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5d5048e | 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 39 40 41 42 43 44 45 46 47 48 49 50 | import OAI.Combinatorics.LowSpaceSubsetSum.Compression.CompressionArrayWork
namespace OAI
/-! # Raw compression lists fit the common writable capacity
These bounds apply before the compact-list guard. Hence even a failed
compression test can materialize its raw block lists within the same space.
-/
namespace LowSpaceSubsetSum.CompressionStorageBounds
variable {n : ℕ}
theorem exponents (hn : 10000 ≤ n) :
compressionHalfSize n ≤ 199*n/1000 ∧
compressionLeftRawSize n ≤ 199*n/1000 ∧
∀ i, compressionRawHalfSize n i ≤ 199*n/1000 := by
have hf := compression_layout_feasible n
rw [compressionHalfSize_eq] at hf ⊢
unfold compressionLeftRawSize compressionRawHalfSize compressionRightRawSize
rw [compressionHalfSize_eq]
refine ⟨by omega, by omega, ?_⟩
intro i
split <;> omega
theorem source_lengths (D : CompressionData n) (e : Equiv.Perm (Fin n))
(hn : 10000 ≤ n) :
(∀ i, ((CompressionArrayBuild.source D e).compact i).length ≤ 199*n/1000) ∧
(CompressionArrayBuild.source D e).left.length ≤ 199*n/1000 ∧
∀ i, ((CompressionArrayBuild.source D e).right i).length ≤ 199*n/1000 := by
have h := exponents hn
refine ⟨?_, ?_, ?_⟩
· intro i
simpa only [CompressionArrayBuild.source, Finset.length_sort, CompressionData.block,
permuteSubset, Finset.card_map, compressionBlock_card] using h.1
· simpa only [CompressionArrayBuild.source, Finset.length_sort, D.leftRaw_card] using h.2.1
· intro i
simpa only [CompressionArrayBuild.source, Finset.length_sort, D.rightRaw_card] using h.2.2 i
theorem raw_bound (a : Fin n → ℤ) (xs : List (Fin n))
(hx : xs.length ≤ 199*n/1000) :
(CompressionWeights.raw a xs).1.length ≤ compressionDictionaryCapacity n := by
rw [CompressionWeights.raw_length]
exact Nat.pow_le_pow_right (by decide) hx
end LowSpaceSubsetSum.CompressionStorageBounds
end OAI
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