Indent the new line in a theorem environment

Question

I have been looking after a solution to this for a while and have found none. I'm trying to create a Theorem environment, through amsthm, such that there will be a linebreak (just like the break theorem model) but with the first line indented. I tried playing around with redefining environments and and stuff, but it didn't help so far. My current code is:

\documentclass{memoir}
    \usepackage{amsthm}
    \usepackage{lipsum}
    \usepackage{amssymb}
    \newtheoremstyle{teo}%〈name〉
        {3pt}%〈Space above〉
        {3pt}%〈Space below〉
        {}%〈Body font〉
        {}%〈Indent amount〉
        {\bfseries}%〈Theorem head font〉
        {:}%〈Punctuation after theorem head〉
        {\newline}%〈Space after theorem head〉
        {\thmname{#1}\thmnumber{ #2}{\mdseries\thmnote{ [#3]}}}%〈Theorem head spec(can be left empty, meaning ‘normal’)〉
    \theoremstyle{teo}
        \newtheorem{thmx}{Theorem}
    \newenvironment{thm}
      {\pushQED{\qed}\renewcommand{\qedsymbol}{$\square$}\thmx}
      {\popQED\endthmx}
    \usepackage{indentfirst}
    \begin{document}
        \begin{thm}[Bézout's Theorem]    
            \lipsum[1]
        \end{thm}
    \end{document}

I'm aiming at an automatized way of achieving a result similar to this:

\documentclass{memoir}
    \usepackage{amsthm}
    \usepackage{lipsum}
    \usepackage{amssymb}
    \newtheoremstyle{teo}%〈name〉
        {3pt}%〈Space above〉
        {3pt}%〈Space below〉
        {}%〈Body font〉
        {}%〈Indent amount〉
        {\bfseries}%〈Theorem head font〉
        {:}%〈Punctuation after theorem head〉
        {\newline}%〈Space after theorem head〉
        {\thmname{#1}\thmnumber{ #2}{\mdseries\thmnote{ [#3]}}}%〈Theorem head spec(can be left empty, meaning ‘normal’)〉
    \theoremstyle{teo}
        \newtheorem{thmx}{Theorem}
    \newenvironment{thm}
      {\pushQED{\qed}\renewcommand{\qedsymbol}{$\square$}\thmx}
      {\popQED\endthmx}
    \usepackage{indentfirst}
    \begin{document}
        \begin{thm}[Bézout's Theorem]    
            \null \hspace{1em} \lipsum[1]
        \end{thm}
    \end{document}

That is to say, with an arbitrary spacement when I type the so said theorem.

I apologize for any bad styles in this question, for I am new to this SE.

Answer 1

We can patch \newtheoremstyle to accept \newline<other tokens>:

\documentclass{memoir}
\usepackage{amssymb}
\usepackage{amsthm}
\usepackage{etoolbox}
\usepackage{lipsum}

\makeatletter
\patchcmd{\newtheoremstyle}
 {\def\@tempb{\newline}}
 {\def\@tempb{\newline}\edef\@tempa{\unexpanded\expandafter{\@car#8\@nil}}}
 {}{}
\patchcmd{\newtheoremstyle}
 {\def\thmheadnl{\newline}}
 {\def\thmheadnl{#8}}
 {}{}
\makeatother

\newtheoremstyle{teo}%〈name〉
  {3pt}%〈Space above〉
  {3pt}%〈Space below〉
  {}%〈Body font〉
  {}%〈Indent amount〉
  {\bfseries}%〈Theorem head font〉
  {:}%〈Punctuation after theorem head〉
  {\newline\hspace*{\parindent}}%〈Space after theorem head〉
  %〈Theorem head spec follows (can be left empty, meaning ‘normal’)〉
  {\thmname{#1}\thmnumber{ #2}{\mdseries\thmnote{ [#3]}}}
\makeatletter
\makeatother

\theoremstyle{teo}

\newtheorem{thmx}{Theorem}
\newenvironment{thm}
  {\pushQED{\qed}\renewcommand{\qedsymbol}{$\square$}\thmx}
  {\popQED\endthmx}

\begin{document}

\begin{thm}[Bézout's Theorem]
\lipsum[1]\lipsum*[2]
\end{thm}

\end{document}

It doesn't seem a good idea, though.

Answer 2

The third parameter of \newtheoremstyle (body font) can be used to change indentation settings. In this case (see also https://tex.stackexchange.com/a/67308) you can use \parshape, which defines the indentation and line length for a specified number of lines (see TeX by Topic, Section 18.2.2). After the lengths have been applied for the specified lines, the remainder of the paragraph will be formatted according to the lengths of the last specified line.

For a theorem, the first line is the theorem title, and the second and third lines are the first and second line of the contents, respectively. In the example below the indents are set to 0pt, \parindent (which is 15pt in this case) and 0pt. The line length is set to \textwidth, which for the second line is decreased by the indent value using \dimexpr, otherwise the line would continue into the right margin. If you want to change the amount of indentation, you should replace \parindent by some other value (e.g., 10mm) for both occurrences.

MWE:

\documentclass{memoir}
\usepackage{amsthm}
\usepackage{amssymb}
\usepackage{lipsum}
\newtheoremstyle{teo}% name
    {3pt}% Space above
    {3pt}% Space below
    {\parshape 3 0pt \textwidth \parindent \dimexpr\textwidth-\parindent 0pt \textwidth}% Body font
    {}% Indent amount
    {\bfseries}% Theorem head font
    {:}% Punctuation after theorem head
    {\newline}% Space after theorem head
    {\thmname{#1}\thmnumber{ #2}{\mdseries\thmnote{ [#3]}}}% Theorem head spec(can be left empty, meaning ‘normal’)
    \theoremstyle{teo}
    \newtheorem{thmx}{Theorem}
    \newenvironment{thm}
      {\pushQED{\qed}\renewcommand{\qedsymbol}{$\square$}\thmx}
      {\popQED\endthmx}

\begin{document}
   \begin{thm}[B\'{e}zout's Theorem]    
      \lipsum[1]
   \end{thm}
\end{document}

Result: