`\subseteq` instead of `\in SUBSET`

As far as I am aware, the expressions A \in SUBSET B and A \subseteq B are equivalent. I find the second one more appealing. However, TLC does not allow the second form in action predicates. In some of my specifications I would like to write

Next ==
    data' \subseteq data

instead of the slightly-more-awkward

Next ==
    data' \in SUBSET data

It might also be reasonable to allow \subseteq in quantifiers as well, as in

\E x \subseteq {1,2,3}: x = {1}

(which is currently not allowed).

[lemmy]

Related scenario:

Validating an inductive invariant candidate IInv with TLC, when the TypeOK conjunct of IInv has as s1 \subseteq s2, TypeOK has to be rewritten to s1 \in SUBSET s2.

Context: https://lamport.azurewebsites.net/tla/proving-safety.pdf (page 9ff)

[lemmy]

A common idiom is to check if some set s is a k-subset for k \in 1..Cardinality(S) of some other set S (but not the empty set): s \in (SUBSET S \ {{}})