-  }
-\__wi_msg_new:nnn { Unknown~option~Arrow~in~code-after }
-  {
-    The~key~'\l_keys_key_tl'~is~unknown~in~
-    \token_to_str:N \Arrow\ in~code-after. \\
-    \c__wi_option_ignored_str \\
-    For~a~list~of~the~available~keys,~type~H~<return>.
-  }
-  {
-    The~available~keys~are~(in~alphabetic~order):~
-    \seq_use:Nnnn \l__wi_options_Arrow_code_after_seq {~and~} {,~} {~and~}.
-  }
-\__wi_msg_new:nn { Too~much~columns~in~WithArrows }
-  {
-    Your~environment~\{\l__wi_type_env_str\}~has~\int_use:N
-    \l__wi_nb_cols_int\ columns~and~you~try~to~use~one~more.~
-    Maybe~you~have~forgotten~a~\c_backslash_str\c_backslash_str.~
-    If~you~really~want~to~use~more~columns~(after~the~arrows)~you~should~use~
-    the~option~'more-columns'~at~a~global~level~or~for~an~environment. \\
-    However,~you~can~go~one~for~this~time.
-  }
-\__wi_msg_new:nn { Too~much~columns~in~DispWithArrows }
-  {
-    Your~environment~\{\l__wi_type_env_str\}~has~\int_use:N
-    \l__wi_nb_cols_int\ columns~and~you~try~to~use~one~more.~
-    Maybe~you~have~forgotten~a~\c_backslash_str\c_backslash_str\
-    at~the~end~of~row~\int_use:N \g__wi_line_int. \\
-    This~error~is~fatal.
-  }
-\__wi_msg_new:nn { Negative~jump }
-  {
-    You~can't~use~a~negative~value~for~the~option~'jump'~of~command~
-    \l__wi_string_Arrow_for_msg_str\
-    in~the~row~\int_use:N \g__wi_line_int\
-    of~your~environment~\{\l__wi_type_env_str\}.~
-    You~can~create~an~arrow~going~backwards~with~the~option~'<-'~of~Tikz. \\
-    \c__wi_option_ignored_str
-  }
-\__wi_msg_new:nn { new-group~without~groups }
-  {
-    You~can't~use~the~option~'new-group'~for~the~command~
-    \l__wi_string_Arrow_for_msg_str\
-    because~you~are~not~in~'groups'~mode.~Try~to~use~the~option~
-    'groups'~in~your~environment~\{\l__wi_type_env_str\}. \\
-    \c__wi_option_ignored_str
-  }
-\__wi_msg_new:nn
-  { Too~few~lines~for~an~arrow }
-  {
-    Line~\l__wi_input_line_str\
-    :~an~arrow~specified~in~the~row~\int_use:N \l__wi_initial_int\
-    of~your~environment~\{\l__wi_type_env_str\}~can't~be~drawn~
-    because~it~arrives~after~the~last~row~of~the~environment. \\
-    If~you~go~on,~this~arrow~will~be~ignored.
-  }
-\__wi_msg_new:nn { WithArrows~outside~math~mode }
-  {
-    The~environment~\{\l__wi_type_env_str\}~should~be~used~only~in~math~mode~
-    like~the~environment~\{aligned\}~of~amsmath. \\
-    Nevertheless,~you~can~go~on.
-  }
-\__wi_msg_new:nn { DispWithArrows~in~math~mode }
-  {
-    The~environment~\{\l__wi_type_env_str\}~should~be~used~only~outside~math~
-    mode~like~the~environment~\{align\}~of~amsmath. \\
-    This~error~is~fatal.
-  }
-\__wi_msg_new:nn { Incompatible~options~in~Arrow }
-  {
-    You~try~to~use~the~option~'\l_keys_key_tl'~but~
-    this~option~is~incompatible~or~redundant~with~the~option~
-    '\l__wi_previous_key_str'~set~in~the~same~command~
-    \l__wi_string_Arrow_for_msg_str. \\
-    \c__wi_option_ignored_str
-  }
-\__wi_msg_new:nn { Incompatible~options }
-  { You~try~to~use~the~option~'\l_keys_key_tl'~but~
-    this~option~is~incompatible~or~redundant~with~the~option~
-    '\l__wi_previous_key_str'~set~in~the~same~command~
-    \bool_if:NT \l__wi_in_code_after_bool
-      {
-        \l__wi_string_Arrow_for_msg_str\
-        in~the~code-after~of~your~environment~\{\l__wi_type_env_str\}
-      }. \\
-    \c__wi_option_ignored_str
-  }
-\__wi_msg_new:nn { Arrow~not~in~last~column }
-  {
-    You~should~use~the~command~\l__wi_string_Arrow_for_msg_str\
-    only~in~the~last~column~(column~\int_use:N\l__wi_nb_cols_int)~
-    of~your~environment~\{\l__wi_type_env_str\}.\\
-    However~you~can~go~on~for~this~time.
