Lax Lean Archive

Correctness of one counting step

Lax362205.CountingStep · concepts/Lax362205/CountingStep.lean · lax-362205

proven

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    Natural Language Statement

    Lemma

    Starting from the correct layer size, valid classifications produce exactly the size of the next layer. Such classifications exist.

    Concept map
    3 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 Lax362205.Counting
    2
    3/-!
    4---
    5title: Correctness of one counting step
    6type: lemma
    7---
    8Starting from the correct layer size, valid classifications produce exactly
    9the size of the next layer. Such classifications exist.
    10-/
    11
    12namespace Lax362205.CountingStep
    13
    14open Lax362205.Reachability Counting
    15
    16axiom correct {N : ℕ} (G : Graph N) (a : Fin N) (k d : ℕ) :
    17 CountStep G a k (layer G a k).card d ↔ d = (layer G a (k + 1)).card
    18
    19end Lax362205.CountingStep
    20
    Show Proof
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