Lax Lean Archive

Linking small terminal subsets

Lax17.SmallLinkedSubsets · concepts/Lax17/SmallLinkedSubsets.lean · lax-17

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    Natural Language Statement

    Theorem

    Disjoint equally large subsets of a node-well-linked set can be linked inside the same cluster.

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

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    Lean source view on GitHub

    1import Lax17.Linkedness
    2
    3/-!
    4---
    5title: Linking small terminal subsets
    6type: theorem
    7---
    8Disjoint equally large subsets of a node-well-linked set can be linked
    9inside the same cluster.
    10-/
    11
    12namespace Lax17.SmallLinkedSubsets
    13
    14universe u
    15
    16/-- Disjoint equally large subsets of a node-well-linked set are linked
    17inside the same cluster. -/
    18axiom smallLinkedSubsets :
    19 ∀ {V : Type u} [DecidableEq V] (G : SimpleGraph V)
    20 (C X A B : Finset V),
    21 Lax17.Linkedness.NodeWellLinkedIn G C X →
    22 A ⊆ X → B ⊆ X → Disjoint A B → A.card = B.card →
    23 Lax17.Linkedness.NodeLinkedIn G C A B
    24
    25end Lax17.SmallLinkedSubsets
    26
    Show Proof
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