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Bradley M. Kuhn

Add Twitter's Bootstrap 3.0.0 CSS and Javascript files, under Apache License 2.0

These files are exactly as they appear the upstream release 3.0.0 of
Bootstrap, which Twitter released under the Apache License 2.0. To extract
these files, I did the following:

I downloaded the following file:
https://github.com/twbs/bootstrap/archive/v3.0.0.zip

with sha256sum of:
$ sha256sum v3.0.0.zip
2d54f345f4abc6bf65ea648c323e9bae577e6febf755650e62555f2d7a222e17 v3.0.0.zip

And extracted from it these two files:
bootstrap-3.0.0/dist/css/bootstrap.css
bootstrap-3.0.0/dist/js/bootstrap.js
which are licensed under the Apache License 2.0.

and placed them into:
rhodecode/public/css/bootstrap.css
rhodecode/public/js/bootstrap.js
respectively.

<!doctype html>
<html>
  <head>
    <meta charset="utf-8">
    <title>CodeMirror: sTeX mode</title>
    <link rel="stylesheet" href="../../lib/codemirror.css">
    <script src="../../lib/codemirror.js"></script>
    <script src="stex.js"></script>
    <style>.CodeMirror {background: #f8f8f8;}</style>
    <link rel="stylesheet" href="../../doc/docs.css">
  </head>
  <body>
    <h1>CodeMirror: sTeX mode</h1>
     <form><textarea id="code" name="code">
\begin{module}[id=bbt-size]
\importmodule[balanced-binary-trees]{balanced-binary-trees}
\importmodule[\KWARCslides{dmath/en/cardinality}]{cardinality}

\begin{frame}
  \frametitle{Size Lemma for Balanced Trees}
  \begin{itemize}
  \item
    \begin{assertion}[id=size-lemma,type=lemma]
    Let $G=\tup{V,E}$ be a \termref[cd=binary-trees]{balanced binary tree}
    of \termref[cd=graph-depth,name=vertex-depth]{depth}$n>i$, then the set
     $\defeq{\livar{V}i}{\setst{\inset{v}{V}}{\gdepth{v} = i}}$ of
    \termref[cd=graphs-intro,name=node]{nodes} at
    \termref[cd=graph-depth,name=vertex-depth]{depth} $i$ has
    \termref[cd=cardinality,name=cardinality]{cardinality} $\power2i$.
   \end{assertion}
  \item
    \begin{sproof}[id=size-lemma-pf,proofend=,for=size-lemma]{via induction over the depth $i$.}
      \begin{spfcases}{We have to consider two cases}
        \begin{spfcase}{$i=0$}
          \begin{spfstep}[display=flow]
            then $\livar{V}i=\set{\livar{v}r}$, where $\livar{v}r$ is the root, so
            $\eq{\card{\livar{V}0},\card{\set{\livar{v}r}},1,\power20}$.
          \end{spfstep}
        \end{spfcase}
        \begin{spfcase}{$i>0$}
          \begin{spfstep}[display=flow]
           then $\livar{V}{i-1}$ contains $\power2{i-1}$ vertexes
           \begin{justification}[method=byIH](IH)\end{justification}
          \end{spfstep}
          \begin{spfstep}
           By the \begin{justification}[method=byDef]definition of a binary
              tree\end{justification}, each $\inset{v}{\livar{V}{i-1}}$ is a leaf or has
            two children that are at depth $i$.
          \end{spfstep}
          \begin{spfstep}
           As $G$ is \termref[cd=balanced-binary-trees,name=balanced-binary-tree]{balanced} and $\gdepth{G}=n>i$, $\livar{V}{i-1}$ cannot contain
            leaves.
          \end{spfstep}
          \begin{spfstep}[type=conclusion]
           Thus $\eq{\card{\livar{V}i},{\atimes[cdot]{2,\card{\livar{V}{i-1}}}},{\atimes[cdot]{2,\power2{i-1}}},\power2i}$.
          \end{spfstep}
        \end{spfcase}
      \end{spfcases}
    \end{sproof}
  \item
    \begin{assertion}[id=fbbt,type=corollary]
      A fully balanced tree of depth $d$ has $\power2{d+1}-1$ nodes.
    \end{assertion}
  \item
      \begin{sproof}[for=fbbt,id=fbbt-pf]{}
        \begin{spfstep}
          Let $\defeq{G}{\tup{V,E}}$ be a fully balanced tree
        \end{spfstep}
        \begin{spfstep}
          Then $\card{V}=\Sumfromto{i}1d{\power2i}= \power2{d+1}-1$.
        \end{spfstep}
      \end{sproof}
    \end{itemize}
  \end{frame}
\begin{note}
  \begin{omtext}[type=conclusion,for=binary-tree]
    This shows that balanced binary trees grow in breadth very quickly, a consequence of
    this is that they are very shallow (and this compute very fast), which is the essence of
    the next result.
  \end{omtext}
\end{note}
\end{module}

%%% Local Variables:
%%% mode: LaTeX
%%% TeX-master: "all"
%%% End: \end{document}
</textarea></form>
    <script>
      var editor = CodeMirror.fromTextArea(document.getElementById("code"), {});
    </script>

    <p><strong>MIME types defined:</strong> <code>text/x-stex</code>.</p>

    <p><strong>Parsing/Highlighting Tests:</strong> <a href="../../test/index.html#stex_*">normal</a>,  <a href="../../test/index.html#verbose,stex_*">verbose</a>.</p>

  </body>
</html>