File size: 4,090 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 | import OAI.Combinatorics.EditApproximation.Refinement.PhysicalRandomBoundedQuery
import OAI.Combinatorics.EditApproximation.Geometry.ChargedGlobalQuery
import OAI.Combinatorics.EditApproximation.Definitions
namespace OAI
/-! The coarse seed, recursive table values, and random scalar sources are
all requested through the memo program. Inactive refinement branches use
the existing explicit coarse/median seed queries. -/
namespace EditApproximation
section Global
variable {σ α : Type*} [DecidableEq α] {M J R : ℕ} [NeZero M] [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)
(readGroup : ℕ → ℕ → PhysicalInternalNode M J → Fin R → GroupScalarKey M F Q → FiniteQuery σ)
(readInteger : ℕ → ℕ → PhysicalInternalNode M J → Fin R →
(ℕ × TargetInterval target.length) → ℕ → FiniteQuery σ)
(initial : PhysicalEntry M J target.length → ℕ)
variable
(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)
(sourceAnswer : σ → ℚ)
/-- Composition with the local source-provider correctness theorem. -/
theorem chargedRandomGlobalQuery_value
(hbody : ∀ parent,
(physicalRandomBoundedQuery source target N P F exponent H Q T S passes copies factor multiplier
tau eta kappa delta readGroup readInteger initial parent).value
(Sum.elim sourceAnswer (fun child => localRequestValue source target N P F exponent H Q T S copies
factor multiplier tau eta kappa delta group integer initial child.val.val)) =
localRequestValue source target N P F exponent H Q T S copies factor multiplier
tau eta kappa delta group integer initial parent.val)
(request : ChargedPhysicalRequest M J target.length passes copies T S) :
(chargedRandomGlobalQuery source target N P F exponent H Q T S passes copies factor multiplier
tau eta kappa delta readGroup readInteger initial request).value
(Sum.elim sourceAnswer (fun child => chargedRequestValue source target N P F exponent H Q T S
passes copies factor multiplier tau eta kappa delta group integer initial child.val)) =
chargedRequestValue source target N P F exponent H Q T S passes copies factor multiplier
tau eta kappa delta group integer initial request := by
cases request with
| inl entry => rfl
| inr parent =>
change _ = localRequestValue source target N P F exponent H Q T S copies factor multiplier
tau eta kappa delta group integer initial parent.val
unfold chargedRandomGlobalQuery
dsimp only
split_ifs with hi hd hw
· rw [FiniteQuery.mapKeys_value]
exact chargedWarmupQuery_value source target N P F exponent H Q T S passes copies
factor multiplier tau eta kappa delta group integer initial parent hi
· rw [FiniteQuery.mapKeys_value,
localRequestValue_terminal source target N P F exponent H Q T S copies factor multiplier
tau eta kappa delta group integer initial parent.val (Or.inr hw)]
exact physicalInitialQuery_value_local source target N P F _ _ _ _ _ _
(chargedSeedQuery_localValue source target N P F exponent H Q T S passes copies
factor multiplier tau eta kappa delta group integer initial parent)
· rw [FiniteQuery.mapKeys_value]
refine Eq.trans ?_ (hbody parent)
congr 1
funext next
cases next <;> rfl
· rw [FiniteQuery.mapKeys_value,
localRequestValue_terminal source target N P F exponent H Q T S copies factor multiplier
tau eta kappa delta group integer initial parent.val (Or.inl hd)]
exact physicalInitialQuery_value_local source target N P F _ _ _ _ _ _
(chargedSeedQuery_localValue source target N P F exponent H Q T S passes copies
factor multiplier tau eta kappa delta group integer initial parent)
end Global
end EditApproximation
end OAI
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