Abstract: Structural analysis is central to Petri Net (PN) research, complementing state-space methods while avoiding their combinatorial issues. It is well studied for classical PNs but much less for High-Level Petri Nets (HLPN). Symmetric Nets (SN), a common HLPN formalism, use compact annotations to encode behavioral symmetries, allowing symbolic reachability graphs and associated lumped Markov chains for stochastic SN. In the past two decades, specific structural techniques for SN have emerged, notably the SNexpression tool, which implements a calculus for symbolic structural relations such as conflict and causality. We propose using this calculus to semi-automatically verify symbolic structural invariants, currently possible only for restricted SN subclasses, for an extended SN formalism (ESN) closed under key functional operators. We focus on flows and outline, at least in theory, how to construct a flow-generating family. We also sketch a framework for formally verifying a wider range of invariant properties. Representative examples illustrate the main concepts.