refstepcounter inside description item

Question

My purpose is to create visual steps in proofs.

I cooked this from the environment description:

\documentclass{article}

\newcounter{subproofcount}
\newcommand{\thesubproffcount}{\arabic{subproofcount}}
\newcommand{\subprooflabel}[1]{\refstepcounter{subproofcount}(\roman{subproofcount}) \underline{\bf #1}}

\newenvironment{subproof}{\let\Olddescriptionlabel\descriptionlabel\let\descriptionlabel\subprooflabel \begin{description}\setcounter{subproofcount}{0}}{\end{description}\let\descriptionlabel\Olddescriptionlabel}



\begin{document}
    Here is a proof.
    \section{Title 1}
    \section{Title 2}
    \begin{subproof}
        \item[\( A\) is open]       \label{ITEMone}
            Let \( \epsilon>0\) etc.
        \item[\( A\) is bounded] 
            Suppose etc. Using \ref{ITEMone}
    \end{subproof}
\end{document}

The items are correctly numbered:

My problem is that \ref{ITEMone} creates a reference to the section (i.e. "2" in this example) instead of a reference to the subproof item (i.e. (i) in the example).

EDIT: Best answer for my use case here : https://tex.stackexchange.com/a/697316/109167

Answer 1

This uses a new list environment. Note that the default \item does not increment the counter when an optional argument is used.

The only remaining question is whether to place the left margin to the left or right of the optional argument.

\documentclass{article}
\usepackage{showframe}% alignment tool

\newcounter{subproofcount}
\renewcommand{\thesubproofcount}{\roman{subproofcount}}
\newcommand{\subprooflabel}[1]{\hbox to \leftmargin{\hfill(\thesubproofcount)\hspace\labelsep}\underline{\bf #1}}
\newcommand{\subproofitem}[1][]{\refstepcounter{subproofcount}\csname @item\endcsname[#1]}

\newenvironment{subproof}{\let\item=\subproofitem
  \list{subproofcount}{\usecounter{subproofcount}\let\makelabel=\subprooflabel}}%
  {\endlist}

\begin{document}
    Here is a proof.
    \section{Title 1}
    \section{Title 2}
    \begin{subproof}
        \item[\( A\) is open]       \label{ITEMone}
            Let \( \epsilon>0\) etc.\\
            Add another line.
        \item[\( A\) is bounded] 
            Suppose etc. Using \ref{ITEMone}
    \end{subproof}
\end{document}

Answer 2

Since the numbers -- (i), (ii), etc -- in the step-by-step proof are at least as visible as the associated descriptive labels, I would create a bespoke enumerated environment called subproof with the help of the enumitem package and its \newlist and \setlist macros. That way, cross-referencing items via \label and \ref is completely straightforward.

\documentclass{article}
\usepackage[normalem]{ulem}  % for \uline macro
\newcommand\descr[1]{{\boldmath\bfseries\uline{#1}}\hphantom{.}}

\usepackage{enumitem}
\newlist{subproof}{enumerate}{1}
\setlist[subproof]{label=(\roman*)}

\begin{document}
\section{Title 1}
\section{Title 2}

\begin{subproof}
    \item \label{ITEMone}
    \descr{\( A\) is open} Let \( \epsilon>0\). Then \dots
    \item 
    \descr{\( A\) is bounded} Using subproof \ref{ITEMone}, we \dots
\end{subproof}
\end{document}