Lax Lean Archive

Proof of `Hitting Set Is NP-Hard` (1st statement)

groundedproofs/Lax496464Proofs/HittingSet/Correct.lean · lax-496464

What this proof establishes

no assumptions

thm✓Lax496464.HittingSetHardness (1st statement)

Assuming the claims on the left, the claim on the right holds — checked by the archive's pipeline. Proof code is not displayed here.

Read the Lean proof on GitHub

In the paper

  • page 9 of this submission's paper

Description

A satisfying assignment gives the set of the elements of its true literals, one per variable; conversely a hitting set of size varsFvars F meets each of the varsFvars F disjoint pairs in exactly one element, which fixes an assignment, and meeting the set of a clause is satisfying the clause.