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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 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 51 52 53 54 55 56 57 58 | import OAI.Combinatorics.EditApproximation.Binary.BinaryGuardSpace
import OAI.Combinatorics.EditApproximation.Binary.BinaryRefinementLists
import OAI.Combinatorics.EditApproximation.Definitions
namespace OAI
namespace EditApproximation.BinaryFraction
theorem centerEligibilityAllocation_le_work (b F : ℕ) (a initial : BinaryFraction) :
centerEligibilityAllocation b F a initial ≤ (centerEligibilityWithWork b F a initial).2 := by
have hd := canonicalMulAllocation_le_work (nat 4) a
have hlo := divAllocation_le_work (nat b) (canonicalMulWithWork (nat 4) a).1
have hfac := canonicalMulAllocation_le_work (nat 8) (nat F)
have hup := canonicalMulAllocation_le_work (canonicalMulWithWork (nat 8) (nat F)).1 (nat b)
have hl := leAllocation_le_work (divWithWork (nat b) (canonicalMulWithWork (nat 4) a).1).1 initial
have hh := leAllocation_le_work initial (canonicalMulWithWork (canonicalMulWithWork (nat 8) (nat F)).1 (nat b)).1
unfold centerEligibilityAllocation centerEligibilityWithWork
dsimp only
omega
theorem refinementScaleGuardAllocation_le_work (F b : ℕ) (a w : BinaryFraction) :
refinementScaleGuardAllocation F b a w ≤ (refinementScaleGuardWithWork F b a w).2 := by
have hd := canonicalMulAllocation_le_work (nat 16) (nat F)
have hlo := divAllocation_le_work w (canonicalMulWithWork (nat 16) (nat F)).1
have hfac := canonicalMulAllocation_le_work (nat 8) a
have hup := canonicalMulAllocation_le_work (canonicalMulWithWork (nat 8) a).1 w
have hl := leAllocation_le_work (divWithWork w (canonicalMulWithWork (nat 16) (nat F)).1).1 (nat b)
have hh := leAllocation_le_work (nat b) (canonicalMulWithWork (canonicalMulWithWork (nat 8) a).1 w).1
unfold refinementScaleGuardAllocation refinementScaleGuardWithWork
dsimp only
omega
theorem queryExponentsAllocation_le_work (N F : ℕ) (a w : BinaryFraction) :
queryExponentsAllocation N F a w ≤ (queryExponentsWithWork N F a w).2 := by
have hf := filterAllocation_le_work
(fun e => ((refinementScaleGuardWithWork F (2 ^ e) a w).1,
(refinementScaleGuardWithWork F (2 ^ e) a w).2 + e + 2))
(fun e => refinementScaleGuardAllocation F (2 ^ e) a w + e + 1)
(List.range (max 1 N.bits.length)) (by
intro e _
have h := refinementScaleGuardAllocation_le_work F (2 ^ e) a w
dsimp only
omega)
unfold queryExponentsAllocation queryExponentsWithWork
dsimp only
omega
end EditApproximation.BinaryFraction
end OAI
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