Lax Lean Archive

Correctness of vertex classification

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

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    Natural Language Statement

    Lemma

    With the correct current count, a vertex has a valid positive or negative classification exactly according to its membership in the next layer.

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    3 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 Lax733996.Counting
    2
    3/-!
    4---
    5title: Correctness of vertex classification
    6type: lemma
    7---
    8With the correct current count, a vertex has a valid positive or negative
    9classification exactly according to its membership in the next layer.
    10-/
    11
    12namespace Lax733996.Classification
    13
    14open Lax733996.Reachability Counting
    15
    16axiom correct {N : ℕ} (G : Graph N) (a v : Fin N) (k : ℕ) (b : Bool) :
    17 Classify G a k (layer G a k).card v b ↔
    18 (b = true ↔ v ∈ layer G a (k + 1))
    19
    20end Lax733996.Classification
    21
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