$\VDash$ Symbol in AMS math packages?

Question

I'm trying to typeset some homework that deals with set theory and in particular I'm trying to write the "model-theoretic" notion of forcing. I put model-theoretic in quotes because I don't know the proper name for it. There's the forcing relation given by $\Vdash$ (i.e. it looks like similar to ||-), and I'm looking for the relation that looks like ||=, i.e. kind of like the $\models$ symbol or $\vDash$ but with an extra vertical line.

The strange thing is that it looks like the AMS packages have $\nVDash$ (i.e. the negation of the symbol I'm looking for) available, but not $\VDash$. Detexify doesn't seem to be helping me here. Are there any symbols which look like the hypothetical $\VDash$ I'm looking for (hopefully within amsmath, amsfonts, or amssymb, as I usually like to cut down on the number of packages I need to install to maintain portability across machines)?

Answer 1

\models is defined as (use \pshow\models where \def\pshow#1{{\let\protect\show #1}}):

\mathrel{|}\joinrel\Relbar

In a similar fashion one could define \mmodels:

\DeclareRobustCommand{\mmodels}{\mathrel{||}\joinrel\Relbar}

Here's a visual of the two:

\documentclass{article}
\DeclareRobustCommand{\mmodels}{\mathrel{||}\joinrel \Relbar}
\begin{document}
$\models\ \mmodels$
\end{document}

Perhaps inserting \mkern-2mu between the two vertical rules would look a little better:

Answer 2

I can propose two workarounds, I call them \VDashA and \VDashB; the former is a bit wider than \vdash and \nVDash, the latter is shrinked horizontally, which makes for a slightly thinner bar.

\documentclass{article}
\usepackage{amsmath,amssymb,trimclip,adjustbox}

\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}

$\Vdash$

$\VDashA$

$\VDashB$

$\nVDash$

\end{document}

Note: in the image I've artificially reduced the vertical space between the lines just to show the symbols nearer to each other and ease the comparison.