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I am writing some equations using subnumcases enviroment as the following:

\documentclass[a4paper]{article}
\usepackage{amsmath}
\usepackage{cases}
\numberwithin{equation}{section}
\begin{document} 
\begin{subnumcases}{}
1=1;\\
2=2;\\
\cdots \notag\\
n-1=n-1;\\
n=n.
\end{subnumcases}

I want to add tags for each equation as the following: the first is labeled by "(1.1.1)" or "(1.1)_1", and the second is labeled by "(1.1.2)" or "(1.1)_2", and the last is labeled by "(1.1.n)" or "(1.1)_n". But here "1.1" is the numbering of this set of equations and should be changed according to the position of the equations. Namely, I want to be able to change some part of the label while also keep the original label.

Does anyone know how to do this? Thanks in advance.

I think this question should be closely related to Aligning labels inside cases environment

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