Text Formatting ⇒ Making an environment for examples and propositions

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I'm looking for a way to make an environment which when given no argument gives an enumeration such as
(1) Bla bla
(2) Bla bla
(a) Bla bla
(b) Bla bla
(i) Bla bla
(ii) Bla bla
(3) Bla bla
where a \ref to ii prints (2aii). When the environment is used with an argument and if the argument string starts with "\ref" it gives (if the argument is "\ref{bla} which prints T") the following list
(T$_1$)
(T$_2$)
(a)
(b)
(i)
(ii)
(T$_3$)
where a \ref to ii prints (T$_2$aii). And if the argument string is anything else (for instance "T") gives the following list
(T)
(a)
(b)
(i)
(ii)
where a \ref to ii prints (Taii). Also if arguments for the environment is used it adds the list items to an index so a list of them and the page they appear on can be printed. For the labels not set by hand, every label except T and T$_n$ in my example, every first level label should automatically use enumitems resume option. So if i use the enivorment again its first level start where it stopped counting on last use. So if I use it now it should continue from the first example since it's the only one with unmodified first level labels, such as:
(4)
(5)
(a)
(b)
(i)
(ii)
(6)