% !TeX root = tcolorbox.tex
% include file of tcolorbox.tex (manual of the LaTeX package tcolorbox)
\clearpage
\section{Library \mylib{theorems}}\label{sec:theorems}%
\tcbset{external/prefix=external/theorems_}%
The library is loaded by a package option or inside the preamble by:
\begin{dispListing}
\tcbuselibrary{theorems}
\end{dispListing}
This also loads the package |amsmath|.

\subsection{Macros of the Library}

\begin{docCommand}{newtcbtheorem}{\oarg{init options}\marg{name}\marg{display name}\marg{options}\marg{prefix}}
  Creates new environments \meta{name} and \meta{name}|*| based on |tcolorbox| to frame a
  (mathematical) theorem. The \meta{display name} is used in the title line
  with a number, e.\,g. \mbox{\flqq Theorem 5.1\frqq}.
  The \meta{options} are given to the underlying |tcolorbox| to control
  the appearance.
  %The \meta{counter} is used for automatic numbering.
  The \meta{init options} allow setting up automatic numbering,
  see \Vref{sec:initkeys}.\par
  The new environment \meta{name} takes one optional and two mandatory
  parameters. The optional parameter supplements the options and should be
  used only in rare cases.
  The first mandatory parameter is the title text for the theorem and
  the second mandatory parameter is a \meta{marker}. The theorem is
  automatically labeled with \meta{prefix}|:|\meta{marker}.\par
  The new environment \meta{name}|*| takes one optional and one mandatory
  parameter and represents an unnumbered variant of the environment \meta{name}.
  This variant is not labeled and not listed in lists of theorems.
%\enlargethispage*{20mm}
\inputpreamblelisting{F}
\begin{dispExample}
\begin{mytheo}{This is my title}{theoexample}
  This is the text of the theorem. The counter is automatically assigned and,
  in this example, prefixed with the section number. This theorem is numbered with
  \ref{th:theoexample} and is given on page \pageref{th:theoexample}.
\end{mytheo}
\end{dispExample}

\begin{dispExample}
\begin{mytheo}[label=myownlabel]{This is my title}{}
  The label parameter can be left empty without \LaTeX\ error.
  Or you may use an own label to reference Theorem \ref{myownlabel}.
\end{mytheo}
\end{dispExample}

\begin{dispExample}
\begin{mytheo}{}{}
  The title can also be left empty without problem. Note that the ':'
  vanished magically.
\end{mytheo}
\end{dispExample}

\begin{dispExample}
\begin{mytheo*}{Unnumbered Theorem}
  This theorem is not numbered.
\end{mytheo*}
\end{dispExample}

\begin{dispExample}
\begin{mytheo*}{}
  This theorem has no number and no title.
\end{mytheo*}
\end{dispExample}
\end{docCommand}


\begin{docCommand}{renewtcbtheorem}{\oarg{init options}\marg{name}\marg{display name}\marg{options}\marg{prefix}}
  Operates like \refCom{newtcbtheorem}, but based on |\renewenvironment| instead of |\newenvironment|.
  An existing environment is redefined.
\end{docCommand}


\begin{docCommand}{tcbmaketheorem}{\marg{name}\marg{display name}\marg{options}\marg{counter}\marg{prefix}}
\smallskip\begin{marker}
\refCom{newtcbtheorem} supersedes this macro.
\end{marker}
\begin{deprecated}
  Creates a new environment \meta{name} based on |tcolorbox| to frame a
  (mathematical) theorem. The \meta{display name} is used in the title line
  with a number, e.\,g. \mbox{\flqq Theorem 5.1\frqq}.
  The \meta{options} are given to the underlying |tcolorbox| to control
  the appearance.
  The \meta{counter} is used for automatic numbering.
  The new environment \meta{name} takes one optional and two mandatory
  parameters. The optional parameter supplements the options and should be
  used only in rare cases.
  The first mandatory parameter is the title text for the theorem and
  the second mandatory parameter is a \meta{marker}. The theorem is
  automatically labeled with \meta{prefix}|:|\meta{marker}.
\end{deprecated}
\end{docCommand}

\clearpage
\begin{docCommand}{tcboxmath}{\oarg{options}\marg{mathematical box content}}
  Creates a \refEnv{tcolorbox} which is fitted to the width of the given
  \meta{mathematical box content}. This box is intended to be applied as
  part of a larger formula and may be used as replacement for the |\boxed|
  macro of |amsmath|.

\begin{dispExample}
\begin{equation}
\tcbset{fonttitle=\scriptsize}
\tcboxmath[colback=LightBlue!25!white,colframe=blue]{ a^2 = 16 }
\quad \Rightarrow \quad
\tcboxmath[colback=Salmon!25!white,colframe=red,title=Implication]%
  { a = 4 ~\vee~ a=-4. }
\end{equation}
\end{dispExample}
\end{docCommand}

\begin{docCommand}{tcbhighmath}{\oarg{options}\marg{mathematical box content}}
  This is a special case of the \refCom{tcboxmath} macro which uses
  the style \refKey{/tcb/highlight math}.
  It is intended to provide context sensitive highlighting of formula parts.
  The color settings via \refKey{/tcb/highlight math style} may be different
  inside theorems or other colored areas and outside.

