Notation for non-empty subset To denote non-empty subsets, I repeatedly find myself writing $A\subset S, A\neq \emptyset$. Is there any established shorthand for this, you know, like $A\subset S$ can be seen as a shorthand for $A\subseteq S, A\neq S$?

If I recall correctly, $A \in \mathcal{P}_{\geq 1}(S)$ is somewhat standard notation for "$A$ is a non-empty subset of $S$."
More generally, I think that $\mathcal{P}_{\geq \kappa}(S)$ is sometimes used to denote the collection of all subsets of $S$ with cardinality greater than or equal to $\kappa.$
