Lax Lean Archive

Exact censuses enumerate the whole layer

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

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    Natural Language Statement

    Lemma

    A census of reachable vertices with the correct cardinality contains every vertex of the layer. Distinctness is enforced by the finite-set representation.

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    Proven claimDefinitionThis conceptRelated conceptA → B: B builds on A
    Evidence

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    • page 1 of this submission's paper

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    1import Lax733996.Counting
    2
    3/-!
    4---
    5title: Exact censuses enumerate the whole layer
    6type: lemma
    7---
    8A census of reachable vertices with the correct cardinality contains every
    9vertex of the layer. Distinctness is enforced by the finite-set representation.
    10-/
    11
    12namespace Lax733996.ExactCensus
    13
    14open Lax733996.Reachability Counting
    15
    16axiom complete {N : ℕ} (G : Graph N) (a : Fin N) (k : ℕ) (S : Finset (Fin N)) :
    17 Census G a k (layer G a k).card S → S = layer G a k
    18
    19end Lax733996.ExactCensus
    20
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