\begin{dispExample}
\tcbset{myformula/.style={colback=yellow!10!white,colframe=red!50!black,
  every box/.style={highlight math style={colback=LightBlue!50!white,colframe=Navy}}
  }}

\begin{align}
  \tcbhighmath{\sum\limits_{n=1}^{\infty} \frac{1}{n}} &= \infty.\\
  \int x^2 ~\text{d}x                     &= \frac13 x^3 + c.
\end{align}

\begin{tcolorbox}[ams align,myformula]
  \tcbhighmath{\sum\limits_{n=1}^{\infty} \frac{1}{n}} &= \infty.\\
  \int x^2 ~\text{d}x                     &= \frac13 x^3 + c.
\end{tcolorbox}
\end{dispExample}

\clearpage
\refCom{tcbhighmath} can be used in symbiosis with the |empheq| package
which allows to specify own boxing commands to mark multiline formulas.

\begin{dispExample}
% \usepackage{empheq}
\begin{empheq}[box=\tcbhighmath]{align}
a&=\sin(z)\\
E&=mc^2 + \int_a^b x\, dx
\end{empheq}

\tcbset{highlight math style={enhanced,
  colframe=red!60!black,colback=yellow!50!white,arc=4pt,boxrule=1pt,
  drop fuzzy shadow}}

\begin{empheq}[box=\tcbhighmath]{align}
a&=\sin(z)\\
E&=mc^2 + \int_a^b x\, dx
\end{empheq}
\end{dispExample}

Besides \refCom{tcbhighmath}, one can easily define an independent new box
based on \refCom{tcbox} which acts like \refCom{tcbhighmath}:

\begin{dispExample}
% \usepackage{empheq}
\newtcbox{\otherbox}[1][]{nobeforeafter,math upper,tcbox raise base,
  enhanced,frame hidden,boxrule=0pt,interior style={top color=green!10!white,
  bottom color=green!10!white,middle color=green!50!yellow},
  fuzzy halo=1pt with green,#1}

\begin{empheq}[box=\otherbox]{align}
a&=\sin(z)\\
E&=mc^2 + \int_a^b x\, dx
\end{empheq}

\begin{equation}
\tcbhighmath{E} = \otherbox{mc^2}
\end{equation}
\end{dispExample}
\end{docCommand}


\clearpage
\subsection{Option Keys of the Library}


\begin{docTcbKey}{separator sign}{=\meta{sign}}{no default, initially |:|}
  The given \meta{sign} is used inside the title text of a theorem
  as separater between display name combined with number and
  the specific title text. It is omitted, if there is no specific title text.

\begin{dispExample}
% \usepackage{amssymb}
\newtcbtheorem[use counter from=mytheo]{sometheorem}{Theorem}%
  {colback=white,colframe=red!50!black,fonttitle=\bfseries,
   separator sign={\ $\blacktriangleright$}}{theo}
\begin{sometheorem}{My example}{}
My theorem text.
\end{sometheorem}
\end{dispExample}
\end{docTcbKey}

\begin{docTcbKey}{separator sign colon}{}{style, no value, initially set}
Sets \refKey{/tcb/separator sign} to the default colon |:| sign.
\end{docTcbKey}

\begin{docTcbKey}{separator sign dash}{}{style, no value}
Sets \refKey{/tcb/separator sign} to an en-dash sign.
\begin{dispExample}
\newtcbtheorem[use counter from=mytheo]{sometheorem}{Theorem}%
  {colback=white,colframe=red!50!black,fonttitle=\bfseries,
   separator sign dash}{theo}
\begin{sometheorem}{My example}{}
My theorem text.
\end{sometheorem}
\end{dispExample}
\end{docTcbKey}

\begin{docTcbKey}{separator sign none}{}{style, no value}
Sets \refKey{/tcb/separator sign} to empty.
\begin{dispExample}
\newtcbtheorem[use counter from=mytheo]{sometheorem}{Theorem}%
  {colback=white,colframe=red!50!black,fonttitle=\bfseries,
   separator sign none}{theo}
\begin{sometheorem}{My example}{}
My theorem text.
\end{sometheorem}
\end{dispExample}
\end{docTcbKey}

\clearpage
\begin{docTcbKey}{description delimiters}{=\marg{left}\marg{right}}{no default, initially empty}
  The given \meta{left} and \meta{right} delimiter signs are used to frame
  the descriptive title text of a theorem.

\begin{dispExample}
\newtcbtheorem[use counter from=mytheo]{sometheorem}{Theorem}%
  {colback=white,colframe=red!50!black,fonttitle=\bfseries,
   description delimiters={\flqq}{\frqq}}{theo}
\begin{sometheorem}{My example}{}
My theorem text.
\end{sometheorem}
\end{dispExample}
\end{docTcbKey}


\begin{docTcbKey}{description delimiters parenthesis}{}{style, no value}
Sets \refKey{/tcb/description delimiters} to |(| and |)|.
\begin{dispExample}
\newtcbtheorem[use counter from=mytheo]{sometheorem}{Theorem}%
  {colback=white,colframe=red!50!black,fonttitle=\bfseries,
   description delimiters parenthesis}{theo}
\begin{sometheorem}{My example}{}
My theorem text.
\end{sometheorem}
\end{dispExample}
\end{docTcbKey}


\begin{docTcbKey}{description delimiters none}{}{style, no value, initially set}
Sets \refKey{/tcb/description delimiters} to the default empty texts.
\end{docTcbKey}


\begin{docTcbKey}{description color}{\colOpt{=\meta{color}}}{default empty, initially empty}
  Sets the \meta{color} of the descriptive title text deviating from \refKey{/tcb/coltitle}.
  The color is reset to \refKey{/tcb/coltitle}, if |description color| is used without value.

