I am stuck with a formatting problem: I have a system with cases within cases, and I would like each subcase to be numbered. Here is a MWE of what I got for the moment:
\documentclass[12pt, a4paper]{article}
\usepackage[english]{babel}
\usepackage[utf8]{inputenc}
\usepackage[overload]{empheq}
\begin{document}
\begin{subequations} \label{eq:systm}
\begin{align}[left={S=\empheqlbrace}]
S_1= {}& \begin{cases}
\vspace{4pt}
A + B + C & \text{if } a < 1, \\
\vspace{4pt}
D + 2(\sum\limits_{i} EF + \\~~~~
2 GH ) + K-L & \text{if }a=1.
\end{cases} \\
S_2 = {}& 1 \\
S_3= {}& \begin{cases}
\sum\limits_{i} I + \sum\limits_{i} J & \text{if } a = 0 \\
0 & \text{otherwise.}
\end{cases}
\end{align}
\end{subequations}
\end{document}
I would like (if possible) the first line to be numbered 1.1a, the second (with the split) 1.1b, the third 1.2, the fourth 1.3a and the last one 1.3b (or something of this type...)
I also really need the splits to be taken in account (in fact I'm dealing with very long equations).
Can you help ? Thank you :)