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aaf4b9f | 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 | import OAI.NumberTheory.Ostmann.MainActualProgression
import OAI.NumberTheory.Ostmann.ZeroDensity.ActualThetaEstimate
namespace OAI
/-! # The main statements after discharging the prime-progression input -/
namespace Ostmann
noncomputable def actualProgressionInput : PublishedProgressionInput :=
progressionInput_of_actual_theta actualProgressionTheta
theorem twoInfiniteSummandsImpossible_without_progression_input
(ls : PublishedAdditiveLargeSieve) (hsize : PublishedSummandSizeBound)
(hSiegel : PublishedSiegelBound) (sieve : PublishedQuadraticLargeSieve)
(hD : PublishedComplexZeroDensity actualCharacterZeros) :
TwoInfiniteSummandsImpossible :=
twoInfiniteSummandsImpossible_of_actual_progression
actualProgressionTheta ls hsize hSiegel sieve hD
theorem inverseGoldbach_without_progression_input
(ls : PublishedAdditiveLargeSieve) (hsize : PublishedSummandSizeBound)
(hSiegel : PublishedSiegelBound) (sieve : PublishedQuadraticLargeSieve)
(hD : PublishedComplexZeroDensity actualCharacterZeros) :
InverseGoldbach :=
inverseGoldbach_of_actual_progression actualProgressionTheta ls hsize hSiegel sieve hD
end Ostmann
end OAI
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