Proof of `Set Cover, Hitting Set, Set Packing, Exact Cover and Set Splitting` (11th statement)
groundedproofs/Lax799700Proofs/Bridge/SetFamily.lean · lax-799700
What this proof establishes
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
Membership from the library's existential second-order definition of SetCover; hardness from the library's reduction out of VertexCover, which is NP-hard by the catalog’s statement for it. Both are transported to the catalog's problems along the agreements.