Lax Lean Archive

Correctness of the SAT verifier

Lax429075.VerifierCorrect · concepts/Lax429075/VerifierCorrect.lean · lax-429075

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    Natural Language Statement

    Lemma

    Membership in SAT is equivalent to the existence of an accepted certificate of length at most the input length.

    Concept map
    6 concepts
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    Proven claimDefinitionThis conceptRelated conceptA → B: B builds on A
    Evidence

    Each proof establishes this claim relative to its assumptions.

    In the paper

    • page 2 of this submission's paper

    Lean source view on GitHub

    1import Lax429075.Satisfiability
    2
    3/-!
    4---
    5title: Correctness of the SAT verifier
    6type: lemma
    7---
    8Membership in SAT is equivalent to the existence of an accepted certificate
    9of length at most the input length.
    10-/
    11
    12namespace Lax429075.VerifierCorrect
    13
    14open Satisfiability Lax434930.PolynomialTime Lax434930.Certificates
    15
    16axiom correct (w : Word) :
    17 w ∈ SAT ↔ ∃ y : Word, y.length ≤ w.length ∧ pair w y ∈ Verifier
    18
    19end Lax429075.VerifierCorrect
    20
    Show Proof
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