\begin{dispExample}
\newtcbtheorem[use counter from=mytheo]{sometheorem}{Theorem}%
  {colback=white,colframe=red!50!black,fonttitle=\bfseries,
   description color=red!25!yellow}{theo}
\begin{sometheorem}{My example}{}
My theorem text.
\end{sometheorem}
\end{dispExample}
\end{docTcbKey}

\clearpage
\begin{docTcbKey}{description font}{\colOpt{=\meta{text}}}{default empty, initially empty}
  Sets \meta{text} (e.\,g.\ font settings) before the descriptive title text deviating from \refKey{/tcb/fonttitle}.
  The \meta{text} is removed, if |description font| is used without value.

\begin{dispExample}
\newtcbtheorem[use counter from=mytheo]{sometheorem}{Theorem}%
  {colback=white,colframe=red!50!black,fonttitle=\bfseries,
   description delimiters={\glqq}{\grqq},
   description font=\mdseries\itshape}{theo}
\begin{sometheorem}{My example}{}
My theorem text.
\end{sometheorem}
\end{dispExample}
\end{docTcbKey}


\begin{docTcbKey}{description formatter}{\colOpt{=\meta{macro}}}{default empty, initially empty}
  Sets \meta{macro} as formatter for the descriptive title text. The \meta{macro}
  has to take one mandatory argument (the description text).\\ 
  Note that \refKey{/tcb/description delimiters}, \refKey{/tcb/description color},
  and \refKey{/tcb/description font} are ignored, if this option is used.\\
  If |description formatter| is used without value, the formatter is reset
  to its standard behavior.

\begin{dispExample}
\newtcbox{\formbox}{enhanced,frame empty,size=minimal,boxsep=2pt,arc=1pt,
  on line,interior style image=goldshade.png}

\newtcbtheorem[use counter from=mytheo]{sometheorem}{Theorem}%
  {colback=white,colframe=red!50!black,fonttitle=\bfseries,
   description formatter=\formbox}{theo}
\begin{sometheorem}{My example}{}
My theorem text.
\end{sometheorem}
\end{dispExample}
\end{docTcbKey}


\begin{docTcbKey}{terminator sign}{=\meta{sign}}{no default, initially empty}
  The given \meta{sign} is used as terminator at the end of the title text of a theorem.

\begin{dispExample}
\newtcbtheorem[use counter from=mytheo]{sometheorem}{Theorem}%
  {colback=white,colframe=red!50!black,fonttitle=\bfseries,
   terminator sign={.}}{theo}
\begin{sometheorem}{My example}{}
My theorem text.
\end{sometheorem}
\end{dispExample}
\end{docTcbKey}

\clearpage
\begin{docTcbKey}{terminator sign colon}{}{style, no value, initially set}
Sets \refKey{/tcb/terminator sign} to the colon |:| sign.
\begin{dispExample}
\newtcbtheorem[use counter from=mytheo]{sometheorem}{Theorem}%
  {colback=white,colframe=red!50!black,fonttitle=\bfseries,
   separator sign dash,terminator sign colon}{theo}
\begin{sometheorem}{My example}{}
My theorem text.
\end{sometheorem}
\end{dispExample}
\end{docTcbKey}

\begin{docTcbKey}{terminator sign dash}{}{style, no value}
Sets \refKey{/tcb/terminator sign} to an en-dash sign.
\begin{dispExample}
\newtcbtheorem[use counter from=mytheo]{sometheorem}{Theorem}%
  {colback=white,colframe=red!50!black,fonttitle=\bfseries,
   terminator sign dash}{theo}
\begin{sometheorem}{My example}{}
My theorem text.
\end{sometheorem}
\end{dispExample}
\end{docTcbKey}

\begin{docTcbKey}{terminator sign none}{}{style, no value}
Sets \refKey{/tcb/terminator sign} to the default empty text.
\end{docTcbKey}


\begin{docTcbKey}{theorem name and number}{}{style, no value, initially set}
Prints theorem name followed by theorem number inside the title.
\begin{dispExample}
\newtcbtheorem[use counter from=mytheo]{sometheorem}{Theorem}%
  {colback=white,colframe=red!50!black,fonttitle=\bfseries,
   theorem name and number}{theo}
\begin{sometheorem}{My example}{}
My theorem text.
\end{sometheorem}
\end{dispExample}
\end{docTcbKey}

