array within frac, using nath package

For some reason, nath uses \uppercase when working on fractions (I've not checked the details, but the error message is about ARRAY being undefined).

This hack seems to work:

\documentclass{article}
\usepackage{nath}
\newenvironment{ARRAY}[2][c]{\lowercase{\array[#1]{#2}}}{\endarray}

\begin{document}
\begin{equation}
  \begin{array}{c}a\\b\\c\end{array}\quad
  \frac{numerator}{denominator}\quad
  \frac{\begin{array}{c}a\\b\\c\end{array}}{denominator}
\end{equation}
\end{document}

---

A less hackish way is to hide array:

\newcommand{\morelines}[1]{\begin{array}{c}#1\end{array}}

and

\begin{equation}
\frac{\morelines{a\\b\\c}}{denominator}
\end{equation}

or even

\newcommand{\morelines}[1]{\begin{array}{c}#1\end{array}}
\newcommand{\deduction}[2]{\frac{\morelines{#1}}{\morelines{#2}}}

and inputting your deduction as

\begin{equation}
\deduction{a\\b\\c}{denominator}
\end{equation}

---

_{I'm more convinced about not using nath.}

After some more trial and error, I found that \hline works in the array environment.

\documentclass{article}
\usepackage{nath}
\begin{document}
\begin{equation}
  \begin{array}{c}
    Hypothesis_1\\
    Hypothesis_2\\
    \hline
    Conclusion_1
  \end{array}
\end{equation}
\end{document}

This gives the visual result I want, and doesn't have \frac{}{}'s semantic mismatch, however the arrays have a different vertical alignment, and tend to collide with what's left and right of them (they need a little more horizontal padding), so egreg's answer is better.

For the particular example in the question, a \matrix could be used as well

\documentclass{article}
\usepackage{nath}
\begin{document}
\begin{equation}
  \frac{\matrix a\\ b\\ c\strut\endmatrix}{`denominator}
\end{equation}
\end{document}