This is a follow-up question to this previous question I asked.
Basically I asked for an environment that not only stores the parent equation value, but also the number of a subequation so a series of subequations could be stretched through a larger section of a document, like so (code reused from Werner's answer to the previous question):
There also has been a variant by egreg where one could decide the format of the subequation number when first defining a series of equations.
While these codes work fantastic, there are sometimes situations where I want to show something similar in a different way, e.g. two different ways of proving the same mathematical theorem, so I do not want to start a new equation series with a different equation number, but rather start a new series of subequations within an already existing equation series, so the equation number (in the following case 1) remains the same, while the format of the subequation number changes and re-counts, like so:
I tried adding this option to the codes I received through my previous question, but since I am new to LaTeX, I was not able to figure it out, although I did understand the codes provided by Werner and egreg at least partly.