Lax Lean Archive

Complementing a logarithmic space language

Lax733996.ComplementClosure · concepts/Lax733996/ComplementClosure.lean · lax-733996

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    Natural Language Statement

    Lemma

    The complement of a language in NL\mathrm{NL} also belongs to NL\mathrm{NL}.

    Concept map
    5 concepts
    100%
    Proven claimDefinitionThis conceptRelated conceptA → B: B builds on A
    Evidence

    Each proof establishes this claim relative to its assumptions.

    In the paper

    • page 3 of this submission's paper

    Lean source view on GitHub

    1import Lax434930.NondeterministicLogarithmicSpace
    2
    3/-!
    4---
    5title: Complementing a logarithmic space language
    6type: lemma
    7---
    8The complement of a language in NL\mathrm{NL} also belongs to NL\mathrm{NL}.
    9-/
    10
    11namespace Lax733996.ComplementClosure
    12
    13open Lax434930.PolynomialTime Lax434930.NondeterministicLogarithmicSpace
    14
    15axiom closed (A : Language) : A ∈ NL → Aᶜ ∈ NL
    16
    17end Lax733996.ComplementClosure
    18
    Show Proof
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