Indent item labels in enumerate like normal paragraph, body of item flush with margin

Question

For an enumerate environment with labels modified as shown, using the enumitem package, how does one combine the various other options (labelindent, leftmargin, etc.) of enumerate so that:

• the start of each entire label "Case (a)" or "Case{b}" is indented by the amount of a normal paragraph indent; and
• the body of each item is flush with the left margin?

The colored markup of the output from the example below should indicate graphically what I want.

[A similar question — and presumably essentially the same method would work — for when the enumerate environment uses lower-case Roman numerals, by means of option label= \upshape(\roman*).]

\documentclass[12pt]{memoir}
\usepackage{amsthm}
\usepackage{enumitem}
\usepackage{lipsum}

\newtheorem{theorem}{Theorem}

\begin{document}

\begin{theorem}
Very important!
\end{theorem}

\begin{proof}

To begin we consider all the possibilities of what may happen and what may not actually happen at all.

We now distinguish two cases.

\begin{enumerate}[label=\emph{Case (\alph*):}]

\item $a = b$.
%
Now we see that\dots\lipsum[1]

\item $a \neq b$. In this case \dots \qedhere

\end{enumerate}

\end{proof}

After establishing that result, to which we shall refer later, we now return to the previous thread of ideas.

\end{document}

Answer 1

Use the wide option for enumerate, and set itemsep and topsep to 0pt:

\documentclass[12pt]{memoir}
\usepackage{amsthm}
\usepackage{enumitem}
\usepackage{lipsum}

\newtheorem{theorem}{Theorem}

\begin{document}

\begin{theorem}
  Very important!
\end{theorem}

\begin{proof}

  To begin we consider all the possibilities of what may happen and what may not actually happen at all.

  We now distinguish two cases.

  \begin{enumerate}[label=\emph{Case (\alph*):},wide, itemsep =0pt, topsep=0pt]
    \item $a = b$.
          %
          Now we see that ... \lipsum[1]

    \item $a ≠ b$. In this case ... \qedhere

  \end{enumerate}

\end{proof}

After establishing that result, to which we shall refer later, we now return to the previous thread of ideas.

\end{document} 

Answer 2

It almost seems more convenient in this case to define something like a theoremcases environment that just sets the Case (.): title at the start of a paragraph every time you call \item (or, say, \caseitem):

\documentclass{memoir}

\usepackage{amsthm}
\usepackage{lipsum}

\newtheorem{theorem}{Theorem}

\newcounter{theoremcases}[theorem]
\renewcommand{\thetheoremcases}{\alph{theoremcases}}
\newcommand{\caseitem}{%
  \par\refstepcounter{theoremcases}%
  \textit{Case~(\thetheoremcases): }%
  \ignorespaces
}
\newenvironment{theoremcases}
  {\let\item\caseitem}
  {}

\begin{document}

\begin{theorem}
Very important!
\end{theorem}

\begin{proof}
To begin we consider all the possibilities of what may happen and what may not actually happen at all.

We now distinguish two cases.

\begin{theoremcases}
  \item $a = b$.
  %
  Now we see that\dots\lipsum[1]

  \item $a \neq b$. In this case \dots \qedhere
\end{theoremcases}
\end{proof}

After establishing that result, to which we shall refer later, we now return to the previous thread of ideas.

\end{document}

The theoremcases environment just makes \item equivalent to \caseitem, for convenience. You can also \label-and-\ref the cases, just like you would using enumitem.