Proof of `Balanced closed parts certify a balanced separator`
groundedproofs/Lax263307Proofs/BalancedPartitions.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
Pick a vertex in each connected component and its unique partition part. Every walk with undeleted vertices stays in that closed part, so the component’s image is contained in it. Injective projection preserves the component cardinality, which is bounded by the part size.