Reduction Using Induced Subnets to Systematically Prove Properties for Free-Choice Nets

We use sequences of t-induced T-nets and p-induced P-nets to convert free-choice nets into T-nets and P-nets while preserving properties such as well-formedness, liveness, lucency, pc-safety, and perpetuality. The approach is general and can be applied to different properties. This allows for more systematic proofs that "peel off" non-trivial parts while retaining the essence of the problem (e.g., lifting properties from T-net and P-net to free-choice nets).