Labelled mapsto with two vertical bars

Question

I would like to use a labeled mapsto (specifically, \xmapsto from \usepackage{mathtools}), but with two vertical bars (as in \Vdash from \usepackage{amsmath,amssymb}).

I tried to adapt the answer from here, but I cannot seem to align the additional vertical line correctly (see below).

What is the correct way to do this? My goal is to have something like the last command in the figures, but with both vertical lines at the same height, and of the same length.

\documentclass[a4paper]{article}

\usepackage[english]{babel}

\usepackage{mathtools}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{trimclip,adjustbox}

\newcommand{\XmapstoA}[1]{%
  \mathrel{\text{\clipbox{0pt {0.40\height} {.8\width} 0pt}{$\Vdash$}}\mkern.9mu}\xmapsto{#1}
}

\newcommand{\XmapstoB}[1]{%
  \mathrel{
    \text{\clipbox{0pt 0pt {.8\width} 0pt}{$\Vdash$}}
    \mkern.9mu
    \text{\adjustbox{width=.87\width,height=\height}{$\xmapsto{#1}$}}
  }
}

\newcommand{\VDashA}{%
  \mathrel{\text{\clipbox{0pt 0pt {.8\width} 0pt}{$\Vdash$}}\mkern.9mu}\vDash
}

\newcommand{\VDashB}{%
  \mathrel{
    \text{\clipbox{0pt 0pt {.8\width} 0pt}{$\Vdash$}}
    \mkern.9mu
    \text{\adjustbox{width=.87\width,height=\height}{$\vDash$}}
  }
}

\begin{document}

\begin{align*}
    \vDash && \text{\textbackslash vDash}\\
    \Vdash && \text{\textbackslash VDash} \\
    \xmapsto{abcdef} && \text{\textbackslash xmapsto\{abcdef\}} \\
    \XmapstoA{abcdef} && \text{\textbackslash XmapstoA\{abcdef\}} \\
    \XmapstoA{ABCDEFG_2^2} && \text{\textbackslash XmapstoA\{ABCDEFG\_2\textasciicircum{}2\}} \\
    \XmapstoB{abcdef} && \text{\textbackslash XmapstoB\{abcdef\}} \\
    \XmapstoB{abcdef^2} && \text{\textbackslash XmapstoB\{abcdef\textasciicircum{}2\}}
\end{align*}



\end{document}

Answer 1

\mapsto is composed with \mapstochar and \rightarrow.

Here I use \mapstochar together with \relbar (the middle part of extendable arrows) with some backing up.

\documentclass{article}
\usepackage{amsmath,mathtools}

\newcommand{\mmapsto}{\mapstochar\relbar\mathrel{\mkern-12mu}\mapsto}
\newcommand{\xmmapsto}{\mapstochar\relbar\mathrel{\mkern-12mu}\xmapsto}

\begin{document}

$a\mmapsto b$

$a\xmmapsto{bcdefg} h$

\end{document}

With the arrow bar only from the rightmost vertical line:

\documentclass{article}
\usepackage{amsmath,mathtools,amssymb}
\usepackage{pict2e}

\makeatletter
\DeclareRobustCommand{\mmapstochar}{%
  \mathrel{\mkern1mu\mathpalette\mmaps@to@char\relax\mkern0.5mu}%
}
\newcommand{\mmaps@to@char}[2]{%
  \vcenter{\hbox{%
    \setlength{\unitlength}{\mmaps@fd{#1}}%
    \linethickness{\variable@rule{#1}}%
    \begin{picture}(0,1)
    \roundcap
    \Line(0,-0.175)(0,1.17)
    \end{picture}%
  }}%
}
\newcommand{\mmaps@fd}[1]{%
  \fontdimen22
  \ifx#1\displaystyle\textfont\else
  \ifx#1\textstyle\textfont\else
  \ifx#1\scriptstyle\scriptfont\else
  \scriptscriptfont\fi\fi\fi2
}
\newcommand{\variable@rule}[1]{%
  \fontdimen8  
  \ifx#1\displaystyle\textfont3\else
    \ifx#1\textstyle\textfont3\else
      \ifx#1\scriptstyle\scriptfont3\else
        \scriptscriptfont3\relax
  \fi\fi\fi
}
\makeatother

\newcommand{\mmapsto}{\mmapstochar\mapsto}
\newcommand{\xmmapsto}{\mmapstochar\xmapsto}

\begin{document}

$a\mapsto b$

$a\mmapsto b$

$a\xmmapsto{bcdefg} h$

$\scriptstyle a\mmapsto b$

\end{document}

Answer 2

Here is a solution adapted from a code found in Mathmode (§ 38 Extensible arrows):

\documentclass{article}
\usepackage{mathtools, amssymb}

 \makeatletter
\newcommand\xVdasharrow[2][]{%
 \ext@arrow 0099{\xVdasharrowfill@}{#1}{#2}}
\def\xVdasharrowfill@{%
\arrowfill@{\vcenter{\hbox{$\Vdash$}}}\relbar\rightarrow }
\makeatother

\begin{document}

 \[ A\xVdasharrow[ \text{very long sentence}]{\text{This is a very very}}B \]%

\end{document}