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caec230 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 | import OAI.MeasureTheory.DyadicAvoidance.GridStabilityFin
import OAI.MeasureTheory.DyadicAvoidance.FiniteTableModel
namespace OAI
universe u_ι
noncomputable section
namespace Problem310.FiniteTableModel
/-- Stable geometry preserves the full dependent selector address. -/
theorem selectorAddress_eq_of_grid_stability {ι : Type u_ι} {a b : ι → ℕ}
{M d : ℕ} (bS : Node M d → Fin M → ℕ) {x t : ℝ}
(hx : x ∈ gridStableCenters a b) (e : ι) (P : Node M d) (i : Fin M)
{n : ℕ} (hresolution : bS P i ≤ b e) (hindex : a e ≤ n)
(ht : t ∈ Set.Icc (1 : ℝ) 2) :
selectorAddress bS P i (x + t * ((2 : ℝ)⁻¹) ^ n) = selectorAddress bS P i x := by
unfold selectorAddress
rw [gridStableCenters_preserves_fin hx e hresolution hindex ht]
/-- Therefore every completion of the random tables preserves the earlier
selector evaluations at a stable center. -/
theorem selectorValue_eq_of_grid_stability {ι : Type u_ι} {a b : ι → ℕ}
{M d : ℕ} (bS : Node M d → Fin M → ℕ) (ω : SelectorTable bS) {x t : ℝ}
(hx : x ∈ gridStableCenters a b) (e : ι) (P : Node M d) (i : Fin M)
{n : ℕ} (hresolution : bS P i ≤ b e) (hindex : a e ≤ n)
(ht : t ∈ Set.Icc (1 : ℝ) 2) :
selectorValue bS ω P.val i (x + t * ((2 : ℝ)⁻¹) ^ n) =
selectorValue bS ω P.val i x := by
rw [selectorValue_valid, selectorValue_valid,
selectorAddress_eq_of_grid_stability bS hx e P i hresolution hindex ht]
end Problem310.FiniteTableModel
end
end OAI
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