Proof of `Restricting an induced almost-embedding to its route union`
groundedproofs/Lax263307Proofs/HostRestriction.lean · lax-263307
What this proof establishes
no assumptions
Assuming the claims on the left, the claim on the right holds — checked by the archive's pipeline. Proof code is not displayed here.
Description
Choose a Fin labeling of the route union. Map vertices inside it to their labels and all other vertices to a fixed label. Every route lies inside the union, so this map preserves its cardinality, connectivity, endpoints, and induced noninteraction. The labeling is a graph isomorphism onto the induced host and therefore preserves the unordered edge count.