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e63eb7f | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 | import OAI.Combinatorics.EditApproximation.Refinement.ComputedFamilyMemoCode
import OAI.Combinatorics.EditApproximation.Refinement.PhysicalFamilySampling
namespace OAI
namespace EditApproximation
theorem computedFamilyRange_bits_le (source target : List ℕ) (N R : ℕ)
(hB : Nat.size (localOnlineMassBound (integerParameters N).M (integerParameters N).P
(inputHeight N)) ≤ inputHeight N)
(key : ComputedFamilyScalarKey source target N R) :
rejectionBitCount (physicalFamilyRange target N (integerParameters N).P (inputSmallLog N)
(40 * smallLogExponent N) (inputHeight N) (inputSmallLog N ^ 80)
(computedSeedPassCount N) (inputHeight N ^ 2) key) ≤ inputHeight N := by
apply physicalFamilyRange_bits_le
· change 2 ^ (heightExponent N / 20) ≤ 2 ^ inputHeight N
apply Nat.pow_le_pow_right (by decide : 0 < (2 : ℕ))
exact (Nat.div_le_self _ _).trans (Nat.lt_two_pow_self.le)
· exact (Nat.lt_size_self _).le.trans (Nat.pow_le_pow_right (by decide : 0 < (2 : ℕ)) hB)
end EditApproximation
end OAI
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