Lax Lean Archive

Draft — mutable and not usable as a dependency; its citation marks the draft state.

Lax307052.ShortPaths

Short paths in a finite graph

concepts/Lax307052/ShortPaths.lean · lax-307052

proven

Loading review…

Community review

Flags

Each flag is tied to a public ORCID identity and explains why this concept may be incorrect.

No flags have been submitted.

    Community review

    Flag this concept

    State precisely what appears incorrect. This explanation will be public under your ORCID name.

    No source line selected.

    Concept map

    Proven claimDefinitionThis conceptRelated conceptA → B: B builds on A

    Evidence

    Each proof establishes this claim relative to its assumptions.

    Lemma

    If one vertex reaches another in a graph with NN vertices, a walk of length less than NN suffices.

    Lean source view on GitHub

    1import Lax307052.Reachability
    2
    3/-!
    4---
    5title: Short paths in a finite graph
    6type: lemma
    7---
    8If one vertex reaches another in a graph with NN vertices, a walk of
    9length less than NN suffices.
    10-/
    11
    12namespace Lax307052.ShortPaths
    13
    14open Reachability
    15
    16axiom short_path {N : ℕ} (G : Graph N) (a b : Fin N) :
    17 Reachable G a b ↔ ∃ k < N, Walk (fun u v => G u v = true) k a b
    18
    19end Lax307052.ShortPaths
    20
    Show Proof

    Builds on

    Used by

    From Mathlib

    none

    Community review

    Discussion

    Ask a question or add context. Endorsements and structured flags are kept in the review panel above; your ORCID profile must share a public name.

    0 comments

    Loading discussion…