Lax Lean Archive

Proof of `Theorem 1` (2nd statement)

groundedproofs/Lax496464Proofs/Ram/Theorem1Final.lean · lax-496464

What this proof establishes

thm✓Lax496464.Theorem1 (2nd 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 8 of this submission's paper

Description

Compose the NP-hardness of Hitting Set with the word RAM reduction of Section 8: the reduction reads the bits of the emitted instance, writes the bits of the constructed shop (TotalReduction.fTotalReduction.f, polynomial-time on the word RAM by TotalFinal.ramPolytimefTotalFinal.ramPolytime_f, hence on a Turing machine), and the numbers of the shop are polynomial in the length of the original input.