Proof of `Valid separating inequalities from independent-set bounds` (1st statement)
groundedproofs/Lax263307Proofs/ComponentCuts.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
The recursive independence bound yields an inequality valid throughout the exact independent-set hull.
Proof strategy
On an indicator vector the left side is zero if the conditioning set is absent, and otherwise equals the size of the intersection with . The upper bound applies to this independent intersection. The halfspace is convex, so the inequality extends to the entire hull.
Attribution
Bonnet–Chang, Lemma 13.