\clearpage
\begin{docTcbKey}{theorem number and name}{}{style, no value}
Prints theorem number followed by theorem name inside the title.
\begin{dispExample}
\newtcbtheorem[use counter from=mytheo]{sometheorem}{Theorem}%
  {colback=white,colframe=red!50!black,fonttitle=\bfseries,
   theorem number and name}{theo}
\begin{sometheorem}{My example}{}
My theorem text.
\end{sometheorem}
\end{dispExample}
\end{docTcbKey}

\begin{docTcbKey}{theorem name}{}{style, no value}
Prints theorem name without number inside the title.
\begin{dispExample}
\newtcbtheorem[use counter from=mytheo]{sometheorem}{Theorem}%
  {colback=white,colframe=red!50!black,fonttitle=\bfseries,
   theorem name,enhanced,watermark text={\thetcbcounter}}{theo}
\begin{sometheorem}{My example}{}
My theorem text.
\end{sometheorem}
\end{dispExample}
\end{docTcbKey}


\begin{docTcbKey}{theorem}{=\marg{display name}\marg{counter}\marg{title}\marg{marker}}{no default}
  This key is internally used by \refCom{tcbmaketheorem}, but can be used
  directly in a |tcolorbox| for a more flexible approach.
  The \meta{display name} is used together with the increased \meta{counter} value
  and the \meta{title} for the title line of the box. Additionally, a
  |\label| with the given \meta{marker} is created.
\begin{dispExample}
% \newcounter{texercise}%  preamble
\begin{tcolorbox}[colback=green!10,colframe=green!50!black,arc=4mm,
                  theorem={Test}{texercise}{Direct usage}{myMarker}]
Here, we see the test \ref{myMarker}.
\end{tcolorbox}
\end{dispExample}
For a common appearance inside the document, the key |theorem| should not be
used directly as in the example above, but as part of a new environment
created by hand or using \refCom{tcbmaketheorem} or using its successor
\refCom{newtcbtheorem}.
\end{docTcbKey}

\clearpage
\begin{docTcbKey}{highlight math}{}{style, no value}
  Predefined style which is used for \refCom{tcbhighmath}.
  It can be changed comfortable with \refKey{/tcb/highlight math style}.
\end{docTcbKey}


\begin{docTcbKey}{highlight math style}{=\meta{style definition}}{style, no default}
  Changes the definition for \refKey{/tcb/highlight math} to the given
  \meta{style definition}. See \refCom{tcbhighmath} for another example.
\begin{dispExample}
% \tcbuselibrary{skins}
\tcbset{highlight math style={enhanced,%<-- needed for the 'remember' options
  colframe=red,colback=red!10!white,boxsep=0pt}}
\begin{align*}
\tcbhighmath[remember as=fx]{f(x)}
     &= \int\limits_{1}^{x} \frac{1}{t^2}~dt
      = \left[ -\frac{1}{t} \right]_{1}^{x}\\
     &= -\frac{1}{x} + \frac{1}{1}\\
     &=
\tcbhighmath[remember,overlay={%
    \draw[blue,very thick,->] (fx.south) to[bend right] ([yshift=2mm]frame.west);}]
  {1-\frac{1}{x}.}
\end{align*}
\end{dispExample}
\end{docTcbKey}

\begin{docTcbKey}{math upper}{}{style, no value}
  Sets the upper part to mathematical mode with font |\displaystyle|.
\end{docTcbKey}

\begin{docTcbKey}{math lower}{}{style, no value}
  Sets the lower part to mathematical mode with font |\displaystyle|.
\end{docTcbKey}

\begin{docTcbKey}{math}{}{style, no value}
  Sets the upper part \emph{and} lower part to mathematical mode with font |\displaystyle|.
\begin{dispExample}
\begin{tcolorbox}[math,colback=yellow!10!white,colframe=red!50!black]
  \sum\limits_{n=1}^{\infty} \frac{1}{n} = \infty.
\end{tcolorbox}
\end{dispExample}
\end{docTcbKey}


\clearpage
\begin{marker}
  The following styles are only tested to work with the original |amsmath| environments.
  If e.g. the |equation| environment is redefined as |gather|, then
  \refKey{/tcb/ams equation} should / could not be used. Obviously, you are encouraged
  to use \refKey{/tcb/ams gather} in this case.
\end{marker}

\begin{docTcbKey}[][doc updated=2014-10-30]{ams equation upper}{}{style, no value}
  Adds an |amsmath| |equation| environment to the start and end
  of the upper part.
\end{docTcbKey}

\begin{docTcbKey}[][doc updated=2014-10-30]{ams equation lower}{}{style, no value}
  Adds an |amsmath| |equation| environment to the start and end
  of the lower part.
\end{docTcbKey}

\begin{docTcbKey}[][doc updated=2014-10-30]{ams equation}{}{style, no value}
  Adds an |amsmath| |equation| environment to the start and end
  of the upper \emph{and} lower part.
\begin{dispExample}
\begin{tcolorbox}[ams equation,colback=yellow!10!white,colframe=red!50!black]
  \sum\limits_{n=1}^{\infty} \frac{1}{n} = \infty.
\end{tcolorbox}
\end{dispExample}
\end{docTcbKey}

\begin{docTcbKey}[][doc updated=2014-10-30]{ams equation* upper}{}{style, no value}
  Adds an |amsmath| |equation*| environment to the start and end
  of the upper part.
\end{docTcbKey}

\begin{docTcbKey}[][doc updated=2014-10-30]{ams equation* lower}{}{style, no value}
  Adds an |amsmath| |equation*| environment to the start and end
  of the lower part.
\end{docTcbKey}

\begin{docTcbKey}[][doc updated=2014-10-30]{ams equation*}{}{style, no value}
  Adds an |amsmath| |equation*| environment to the start and end
  of the upper \emph{and} lower part.
\begin{dispExample}
\begin{tcolorbox}[ams equation*,colback=yellow!10!white,colframe=red!50!black]
  \sum\limits_{n=1}^{\infty} \frac{1}{n} = \infty.
\end{tcolorbox}
\end{dispExample}
\end{docTcbKey}

