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The next reachable layer

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

proven

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    Natural Language Statement

    Lemma

    A vertex belongs to the next layer precisely when it is the source or has an incoming edge from the current layer.

    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 Lax733996.Counting
    2
    3/-!
    4---
    5title: The next reachable layer
    6type: lemma
    7---
    8A vertex belongs to the next layer precisely when it is the source or has
    9an incoming edge from the current layer.
    10-/
    11
    12namespace Lax733996.SuccessorLayer
    13
    14open Lax733996.Reachability Counting
    15
    16axiom successor {N : ℕ} (G : Graph N) (a v : Fin N) (k : ℕ) :
    17 v ∈ layer G a (k + 1) ↔ v = a ∨ ∃ u ∈ layer G a k, G u v = true
    18
    19end Lax733996.SuccessorLayer
    20
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