Is there any notation for all elements of a sequence coming from another set?

Question

Let $\{ A(\lambda, i) \}_{i=0}^{N-1}$ be a sequence denoted by $A(\lambda)$ and $B$ be a set. Is there any established notation to show that all elements of $A(\lambda)$ come from the set $B$ ? The notation should be between $A(\lambda)$ and $B$.

For example, I have created the following notation. Let us suppose $A(\lambda) \leftarrowtail B$ denotes $$ A(\lambda, i) \in B \text{ for all } i \in \{0,\ldots,N-1 \}. $$

Is there any already established notation to achieve this relationship?

Answer 1

Could you just use the strict subset notation $\subset$ Thus just have

$$A(\lambda)\subset B$$