OAI/Geometry/HyperbolicGroups/BalancedGrouping.lean

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  1. theorem OAI.HyperbolicObstruction.PlanarRecursion.balanced_grouping line 16

    Source documentation

    Group blocks of size at most half into two groups of size at most two thirds. The total may be less than n because removed vertices are absent.

    theorem balanced_grouping (w : I → ℕ) (n : ℕ) (htotal : ∑ i, w i ≤ n)
        (hblock : ∀ i, 2*w i ≤ n) :
        ∃ A : Finset I, 3*(∑ i ∈ A, w i) ≤ 2*n ∧ 3*(∑ i ∈ Aᶜ, w i) ≤ 2*n := by
    …