Is this valid syntax for constraining nested tuples within a set? I've got something like this snippet for something I'm working on: $$ S = \lbrace (a, (b_0, \dots, b_n), c) : a \in A, \lbrace b_0, \dots, b_n \rbrace \subseteq B, c \in C, n \in {\mathbb N} \rbrace $$ My goal here is to specify in the set constraint that the tuple $(b_0, \dots, b_n)$'s elements should all be members of set B, even though the tuple itself could contain duplicates. Is this even valid, and is there a better way to express this that I'm missing?

It is not including when the b's are not unique.
S = $\cup${ A × $B^n$× C : n in N } includes nonunique b's.