-  }
-\__wi_msg_new:nn { Wrong~line~in~Arrow }
-  {
-    The~specification~of~line~'#1'~you~use~in~the~command~
-    \l__wi_string_Arrow_for_msg_str\
-    in~the~'code-after'~of~\{\l__wi_type_env_str\}~doesn't~exist. \\
-    \c__wi_option_ignored_str
-  }
-\__wi_msg_new:nn { Both~lines~are~equal }
-  {
-    In~the~'code-after'~of~\{\l__wi_type_env_str\}~you~try~to~
-    draw~an~arrow~going~to~it~self~from~the~line~'#1'.~This~is~not~possible. \\
-    \c__wi_option_ignored_str
-  }
-\__wi_msg_new:nn { Wrong~line~specification~in~MultiArrow }
-  {
-    The~specification~of~line~'#1'~doesn't~exist. \\
-    If~you~go~on,~it~will~be~ignored~for~\token_to_str:N \MultiArrow.
-  }
-\__wi_msg_new:nn { Too~small~specification~for~MultiArrow }
-  {
-    The~specification~of~lines~you~gave~to~\token_to_str:N \MultiArrow\
-    is~too~small:~you~need~at~least~two~lines. \\
-    \c__wi_option_ignored_str
-  }
-\__wi_msg_new:nn { tag*~without~amsmath }
-  {
-    We~can't~use~\token_to_str:N\tag*~because~you~haven't~loaded~amsmath~
-    (or~mathtools). \\
-    If~you~go~on,~the~command~\token_to_str:N\tag\
-    will~be~used~instead.
-  }
-\__wi_msg_new:nn { Not~allowed~in~DispWithArrows }
-  {
-    The~command~\token_to_str:N #1
-    is~allowed~only~in~the~last~column~
-    (column~\int_use:N\l__wi_nb_cols_int)~of~\{\l__wi_type_env_str\}. \\
-    \c__wi_option_ignored_str
-  }
-\__wi_msg_new:nn { Not~allowed~in~WithArrows }
-  {
-    The~command~\token_to_str:N #1 is~not~allowed~in~\{\l__wi_type_env_str\}~
-    (it's~allowed~in~the~last~column~of~\{DispWithArrows\}). \\
-    \c__wi_option_ignored_str
-  }
-\__wi_msg_new:nn { Multiple~tags }
-  {
-    You~can't~use~twice~the~command~\token_to_str:N\tag\
-    in~a~line~of~the~environment~\{\l__wi_type_env_str\}. \\
-    If~you~go~on,~the~tag~'#1'~will~be~used.
-  }
-\__wi_msg_new:nn { Multiple~labels }
-  {
-    Normally,~we~can't~use~the~command~\token_to_str:N\label\
-    twice~in~a~line~of~the~environment~\{\l__wi_type_env_str\}. \\
-    However,~you~can~go~on.~
-    \bool_if:NT \c__wi_showlabels_loaded_bool
-      { However,~only~the~last~label~will~be~shown~by~showlabels.~ }
-    If~you~don't~want~to~see~this~message~again,~you~can~use~the~option~
-    'allow-multiple-labels'~at~the~global~or~environment~level.
-  }
-\__wi_msg_new:nn { Multiple~labels~with~cleveref }
-  {
-    Since~you~use~cleveref,~you~can't~use~the~command~\token_to_str:N\label\
-    twice~in~a~line~of~the~environment~\{\l__wi_type_env_str\}. \\
-    If~you~go~on,~you~may~have~undefined~references.
-  }
-\__wi_msg_new:nn { Inexistent~v-node }
-  {
-    There~is~a~problem.~Maybe~you~have~put~a~command~\token_to_str:N\cr\
-    instead~of~a~command~\token_to_str:N\\~at~the~end~of~
-    the~row~\l_tmpa_int\
-    of~your~environment~\{\l__wi_type_env_str\}. \\
-    This~error~is~fatal.
-  }
-\__wi_msg_new:nn { Option~xoffset~forbidden }
-  {
-    You~can't~use~the~option~'xoffset'~in~the~command~
-    \l__wi_string_Arrow_for_msg_str\
-    while~you~are~using~the~option~
-    ' \int_compare:nNnTF \l__wi_pos_arrow_int = 7
-        { group }
-        { groups } '. \\
-    \c__wi_option_ignored_str
-  }
-\__wi_msg_new:nnn { Duplicate~name }
-  {
-    The~name~'\l_keys_value_tl'~is~already~used~and~you~shouldn't~use~
-    the~same~environment~name~twice.~You~can~go~on,~but,~
-    maybe,~you~will~have~incorrect~results. \\
-    For~a~list~of~the~names~already~used,~type~H~<return>. \\
-    If~you~don't~want~to~see~this~message~again,~use~the~option~
-    'allow-duplicate-names'.
-  }
-  {
-    The~names~already~defined~in~this~document~are:~
-    \seq_use:Nnnn \g__wi_names_seq { ,~ } { ,~ } { ~and~ }.
