OAI/NumberTheory/Ostmann/Arithmetic/MovingFullHarmonicCost.lean

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2 declarations, 0 contain sorry, 0 declared as axioms

1. theorem OAI.Ostmann.moving_harmonic_full_counterpart_le line 11
2. theorem OAI.Ostmann.movingTemplate_restored_full_harmonic_cost_le line 46

   Source documentation

   Both the small-cell endpoints and the terminal bulk bin remain in the same denominator, so the compensation cost can cancel against their sum.

   theorem movingTemplate_restored_full_harmonic_cost_le {σ : Type} [Fintype σ]
       (value tier : σ → ℕ) (hvalue : ∀ a, 0 < value a) (k : ℕ)
       (outside : List ℕ) (cb cd : ℝ) (μ : ℕ → σ → ℝ)
       (hμ : ∀ j a, μ j a ≠ 0 → tier a = j)
       (childBound pivotBound V : ℕ → ℕ) (F : MovingSlotState σ → ℤ → ℂ)
       (φ : ℝ → ℝ) (G : ℕ → ℝ) (n r m : ℕ) (s : ℤ)
       (u : TreeLeafIndex n × Fin 4 → σ) (hu : (∏ i, μ n (u i)) ≠ 0)
       (y : MovingRegularSlot n r m → σ) (hn : n < k)
       (hsmall : ∀ j : TreeLeafIndex n × Fin r, tier (y (j.1, .inl j.2)) ≠ k)
       (hbulk : ∀ j : TreeLeafIndex n × Fin m, tier (y (j.1, .inr j.2)) = k)
       (lower : TreeLeafIndex n × Fin r → ℝ)
       (hlower : ∀ j, Real.exp (lower j) ≤ (value (y (j.1, .inl j.2)) : ℝ))
   …

   Mentions: OAI.Ostmann.MovingSlotState, OAI.Ostmann.TreeLeafIndex, OAI.Ostmann.MovingRegularSlot