File size: 6,431 Bytes
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 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 | import OAI.Combinatorics.EditApproximation.Queries.QueryLocalRepresentativeSpace
import OAI.Combinatorics.EditApproximation.Binary.BinaryContinuationSpace
import OAI.Combinatorics.EditApproximation.Queries.QueryRefinementFinish
import OAI.Combinatorics.EditApproximation.Binary.BinaryWarmupReads
import OAI.Combinatorics.EditApproximation.Definitions
namespace OAI
namespace EditApproximation.BinaryFraction
theorem endpointActionAllocation_le_work {ny M : ℕ} (center : TargetInterval ny)
(states : Fin M → TargetInterval ny) :
endpointActionAllocation center states ≤ (endpointActionWithWork center states).2 := by
have h := endpointConnectionAllocation_le_work center states
unfold endpointActionAllocation endpointActionWithWork
dsimp only
omega
theorem wideActionsFromRepresentativesAllocation_le_work {nx ny : ℕ} (M : ℕ) (parent : TargetInterval nx)
(representatives : List (ℕ × TargetInterval ny)) (P : ℕ) :
wideActionsFromRepresentativesAllocation M parent representatives P ≤
(wideActionsFromRepresentativesWithWork M parent representatives P).2 := by
apply arithmeticFlatMapAllocation_le_work
intro br _
have hw := wideActionGridAllocation_le_work M parent br.2 br.1 P
have ha := arithmeticMapAllocation_le_work (fun states : Vector (TargetInterval ny) M => endpointActionWithWork br.2 states.get)
(fun states => endpointActionAllocation br.2 states.get)
(wideActionGridWithWork M parent br.2 br.1 P).1 (fun states _ => endpointActionAllocation_le_work br.2 states.get)
dsimp only
omega
theorem physicalContinuationReadAllocation_le_work {nx ny M : ℕ} (parent : TargetInterval nx)
(representatives : List (ℕ × TargetInterval ny)) (P F : ℕ) (delta fallback : BinaryFraction)
(old current : Fin M × TargetInterval ny → BinaryFraction × ℕ)
(oldAllocation currentAllocation : Fin M × TargetInterval ny → ℕ)
(groups online : List (BinaryBellmanAction (TargetInterval ny) (Fin M × TargetInterval ny) M))
(query : TargetInterval ny)
(ho : ∀ input, oldAllocation input ≤ (old input).2)
(hc : ∀ input, currentAllocation input ≤ (current input).2) :
physicalContinuationReadAllocation parent representatives P F delta fallback old current oldAllocation currentAllocation groups online query ≤
(physicalContinuationReadWithWork parent representatives P F delta fallback old current groups online query).2 := by
have hw := wideActionsFromRepresentativesAllocation_le_work M parent representatives P
have hl := canonicalMulAllocation_le_work (nat 128) (nat F)
have hf := localContinuationReadAllocation_le_work endpointDistanceWithWork endpointDistanceAllocation
(canonicalMulWithWork (nat 128) (nat F)).1 delta fallback old current oldAllocation currentAllocation query
(wideActionsFromRepresentativesWithWork M parent representatives P).1 groups online
(endpointDistanceAllocation_le_work query) ho hc
unfold physicalContinuationReadAllocation physicalContinuationReadWithWork
dsimp only
omega
theorem queryRefinementFinishAllocation_le_work {nx ny M : ℕ} (parent : TargetInterval nx) (N P F : ℕ)
(a delta : BinaryFraction) (initial : TargetInterval ny → BinaryFraction × ℕ)
(initialAllocation : TargetInterval ny → ℕ) (t : ℕ)
(earlierKeys : List (Fin M × ℕ × TargetInterval ny)) (earlierWords : List BinaryFraction)
(groups online : List (BinaryBellmanAction (TargetInterval ny) (Fin M × TargetInterval ny) M))
(currentKeys : List (Fin M × TargetInterval ny)) (currentWords : List BinaryFraction)
(query : TargetInterval ny) (hi : ∀ r, initialAllocation r ≤ (initial r).2) :
queryRefinementFinishAllocation parent N P F a delta initial initialAllocation t earlierKeys earlierWords
groups online currentKeys currentWords query ≤
(queryRefinementFinishWithWork parent N P F a delta initial t earlierKeys earlierWords groups online currentKeys currentWords query).2 := by
have hq := hi query
have hr := localRepresentativeReadAllocation_le_work N P F a initial initialAllocation query hi
have hf := physicalContinuationReadAllocation_le_work parent (localRepresentativeReadWithWork N P F a initial query).1
P F delta (initial query).1
(queryHistoryReadWithWork earlierKeys earlierWords (t - 1))
(fun input => queryChildReadWithWork currentKeys currentWords input.1 input.2)
(queryHistoryReadAllocation earlierKeys earlierWords (t - 1))
(fun input => queryChildReadAllocation currentKeys currentWords input.1 input.2) groups online query
(queryHistoryReadAllocation_le_work earlierKeys earlierWords (t - 1))
(fun input => queryChildReadAllocation_le_work currentKeys currentWords input.1 input.2)
unfold queryRefinementFinishAllocation queryRefinementFinishWithWork
dsimp only
omega
theorem localWarmupReadAllocation_le_work {nx ny M : ℕ} (parent : TargetInterval nx)
(N P F : ℕ) (a : BinaryFraction) (initial : TargetInterval ny → BinaryFraction × ℕ)
(initialAllocation : TargetInterval ny → ℕ) (child : Fin M × TargetInterval ny → BinaryFraction × ℕ)
(childAllocation : Fin M × TargetInterval ny → ℕ) (query : TargetInterval ny)
(hi : ∀ r, initialAllocation r ≤ (initial r).2)
(hc : ∀ input, childAllocation input ≤ (child input).2) :
localWarmupReadAllocation parent N P F a initial initialAllocation child childAllocation query ≤
(localWarmupReadKernelWithWork parent N P F a initial child query).2 := by
have hq := hi query
have hr := localRepresentativeReadAllocation_le_work N P F a initial initialAllocation query hi
have hw := wideActionsFromRepresentativesAllocation_le_work M parent
(localRepresentativeReadWithWork N P F a initial query).1 P
have hl := canonicalMulAllocation_le_work (nat 128) (nat F)
have hb := bellmanReadAllocation_le_work endpointDistanceWithWork endpointDistanceAllocation
(canonicalMulWithWork (nat 128) (nat F)).1 (initial query).1 child childAllocation query
(wideActionsFromRepresentativesWithWork M parent (localRepresentativeReadWithWork N P F a initial query).1 P).1
(fun action _ => endpointDistanceAllocation_le_work query action.center)
(fun action _ i => hc (action.childState i))
unfold localWarmupReadAllocation localWarmupReadKernelWithWork
dsimp only
omega
end EditApproximation.BinaryFraction
end OAI
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