-  }
-\NewDocumentCommand \WithArrowsNewStyle { m m }
-  {
-    \keys_if_exist:nnTF { WithArrows / Global } { #1 }
-      { \__wi_error:nn { Key~already~defined } { #1 } }
-      {
-        \keys_define:nn { WithArrows / Global }
-          {
-            #1 .code:n =
-             { \keys_set_known:nn { WithArrows / WithArrowsOptions } { #2 } }
-          }
-        \seq_put_right:Nx \l__wi_options_WithArrows_seq { \tl_to_str:n { #1 } }
-        \seq_put_right:Nx \l__wi_options_DispWithArrows_seq
-          { \tl_to_str:n { #1 } }
-        \seq_put_right:Nx \l__wi_options_WithArrowsOptions_seq
-          { \tl_to_str:N { #1 } }
-        \group_begin:
-          \msg_set:nnn { witharrows } { Unknown~option~WithArrowsOptions }
-            {
-              The~key~'\l_keys_key_tl'~can't~be~set~in~the~
-              definition~of~a~style.~You~can~go~on~for~this~time~
-              but~you~should~suppress~this~key.
-            }
-          \WithArrowsOptions { #2 }
-        \group_end:
-      }
-  }
-\__wi_msg_new:nn { Key~already~defined }
-  {
-    The~key~'#1'~is~already~defined. \\
-    If~you~go~on,~your~instruction~\token_to_str:N\WithArrowsNewStyle\
-    will~be~ignored.
-  }
-\tl_const:Nn \c__wi_tikz_code_up_tl
-  {
-    \draw [ rounded~corners ]
-       let \p1 = (#1) ,
-           \p2 = (#2)
-       in (\p1) -- node {
-                          \dim_set:Nn \l_tmpa_dim { \x2 - \x1 }
-                          \begin { varwidth } \l_tmpa_dim
-                            \raggedright
-                            #3
-                          \end { varwidth }
-                        }
-          (\x2,\y1) -- (\p2) ;
-  }
-\tl_const:Nn \c__wi_tikz_code_down_tl
-  {
-    \draw [ rounded~corners ]
-      let \p1 = (#1) ,
-          \p2 = (#2)
-      in (\p1) -- (\x1,\y2) --
-               node {
-                      \dim_set:Nn \l_tmpa_dim { \x1 - \x2 }
-                      \begin { varwidth } \l_tmpa_dim
-                        \raggedright
-                        #3
-                      \end { varwidth }
-                    }
-               (\p2) ;
-  }
-\keys_define:nn { WithArrows / Arrow / FirstPass }
-  {
-    up   .code:n = \__wi_set_independent: ,
-    down .code:n = \__wi_set_independent: ,
-    up   .default:n = NoValue ,
-    down .default:n = NoValue
-  }
-\keys_define:nn { WithArrows / Arrow / SecondPass }
-  {
-    up .code:n =
-      \str_if_empty:NT \l__wi_previous_key_str
-        {
-          \str_set:Nn \l__wi_previous_key_str { up }
-          \bool_if:NTF \c__wi_varwidth_loaded_bool
-            {
-              \cs_if_exist:cTF { tikz@library@calc@loaded }
-                {
-                  \int_set:Nn \l__wi_pos_arrow_int \c_one_int
-                  \bool_set_false:N \l__wi_wrap_lines_bool
-                  \tl_set_eq:NN \l__wi_tikz_code_tl
-                    \c__wi_tikz_code_up_tl
-                }
-                { \__wi_error:n { calc~not~loaded } }
-            }
-            { \__wi_error:n { varwidth~not~loaded } }
-        } ,
-    down .code:n =
-      \str_if_empty:NT \l__wi_previous_key_str
-        {
-          \str_set:Nn \l__wi_previous_key_str { down }
-          \bool_if:NTF \c__wi_varwidth_loaded_bool
-            {
-              \cs_if_exist:cTF { tikz@library@calc@loaded }
-                {
-                  \int_set:Nn \l__wi_pos_arrow_int \c_one_int
-                  \bool_set_false:N \l__wi_wrap_lines_bool
-                  \tl_set_eq:NN \l__wi_tikz_code_tl
-                    \c__wi_tikz_code_down_tl
-                }
-                { \__wi_error:n { calc~not~loaded } }
-            }
-            { \__wi_error:n { varwidth~not~loaded } }
-        }
-  }
-\seq_put_right:Nn \l__wi_options_Arrow_seq { down }
-\seq_put_right:Nn \l__wi_options_Arrow_seq { up }
-\__wi_msg_new:nn { varwidth~not~loaded }
-  {
-    You~can't~use~the~option~'\l_keys_key_tl'~because~
-    you~don't~have~loaded~the~package~'varwidth'. \\
-    \c__wi_option_ignored_str
-  }
-\__wi_msg_new:nn { calc~not~loaded }
-  {
-    You~can't~use~the~option~'\l_keys_key_tl'~because~you~don't~have~loaded~the~
-    Tikz~library~'calc'.You~should~add~'\token_to_str:N\usetikzlibrary{calc}'
-    ~in~the~preamble~of~your~document. \\
-    \c__wi_option_ignored_str
-  }
-\endinput
-%%
-%% End of file `witharrows.sty'.