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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 | import OAI.Combinatorics.EditApproximation.Refinement.PhysicalPreparedInputBounds
import OAI.Combinatorics.EditApproximation.Geometry.RefinementBufferRanges
namespace OAI
/-! A refinement continuation has a separate current-index buffer.
Only the earlier-history buffer enters the online objective, so its
range invariant does not require any relation at unused current keys. -/
namespace EditApproximation
namespace BinaryFraction
theorem PreparedKernelNumericBounds.with_independent_cached_values {nx ny M : ℕ}
{N P F exponent H Q eM eF B E S t : ℕ}
{tau a eta kappa delta : BinaryFraction}
{integer : ℕ → TargetInterval ny → ℕ}
(hn : PreparedKernelNumericBounds (nx := nx) (M := M)
N P F exponent H Q eM eF B E S t tau a eta kappa delta integer)
(parentInitial : TargetInterval ny → BinaryFraction)
(childMass childInitial : Fin M → TargetInterval ny → BinaryFraction)
(old current : Fin M × TargetInterval ny → BinaryFraction)
(history : ℕ → Fin M × TargetInterval ny → BinaryFraction)
(hp : ∀ r, (parentInitial r).width ≤ B)
(hm : ∀ i r, (childMass i r).width ≤ B)
(hi : ∀ i r, (childInitial i r).width ≤ B)
(ho : ∀ input, (old input).width ≤ B)
(hc : ∀ input, (current input).width ≤ B)
(hh : ∀ s ≤ t + 1, ∀ i r, (history s (i, r)).width ≤ B)
(hpnonneg : ∀ r, 0 ≤ (parentInitial r).value)
(hrange : ∀ s ≤ t + 1, ∀ i r, 0 ≤ (history s (i, r)).value ∧
(history s (i, r)).value ≤ (childInitial i r).value) :
PreparedKernelInputBounds (nx := nx) N P F exponent H Q eM eF B E S t
tau a eta kappa delta parentInitial childMass childInitial old current history integer := by
exact { (hn.with_cached_values parentInitial childMass childInitial history
hp hm hi hh hpnonneg hrange) with oldSize := ho, currentSize := hc }
end BinaryFraction
end EditApproximation
end OAI
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