Lax Lean Archive

Correctness of the count sequence

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

proven

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    Natural Language Statement

    Lemma

    The initial layer consists of the source. Inductive counting certifies exactly the successive layer sizes, including the final size after NN steps.

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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 Lax362205.Counting
    2
    3/-!
    4---
    5title: Correctness of the count sequence
    6type: lemma
    7---
    8The initial layer consists of the source. Inductive counting certifies
    9exactly the successive layer sizes, including the final size after NN steps.
    10-/
    11
    12namespace Lax362205.CountingTrace
    13
    14open Lax362205.Reachability Counting
    15
    16axiom correct {N : ℕ} (G : Graph N) (a : Fin N) (counts : ℕ → ℕ) :
    17 CountTrace G a counts ↔ ∀ k ≤ N, counts k = (layer G a k).card
    18
    19end Lax362205.CountingTrace
    20
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