\clearpage
\begin{docTcbKey}{ams align upper}{}{style, no value}
  Adds an |amsmath| |align| environment to the start and end
  of the upper part.
\end{docTcbKey}

\begin{docTcbKey}{ams align lower}{}{style, no value}
  Adds an |amsmath| |align| environment to the start and end
  of the lower part.
\end{docTcbKey}

\begin{docTcbKey}{ams align}{}{style, no value}
  Adds an |amsmath| |align| environment to the start and end
  of the upper \emph{and} lower part.
\begin{dispExample}
\begin{tcolorbox}[ams align,colback=yellow!10!white,colframe=red!50!black]
  \sum\limits_{n=1}^{\infty} \frac{1}{n} &= \infty.\\
  \int x^2 ~\text{d}x                     &= \frac13 x^3 + c.
\end{tcolorbox}
\end{dispExample}
\end{docTcbKey}

\begin{docTcbKey}{ams align* upper}{}{style, no value}
  Adds an |amsmath| |align*| environment to the start and end
  of the upper part.
\end{docTcbKey}

\begin{docTcbKey}{ams align* lower}{}{style, no value}
  Adds an |amsmath| |align*| environment to the start and end
  of the lower part.
\end{docTcbKey}

\begin{docTcbKey}{ams align*}{}{style, no value}
  Adds an |amsmath| |align*| environment to the start and end
  of the upper \emph{and} lower part.
\begin{dispExample}
\begin{tcolorbox}[ams align*,colback=yellow!10!white,colframe=red!50!black]
  \sum\limits_{n=1}^{\infty} \frac{1}{n} &= \infty.\\
  \int x^2 ~\text{d}x                     &= \frac13 x^3 + c.
\end{tcolorbox}
\end{dispExample}
\end{docTcbKey}

\clearpage
\begin{docTcbKey}{ams gather upper}{}{style, no value}
  Adds an |amsmath| |gather| environment to the start and end
  of the upper part.
\end{docTcbKey}

\begin{docTcbKey}{ams gather lower}{}{style, no value}
  Adds an |amsmath| |gather| environment to the start and end
  of the lower part.
\end{docTcbKey}

\begin{docTcbKey}{ams gather}{}{style, no value}
  Adds an |amsmath| |gather| environment to the start and end
  of the upper \emph{and} lower part.
\begin{dispExample}
\begin{tcolorbox}[ams gather,colback=yellow!10!white,colframe=red!50!black]
  \sum\limits_{n=1}^{\infty} \frac{1}{n} = \infty.\\
  \int x^2 ~\text{d}x = \frac13 x^3 + c.
\end{tcolorbox}
\end{dispExample}
\end{docTcbKey}

\begin{docTcbKey}{ams gather* upper}{}{style, no value}
  Adds an |amsmath| |gather*| environment to the start and end
  of the upper part.
\end{docTcbKey}

\begin{docTcbKey}{ams gather* lower}{}{style, no value}
  Adds an |amsmath| |gather*| environment to the start and end
  of the lower part.
\end{docTcbKey}

\begin{docTcbKey}{ams gather*}{}{style, no value}
  Adds an |amsmath| |gather*| environment to the start and end
  of the upper \emph{and} lower part.
\begin{dispExample}
\begin{tcolorbox}[ams gather*,colback=yellow!10!white,colframe=red!50!black]
  \sum\limits_{n=1}^{\infty} \frac{1}{n} = \infty.\\
  \int x^2 ~\text{d}x = \frac13 x^3 + c.
\end{tcolorbox}
\end{dispExample}
\end{docTcbKey}


\clearpage
\begin{docTcbKey}{ams nodisplayskip upper}{}{style, no value}
  Neutralizes the |\abovedisplayskip| of a following |align| or |gather|
  environment for the upper part. Note that the text content has to
  start with such a formula.
\end{docTcbKey}


\begin{docTcbKey}{ams nodisplayskip lower}{}{style, no value}
  Neutralizes the |\abovedisplayskip| of a following |align| or |gather|
  environment for the lower part. Note that the text content has to
  start with such a formula.
\end{docTcbKey}


\begin{docTcbKey}{ams nodisplayskip}{}{style, no value}
  Neutralizes the |\abovedisplayskip| of a following |align| or |gather|
  environment for the upper part \emph{and} lower part.
  Note that the text content has to start with such a formula.
\begin{dispExample}
\begin{tcolorbox}[ams nodisplayskip,colback=yellow!10!white,colframe=red!50!black]
  \begin{gather}
  \sum\limits_{n=1}^{\infty} \frac{1}{n} = \infty.\\
  \int x^2 ~\text{d}x = \frac13 x^3 + c.
  \end{gather}
  And now for something completely different.
\end{tcolorbox}
\end{dispExample}
\end{docTcbKey}

