Lax Lean Archive

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

Lax307052.SplitWalk

Splitting a bounded walk

concepts/Lax307052/SplitWalk.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

    A walk of length at most r+sr+s can be split at a vertex into walks of length at most rr and at most ss.

    Lean source view on GitHub

    1import Lax307052.Reachability
    2
    3/-!
    4---
    5title: Splitting a bounded walk
    6type: lemma
    7---
    8A walk of length at most r+sr+s can be split at a vertex into walks of
    9length at most rr and at most ss.
    10-/
    11
    12namespace Lax307052.SplitWalk
    13
    14open Reachability
    15
    16axiom split {α : Type} (R : α → α → Prop) (r s : ℕ) (a b : α) :
    17 Within R (r + s) a b ↔ ∃ m, Within R r a m ∧ Within R s m b
    18
    19end Lax307052.SplitWalk
    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…