Using custom item labels in itemize environment inside an `mdframed` box causes content to slip out of box?

Question

Consider the following MWnotE:

\documentclass{article}

\usepackage{amsmath}
\usepackage{amsthm}
\usepackage{mdframed} % noteboxes, boxes, etc.

\newmdenv{notebox}

\begin{document}
    \section{Cats}
        Here is an important theorem.

        \begin{notebox}
            Let $X$ be a graph with $k$ vertices. Then, the earth is flat.

            \begin{proof}
                It suffices to show that the following conditions hold: 

                    \begin{itemize}
                        \item[Closure.] 
                        \begin{equation*}
                            0/0 = 0
                        \end{equation*}
                    \end{itemize}
            \end{proof}
        \end{notebox}

\end{document}

It produces as output the following:

How do I fix this?

Answer 1

Edit: I could do it even better than @ChristianHupfer but did not wanted to make clear how much better I am :P ... So, just leaving this non elegant but simple way as a "working solution".

A solution is to use enumitem's leftmargin option, like:

\documentclass{article}
\usepackage{enumitem}
\usepackage{amsmath}
\usepackage{amsthm}
\usepackage{mdframed} % noteboxes, boxes, etc.

\newmdenv{notebox}

\begin{document}
    \section{Cats}
        Here is an important theorem.

        \begin{notebox}
            Let $X$ be a graph with $k$ vertices. Then, the earth is flat.

            \begin{proof}
                It suffices to show that the following conditions hold: 

                    \begin{itemize}[leftmargin=40pt]
                        \item[Closure.] 
                        \begin{equation*}
                            0/0 = 0
                        \end{equation*}
                    \end{itemize}
            \end{proof}
        \end{notebox}

\end{document}

Answer 2

Similar to koleygr's idea, but using labelsep=0pt and automatic adjustement of \leftmargin with leftmargin=* from enumitem in conjunction with removal of the itemize label by label={}.

This could be done with a \newlist and \setlist as well.

\documentclass{article}

\usepackage{amsmath}
\usepackage{amsthm}
\usepackage{mdframed} % noteboxes, boxes, etc.

\usepackage{enumitem}

\newmdenv{notebox}


\begin{document}
    \section{Cats}
        Here is an important theorem.

        \begin{notebox}
            Let $X$ be a graph with $k$ vertices. Then, the earth is flat.

            \begin{proof}
              It suffices to show that the following conditions hold: 

              \begin{itemize}[label={},labelsep=0pt,leftmargin=*]
              \item Closure.
                \begin{equation*}
                  0/0 = 0
                \end{equation*}
              \item Foo

              \end{itemize}
            \end{proof}
          \end{notebox}

        \begin{notebox}[innerleftmargin=2cm]
            Let $X$ be a graph with $k$ vertices. Then, the earth is flat.

            \begin{proof}
              It suffices to show that the following conditions hold: 

              \begin{itemize}[label={},labelsep=0pt,leftmargin=*]
              \item Closure.
                \begin{equation*}
                  0/0 = 0
                \end{equation*}
              \end{itemize}
            \end{proof}
          \end{notebox}

\end{document}