I've redefined the proof environment to make the heading boldface by adapting the code from the amsthm documentation (p. 11). I've literally just deleted \itshape and typed \bfseries instead, nothing else was changed.
(Note: It doesn't even matter whether one changes the italics to boldface, the same problem arises when one copies the provided code from the documentation directly into the document.)
Unfortunately, lists now start on the second line instead of beginning right after the heading. Can this be fixed?
\documentclass[]{article}
\usepackage{amsthm, lipsum}
\makeatletter
\renewenvironment{proof}[1][\proofname]{\par
\pushQED{\qed}%
\normalfont \topsep6\p@\@plus6\p@\relax
\trivlist
\item\relax
{\bfseries
#1\@addpunct{.}}\hspace\labelsep\ignorespaces
}{%
\popQED\endtrivlist\@endpefalse
}
\makeatother
\begin{document}
\begin{proof}
\begin{enumerate}
\item \lipsum[66]
\item \lipsum[66]
\end{enumerate}
\end{proof}
\end{document}
\newlength{\@thlabel@width}\newcommand{\thmenumhspace}{\settowidth{\@thlabel@width}{\upshape(i)}\sbox{\@labels}{\unhbox\@labels\hspace{\dimexpr-\leftmargin+\labelsep+\@thlabel@width-\itemindent}}}and then\begin{enumerate}\thmenumhspaceto get a better spacing in this case, where the item begins the environment. – Sigur Jan 27 '16 at 22:08