Lax Lean Archive

A bounded satisfying assignment

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

proven

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    Natural Language Statement

    Lemma

    A satisfiable formula has a certificate whose length is at most the length of its binary encoding. Only variables occurring in the formula matter.

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

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    In the paper

    • page 2 of this submission's paper

    Lean source view on GitHub

    1import Lax429075.Satisfiability
    2
    3/-!
    4---
    5title: A bounded satisfying assignment
    6type: lemma
    7---
    8A satisfiable formula has a certificate whose length is at most the length
    9of its binary encoding. Only variables occurring in the formula matter.
    10-/
    11
    12namespace Lax429075.FiniteWitness
    13
    14open CNF Encoding Satisfiability Lax434930.PolynomialTime
    15
    16axiom bounded (F : Formula) :
    17 Satisfiable F ↔ ∃ y : Word, y.length ≤ (encodeCNF F).length ∧ eval F (assignment y) = true
    18
    19end Lax429075.FiniteWitness
    20
    Show Proof
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