\bigskip
New colored mathematical environments are easily created using
\refCom{newtcolorbox}:

\begin{dispExample}
\newtcolorbox{mymath}{ams gather*,colback=yellow!10!white,colframe=red!50!black}

\begin{mymath}
  \sum\limits_{n=1}^{\infty} \frac{1}{n} = \infty.\\
  \int x^2 ~\text{d}x = \frac13 x^3 + c.
\end{mymath}
\end{dispExample}

\bigskip
\begin{marker}
  All described options like \refKey{/tcb/ams gather upper}, \refKey{/tcb/ams gather lower},
  \refKey{/tcb/ams gather} are (partially) setting (overwritting) the
  keys \refKey{/tcb/before upper}, \refKey{/tcb/after upper},
  \refKey{/tcb/before lower}, \refKey{/tcb/after lower}.\par
  Therefore, e.\,g.\ |\tcbset{ams gather,before upper={\text{Pythagoras:}}}|
  produces an invalid result. For this case, you are invited to use\\
  |\tcbset{ams gather,before upper app={\text{Pythagoras:}}}|,\\
  see \refKey{/tcb/before upper app}.
\end{marker}


\clearpage
\begin{docTcbKey}{theorem style}{=\meta{name}}{no default, initially |standard|}
Applies a predefined style \meta{name} to the theorem environment. Some of
the feasible \meta{name} values resemble style names from the packages |theorem|
and |ntheorem| to give convenient access to known patterns.
\begin{marker}
The styles alter \refKey{/tcb/separator sign}, \refKey{/tcb/description delimiters},
\refKey{/tcb/terminator sign}, and more. Therefore, one should apply such
keys \emph{after} a theorem style.
\end{marker}

For the following examples, we use:
\inputpreamblelisting{J}

The predefined styles are:
\begin{itemize}
%
\item\docValue{standard}: This is the initial value.
\begin{dispExample}
\begin{theorem}[theorem style=standard]{standard}{}
This is my theorem. \begin{equation*} a^2 + b^2 = c^2. \end{equation*}
\end{theorem}
\end{dispExample}
%
\item\docValue{change standard}
\begin{dispExample}
\begin{theorem}[theorem style=change standard]{change standard}{}
This is my theorem. \begin{equation*} a^2 + b^2 = c^2. \end{equation*}
\end{theorem}
\end{dispExample}
%
\item\docValue{plain}
\begin{dispExample}
\begin{theorem}[theorem style=plain]{plain}{}
This is my theorem. \begin{equation*} a^2 + b^2 = c^2. \end{equation*}
\end{theorem}
\end{dispExample}
%
\clearpage
\item\docValue{break}
\begin{dispExample}
\begin{theorem}[theorem style=break]{break}{}
This is my theorem. \begin{equation*} a^2 + b^2 = c^2. \end{equation*}
\end{theorem}
\end{dispExample}
%
\item\docValue{plain apart}
\begin{dispExample}
\begin{theorem}[theorem style=plain apart]{plain apart}{}
This is my theorem. \begin{equation*} a^2 + b^2 = c^2. \end{equation*}
\end{theorem}
\end{dispExample}
%
\item\docValue{change}
\begin{dispExample}
\begin{theorem}[theorem style=change]{change}{}
This is my theorem. \begin{equation*} a^2 + b^2 = c^2. \end{equation*}
\end{theorem}
\end{dispExample}
%
\item\docValue{change break}
\begin{dispExample}
\begin{theorem}[theorem style=change break]{change break}{}
This is my theorem. \begin{equation*} a^2 + b^2 = c^2. \end{equation*}
\end{theorem}
\end{dispExample}
%
\item\docValue{change apart}
\begin{dispExample}
\begin{theorem}[theorem style=change apart]{change apart}{}
This is my theorem. \begin{equation*} a^2 + b^2 = c^2. \end{equation*}
\end{theorem}
\end{dispExample}
%
\clearpage
\item\docValue{margin}
\begin{dispExample}
\begin{theorem}[theorem style=margin,left=10mm]{margin}{}
This is my theorem. \begin{equation*} a^2 + b^2 = c^2. \end{equation*}
\end{theorem}
\begin{theorem}[theorem style=margin,left=10mm,oversize]{margin}{}
This is my theorem. \begin{equation*} a^2 + b^2 = c^2. \end{equation*}
\end{theorem}
\end{dispExample}
%
\item\docValue{margin break}
\begin{dispExample}
\begin{theorem}[theorem style=margin break,left=10mm]{margin break}{}
This is my theorem. \begin{equation*} a^2 + b^2 = c^2. \end{equation*}
\end{theorem}
\begin{theorem}[theorem style=margin break,left=10mm,oversize]{margin break}{}
This is my theorem. \begin{equation*} a^2 + b^2 = c^2. \end{equation*}
\end{theorem}
\end{dispExample}
%
\item\docValue{margin apart}
\begin{dispExample}
\begin{theorem}[theorem style=margin apart,left=10mm]{margin apart}{}
This is my theorem. \begin{equation*} a^2 + b^2 = c^2. \end{equation*}
\end{theorem}
\begin{theorem}[theorem style=margin apart,left=10mm,oversize]{margin apart}{}
This is my theorem. \begin{equation*} a^2 + b^2 = c^2. \end{equation*}
\end{theorem}
\end{dispExample}
%
\end{itemize}
\end{docTcbKey}


%
\clearpage
\subsection{Examples for Definitions and Theorems}
In the following, the application of \refCom{tcbmaketheorem}
to highlight mathematical definitions, theorems, or the like is demonstrated.

