Unindented proof in amsbook

Question

I am using the proof environment in amsbook. Unlike amsart, the proof is automatically indented. Is there a way of cancelling the indentation?

\documentclass{amsbook}
\begin{document}
\noindent This is a non-indented sentence.
\begin{proof}
This is a proof.
\end{proof}
\end{document}

Answer 1

Say

\usepackage{etoolbox}
\expandafter\patchcmd\csname\string\proof\endcsname
  {\normalparindent}{0pt }{}{}

which is equivalent (but shorter) to redefining the proof environment as follows

\makeatletter
\renewenvironment{proof}[1][\proofname]{\par
  \pushQED{\qed}%
  \normalfont \topsep6\p@\@plus6\p@\relax
  \trivlist
  \itemindent\z@ % original has \normalparindent
  \item[\hskip\labelsep
        \scshape
    #1\@addpunct{.}]\ignorespaces
}{%
  \popQED\endtrivlist\@endpefalse
}
\makeatother

Answer 2

amsbook defines \normalparindent (18 pt) and uses it for \itemindent within the proof environment. Here's a redefinition which avoids that, I simply redefined and commented one line out:

\makeatletter
\renewenvironment{proof}[1][\proofname]{\par
  \pushQED{\qed}%
  \normalfont \topsep6\p@\@plus6\p@\relax
  \trivlist
  %\itemindent\normalparindent
  \item[\hskip\labelsep
        \scshape
    #1\@addpunct{.}]\ignorespaces
}{%
  \popQED\endtrivlist\@endpefalse
}
\makeatother