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Lax307052.Recursion

Correctness of recursive reachability

concepts/Lax307052/Recursion.lean · lax-307052

proven

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    Proven claimDefinitionThis conceptRelated conceptA → B: B builds on A

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    Lemma

    At recursion depth kk, the search accepts exactly the vertex pairs joined by a walk of length at most 2k2^k.

    Lean source view on GitHub

    1import Lax307052.SplitWalk
    2
    3/-!
    4---
    5title: Correctness of recursive reachability
    6type: lemma
    7---
    8At recursion depth kk, the search accepts exactly the vertex pairs
    9joined by a walk of length at most 2k2^k.
    10-/
    11
    12namespace Lax307052.Recursion
    13
    14open Reachability
    15
    16axiom search_correct {N : ℕ} (G : Graph N) (k : ℕ) (a b : Fin N) :
    17 search G k a b = true ↔ Within (fun u v => G u v = true) (2 ^ k) a b
    18
    19end Lax307052.Recursion
    20
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