How to tell if one smaller petri net pattern exist in a bigger petri net (from behavioral aspect)?

Question

I'm working with Petri nets to model some concurrent systems, and I need to determine if a smaller Petri net pattern (let's call it N_small) exists within a larger Petri net (N_big), but from a behavioral aspect rather than a structural one (there are special cases: same behavior but different structures).

In other words, I want to verify if the behavior represented by N_small (sequence of transitions, concurrent executions, etc.) can be found within the behaviors of N_big. The exact structure (places, transitions, arcs) doesn't need to match perfectly, but the possible sequences of events (behavior) should correspond.

What I am currently doing is generating a reachability graph for both N_small and N_big, and then I have RG_small and RG_big.

Intuitively, I think, by checking if RG_small is a subgraph of RG_big can tell if the behavior of N_small exist in N_big.

I think someone should have already proved it. But I didn't find relevant resources or books, and I'm unsure how to prove it in a formal way. Any guidance on this topic would be greatly appreciated!