How to achieve enumerated list or perhaps table of this form?

I'm trying to replicate a list in some mathematics that I'm looking at and am struggling to figure out how to do it. So far I've tried using a table and it's not looking great.

Below is a link showing firstly what I've managed to do so far, and then what I am aiming for:

Does anyone have any ideas about how I could improve it?

This is my code so far:

\begin{enumerate}[label=\Roman{*}., ref=(\roman{*})]
\setcounter{enumi}{3}
\item Composition. Subroutine $R_N (y = f(x_1 , \ldots , x_n ))$ using subroutines for $g, h$, where \hfill \hfill \linebreak $f(x_1 , \ldots , x_n ) = g(h_1 (x_1 , \ldots , x_n ), \ldots , h_m (x_1 , \ldots , x_n ))$.
\\[1\baselineskip]
\begin{tabular}{ r c l }
1. & $R_{N+1}(N+1 \ =$ & $g_1 (x_1 , \ldots , x_n))$  \\
$\vdots$ & $\vdots$ & $\vdots$ \\
m. & $R_{N+m}(N+1 \ =$ & $g_m (x_1 , \ldots , x_n))$  \\
m+1. & $R_{N+m}(y \ =$ & $h(N+1, \ldots , N+m))$ \\

\end{tabular}

\end{enumerate}

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I embedded the images for you ;) It's a nice question (dispite tabular not being a good option here IMHO). Just two things: (1) It is better to inlude a full Minimal Working Example into your question. (2) Wouldn't you prefer some better name than user2041080? You can change it in your profile ;) – yo' Feb 24 '13 at 13:52

I would go for a solution using align* from the amsmath package:

\documentclass{article}

\pagestyle{empty}

\usepackage{enumitem}

\usepackage{amsmath}

\begin{document}

\begin{enumerate}[label=\Roman{*}., ref=(\roman{*})]
%\setcounter{enumi}{3}
\item Composition. Subroutine $R_N (y = f(x_1 , \dots , x_n ))$ using subroutines for $g, h$, where
\begin{align*}
&&   f(x_1 , \dots , x_n ) &= g(h_1 (x_1 , \dots , x_n ), \dots , h_m (x_1 , \dots , x_n )).
\\[\medskipamount]
1.&&   R_{N+1}(N+1 &= g_1 (x_1 , \dots , x_n))
\\
m.&&   R_{N+m}(N+1 &= g_m (x_1 , \dots , x_n))
\\
m+1.&& R_{N+m}(y &= h(N+1, \dots , N+m)) \\
\end{align*}

\end{enumerate}

\end{document}


Remarks:

1. align* has several pairs of columns aligned as rl<glue here>rl<glue here>rl... with a correct space between r and l for relations.

2. I manually adjusted positions of \vdots using \, \quad and \qquad horizontal spaces.

3. Using \dotsc (c as comma) is prefered over \ldots. Here, the command \dots can be used as well (it finds the correct dots according to the next character, which is , in this case).

4. Everything should have a proper punctuation. However, I'm not sure I understand the meaning of the equations therefore I can't add it.

5. I don't think it is a good idea to label with I, II, ... and reference as (i), (ii), ...

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Thanks very much for all your help! I'm new to using Latex and have sort of been thrown in at the deep end somewhat. One quick question regarding your remarks, namely remark 5; could you explain it differently? I'm struggling to understand how the items labeled with I, II etc are referenced by (i), (ii), etc – hamchapman Feb 24 '13 at 14:30
Your example contains a line \begin{enumerate}[label=\Roman{*}., ref=(\roman{*})]. This makes the enumeration labelled by uppercase Roman numeral. But if you reference any of the items (using \label{thisismyitem} in the item and \ref{thisismyitem} in the place of reference), the reference would eventually show up as lowercase roman numeral in parentheses. – yo' Feb 24 '13 at 18:54