Proof environment - line break after the "Proof."

Question

I want to make the proof environment in amsthm package to auto add a line break right after the "Proof."

I tried the following code, which also removed the QED sign, but it doesn't work: No linebreak is added.

\makeatletter
\renewenvironment{proof}[1][\proofname]{\par
    \normalfont \topsep6\p@\@plus6\p@\relax
    \trivlist
    \item[\hskip\labelsep
        \itshape
        #1\@addpunct{.} \newline] }%\ignorespaces}
\makeatother

Answer 1

a manual way to drop to a new line immediately after the proof heading is to insert

$ $\newline

but it's possible to build on the existing proof definition and thereby retain the ability to use the \qedhere facility to move the "tombstone" up to the actual last line of the proof.

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

\newenvironment{myproof}[1][\proofname]{%
  \begin{proof}[#1]$ $\par\nobreak\ignorespaces
}{%
  \end{proof}
}

\begin{document}

\begin{proof}
  $ $\newline
    First line of my proof

    Intermediary lines of my proof:
  \begin{itemize}
   \item next-to-last line
   \item last line of my proof
  \qedhere
  \end{itemize}
\end{proof}

\begin{myproof}[Proof of my theorem]
    First line of my proof

    Intermediary lines of my proof:
  \begin{itemize}
   \item next-to-last line
   \item last line of my proof
  \qedhere
  \end{itemize}
\end{myproof}

\begin{myproof}
    First line of my proof

    Intermediary lines of my proof:
  \begin{itemize}
   \item next-to-last line
   \item last line of my proof
  \qedhere
  \end{itemize}
\end{myproof}

\end{document}

Answer 2

First, I wouldn't redefine the proof environment. I would just make my own. Secondly, the placement of your \newline needs to be placed outside of the square brackets. Here's a working example:

\documentclass{article}
\usepackage{amsmath,amssymb,amsthm}
\makeatletter
\newenvironment{myproof}[1][\proofname]{\par
    \pushQED{\qed}%
    \normalfont \topsep6\p@\@plus6\p@\relax
    \trivlist
    \item[\hskip\labelsep
        \itshape
        #1\@addpunct{.} ]\mbox{}\par\nobreak}
    {\popQED\endtrivlist\@endpefalse}
\makeatother
\usepackage{lipsum}
\begin{document}

\begin{myproof}
    First line of my proof

    Intermediary lines of my proof:
    \lipsum[1]

    last line of my proof
\end{myproof}

\end{document}

But because of the \newline The indentation of the paragraphs doesn't look good to me. So, I would recommend changing the \newline to \par to force a paragraph break. So the code for the new environment would be

\makeatletter
\newenvironment{myproof}[1][\proofname]{\par
    \pushQED{\qed}%
    \normalfont \topsep6\p@\@plus6\p@\relax
    \trivlist
    \item[\hskip\labelsep
        \itshape
        #1\@addpunct{.} ]\mbox{}\par\nobreak}
    {\popQED\endtrivlist\@endpefalse}
\makeatother

which results in

Answer 3

I would definitely consider the ntheorem package for this; it has a lot of very useful pre-defined styles, including break which is perfect for what you want; note that this won't ever orphan your Proof from its body.

\theoremstyle{nonumberbreak}
\theoremsymbol{\ensuremath{\diamondsuit}}
\theorembodyfont{}
\theoremheaderfont{\itshape}
\renewtheorem{proof}{Proof}

It also has a robust algorithm for assigning a theoremmark, which can be whatever symbol you want.

\documentclass{article}
\usepackage{amsmath}
\usepackage[amsmath,standard,thmmarks]{ntheorem} 

\theoremstyle{nonumberbreak}
\theoremsymbol{\ensuremath{\diamondsuit}}
\theorembodyfont{}
\theoremheaderfont{\itshape}
\renewtheorem{proof}{Proof}

\begin{document}

\begin{proof}
  Your proof goes here
  Your proof goes here
  Your proof goes here
  Your proof goes here
  Your proof goes here
  Your proof goes here
  Your proof goes here
  Your proof goes here
  Your proof goes here
  Your proof goes here
  Your proof goes here
\end{proof}

\end{document}

For further reading, you might also like to have a look at the question and answers here Definitive guide to trivlists; you'll see it is all about having an environment with a heading on a new line (that won't get orphaned).