At first, additional |tcb| keys are created for the appearance of
the colored boxes. It is assumed that theorems and corollaries should be
identically colored.
All following environments are numbered with a common counter, but this
can be changed easily. Here, the counter output is supplemented by
the subsection number.
Further, the |cleveref| package \cite{cubitt:2013a} is used for clever
references.

\inputpreamblelisting{G}

By \refCom{newtcbtheorem}, commonly numbered theorem environments are
created now. |defstyle| and |theostyle| are used for the appearance.

Now, everything is prepared for the following examples.

\begin{dispExample}
The following theorem is numbered as \Cref{theo:diffbarstetig} and
referenced with the marker \texttt{theo:diffbarstetig}.\bigskip

\begin{Theorem}{Differenzierbarkeit bedingt Stetigkeit, wobei diese Benennung
  zu Testzwecken ungew\"{o}hnlich lang ist}{diffbarstetig}%
  Eine Funktion $f:I\to\mathbb{R}$ ist in $x_0\in I$ stetig, wenn $f$ in
  $x_0$ differenzierbar ist.
\end{Theorem}
\end{dispExample}


\begin{dispExample}
The following definition is numbered as \Cref{def:diffbarkeit} and
referenced with the marker \texttt{def:diffbarkeit}.\bigskip

\begin{Definition}{Differenzierbarkeit}{diffbarkeit}
  Eine Funktion $f:~I\to\mathbb{R}$ auf einem Intervall $I$ hei\ss{}t in
  $x_0\in I$ differenzierbar oder linear approximierbar,
  wenn der Grenzwert
  \begin{equation*}
  \lim\limits_{x\to x_0}\frac{f(x)-f(x_0)}{x-x_0}=
  \lim\limits_{h\to 0}\frac{f(x_0+h)-f(x_0)}{h}
  \end{equation*}
  existiert. Bei Existenz hei\ss{}t dieser Grenzwert Ableitung
  oder Differentialquotient von $f$ in $x_0$ und man
  schreibt f\"{u}r ihn
  \begin{equation*}
  f'(x_0)\quad\text{oder}\quad\frac{df}{dx}(x_0).
  \end{equation*}
\end{Definition}
\end{dispExample}


\begin{dispExample}
The following corollary is numbered as \Cref{cor:nullstellen} and
referenced with the marker \texttt{cor:nullstellen}.\bigskip

\begin{Corollary}{Nullstellenexistenz}{nullstellen}
  Ist $f:[a,b]\to\mathbb{R}$ stetig und haben $f(a)$ und $f(b)$ entgegengesetzte
  Vorzeichen, also $f(a)f(b)<0$, so besitzt $f$ eine Nullstelle $x_0\in]a,b[$,
  also $f(x_0)=0$.
\end{Corollary}
\end{dispExample}


\begin{dispExample}
\begin{Theorem}[boxrule=2mm,toptitle=-1.5mm,bottomtitle=-1.5mm]{%
    Hinreichende Bedingung f\"{u}r Wendepunkte}{wendehinreichend}%
  $f$ sei eine auf einem Intervall $]a,b[$ dreimal stetig differenzierbare Funktion.
  Ist $f''(x_0)=0$ in $x_0\in]a,b[$ und $f'''(x_0)\ne 0$, so ist
  $(x_0,f(x_0))$ ein Wendepunkt von $f$.
\end{Theorem}
\end{dispExample}

\begin{dispExample}
% \usepackage{varioref}
% \usepackage{cleveref}
% \tcbuselibrary{skins}
\newtcbtheorem[use counter from=Definition]{YetAnotherTheorem}{Theorem}%
  {theorem style=plain apart,label type=theorem,enhanced,frame hidden,
  boxrule=2mm,titlerule=0mm,toptitle=1mm,bottomtitle=1mm,
  fonttitle=\bfseries\large,fontupper=\normalsize,
  coltitle=green!35!black,colbacktitle=green!15!white,
  colback=green!50!yellow!15!white,borderline={1pt}{0pt}{green!25!blue},
  }{theo}

\begin{YetAnotherTheorem}{Mittelwertsatz f\"{u}r $n$ Variable}{meanvaluetheorem}%
  Es sei $n\in\mathbb{N}$, $D\subseteq\mathbb{R}^n$ eine offene Menge und
  $f\in C^{1}(D,\mathbb{R})$. Dann gibt es auf jeder Strecke
  $[x_0,x]\subset D$ einen Punkt $\xi\in[x_0,x]$, so dass gilt
  \begin{equation*}
  f(x)-f(x_0) = \operatorname{grad} f(\xi)^{\top}(x-x_0)
  \end{equation*}
\end{YetAnotherTheorem}

\medskip
Here, |cleveref| support is used to reference \Cref{theo:meanvaluetheorem}
on \Cpageref{theo:meanvaluetheorem}. This \namecref{theo:meanvaluetheorem}
can also be referenced by |\Vref| resulting in \Vref{theo:meanvaluetheorem}.
\end{dispExample}

\begin{marker}
Note that \refKey{/tcb/label type} was used in the example above to feed
|cleveref| \cite{cubitt:2013a} with the needed name information.
\end{marker}

