File size: 2,916 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 | import OAI.Combinatorics.EditApproximation.Queries.QueryBoundedActiveCost
namespace OAI
namespace EditApproximation
section History
variable {σ α : Type*} [DecidableEq α] {M J R : ℕ} [NeZero R]
(source target : List α) (N P F exponent H Q T S passes copies : ℕ)
(factor : ℕ → ℚ) (multiplier : ℕ → ℕ) (tau eta kappa delta : ℚ)
(group : ℕ → ℕ → PhysicalInternalNode M J → Fin R → CellGroupDraws M F Q)
(integer : ℕ → ℕ → PhysicalInternalNode M J → Fin R → ℕ → TargetInterval target.length → ℕ)
(initial : PhysicalEntry M J target.length → ℕ)
(parent : {r : PhysicalTableRequest M J target.length // r.Bounded (passes + 1) copies T S})
(hindex : T < parent.val.index) (hbelow : parent.val.node.1.val < J)
(oracle : QueryBoundedChild (σ := σ) (passes + 1) copies T S parent → BinaryFraction)
local notation "requestValue" => localRequestValue source target N P F exponent H Q T S copies
factor multiplier tau eta kappa delta group integer initial
local notation "rawOracle" => queryRestrictedPhysicalOracle (passes + 1) copies T S parent oracle
local notation "tableOracle" => (fun key => queryActiveOracle T parent.val hindex S rawOracle (Sum.inr key))
theorem queryBoundedSemantic_nonneg (hdelta : 0 ≤ delta)
(hread : ∀ key, (oracle (Sum.inr key)).value = requestValue key.val.val)
(key) : 0 ≤ (oracle (Sum.inr key)).value := by
rw [hread]
exact (localRequestValue_bounds source target N P F exponent H Q T S copies factor multiplier
tau eta kappa delta group integer initial hdelta key.val.val).1
theorem queryFamilyBoundedActive_history_bound (hdelta : 0 ≤ delta)
(hread : ∀ key, (oracle (Sum.inr key)).value = requestValue key.val.val)
(input : Fin M × ℕ × TargetInterval target.length) :
((queryPhysicalEarlierRead copies parent.val.pass parent.val.copy T S (parent.val.index - T)
parent.val.node hbelow parent.val.state input).value tableOracle).value ≤
((queryPhysicalWarmupRead copies parent.val.pass parent.val.copy T S (parent.val.index - T)
(Nat.sub_pos_of_lt hindex) parent.val.node parent.val.state
(physicalChild parent.val.node hbelow input.1) (by change parent.val.node.1.val ≤ parent.val.node.1.val + 1; omega)
0 (Nat.zero_le T) input.2.2).value tableOracle).value := by
have ht : parent.val.index - T ≤ S := by have := parent.property.2.2; omega
have h := queryRestrictedPhysicalOracle_history_bound source target N P F exponent H Q T S copies
factor multiplier tau eta kappa delta group integer initial (passes + 1) parent.val.pass parent.val.copy
(parent.val.index - T) (Nat.sub_pos_of_lt hindex) ht parent.property.1 parent.property.2.1 hdelta
parent.val.node hbelow parent.val.state parent (queryRefinementRequest_eq T parent.val hindex).symm
oracle hread input
exact h
end History
end EditApproximation
end OAI
|