\clearpage

\begin{dispExample}
Here, using |\Vref| resulting in \Vref{theo:meanvaluetheorem} is more interesting\ldots
\end{dispExample}


\begin{dispExample}
% \tcbuselibrary{skins}
\newtcbtheorem[use counter from=Definition]{YetAnotherTheorem}{Theorem}%
  {theorem style=change apart,enhanced,arc=0mm,outer arc=0mm,
  boxrule=0mm,toprule=1mm,bottomrule=1mm,left=1mm,right=1mm,
  titlerule=0mm,toptitle=0mm,bottomtitle=1mm,top=0mm,
  colframe=red!50!black,colback=red!5!white,coltitle=red!50!black,
  title style={top color=yellow!50!white,bottom color=red!5!white,
    middle color=yellow!50!white},
  fonttitle=\bfseries\sffamily\normalsize,fontupper=\normalsize\itshape,
  }{theo}

\begin{YetAnotherTheorem}{Mittelwertsatz f\"{u}r $n$ Variable}{mittelwertsatz_n2}%
  Es sei $n\in\mathbb{N}$, $D\subseteq\mathbb{R}^n$ eine offene Menge und
  $f\in C^{1}(D,\mathbb{R})$. Dann gibt es auf jeder Strecke
  $[x_0,x]\subset D$ einen Punkt $\xi\in[x_0,x]$, so dass gilt
  \begin{equation*}
  f(x)-f(x_0) = \operatorname{grad} f(\xi)^{\top}(x-x_0)
  \end{equation*}
\end{YetAnotherTheorem}
\end{dispExample}


\begin{dispExample}
% \usepackage{varwidth}   \tcbuselibrary{skins}
\newtcbtheorem[use counter from=Definition]{YetAnotherTheorem}{Theorem}%
{enhanced,frame empty,interior empty,colframe=ForestGreen!50!white,
  coltitle=ForestGreen!50!black,fonttitle=\bfseries,colbacktitle=ForestGreen!15!white,
  borderline={0.5mm}{0mm}{ForestGreen!15!white},
  borderline={0.5mm}{0mm}{ForestGreen!50!white,dashed},
  attach boxed title to top center={yshift=-2mm},
  boxed title style={boxrule=0.4pt},varwidth boxed title}{theo}

\begin{YetAnotherTheorem}{Mittelwertsatz f\"{u}r $n$ Variable}{mittelwertsatz_n3}%
  Es sei $n\in\mathbb{N}$, $D\subseteq\mathbb{R}^n$ eine offene Menge und
  $f\in C^{1}(D,\mathbb{R})$. Dann gibt es auf jeder Strecke
  $[x_0,x]\subset D$ einen Punkt $\xi\in[x_0,x]$, so dass gilt
  \begin{equation*}
  f(x)-f(x_0) = \operatorname{grad} f(\xi)^{\top}(x-x_0)
  \end{equation*}
\end{YetAnotherTheorem}
\end{dispExample}


\clearpage
You need more attention for your theorems? Here, you are \ldots

\begin{dispExample}
% tcbuselibrary{skins}  % preamble
\begin{Theorem}[enhanced,
    fuzzy halo=3mm with yellow,
    fuzzy halo=2mm with red,
    fuzzy halo=1mm with yellow,
    watermark color=red!35!white,
    watermark text={Overacting\\Fundamental Theorem}]%
  {Fundamental Theorem of Theorems}{fundamental}%
  \lipsum[1-2]
\end{Theorem}
\end{dispExample}

Let's try a more conservative approach:

\begin{dispExample}
% \tcbuselibrary{skins}
\newtcbtheorem[use counter from=Definition]{YetAnotherTheorem}{Theorem}%
  {theorem style=plain,enhanced,colframe=blue!50!black,colback=yellow!20!white,
   coltitle=red!50!black,fonttitle=\upshape\bfseries,fontupper=\itshape,
   drop fuzzy shadow=blue!50!black!50!white,boxrule=0.4pt}{theo}

\begin{YetAnotherTheorem}{Mittelwertsatz f\"{u}r $n$ Variable}{mittelwertsatz_n4}%
  Es sei $n\in\mathbb{N}$, $D\subseteq\mathbb{R}^n$ eine offene Menge und
  $f\in C^{1}(D,\mathbb{R})$. Dann gibt es auf jeder Strecke
  $[x_0,x]\subset D$ einen Punkt $\xi\in[x_0,x]$, so dass gilt
  \begin{equation*}
  f(x)-f(x_0) = \operatorname{grad} f(\xi)^{\top}(x-x_0)
  \end{equation*}
\end{YetAnotherTheorem}
\end{dispExample}


\clearpage
\subsection{Using other theorem environments with \texttt{tcolorbox}}\label{subsec:theorems_other}

Instead of creating theorem environments with the methods described before,
environments from other packages can be boxed with a |tcolorbox|.

Environments may be created e.g. by methods from the |theorem| package or
the |amsthm| package. \refCom{tcolorboxenvironment} can be used to put a box
around these environments.

\inputpreamblelisting{K}

\begin{dispExample}
\begin{lem}
  \lipsum[2]
\end{lem}

\lipsum[3]

\begin{proof}
  \lipsum*[4]
\end{proof}
\end{dispExample}
