| import OAI.NumberTheory.Ostmann.Complete | |
| namespace OAI | |
| /-! # Main statements of The additive indecomposability of the primes -/ | |
| namespace OstmannPaper | |
| open scoped symmDiff | |
| /-- Theorem 1.1, including every finite modification of the primes. -/ | |
| theorem inverse_goldbach (A B : Set ℕ) (hA : A.Nontrivial) (hB : B.Nontrivial) : | |
| (Ostmann.sumset A B ∆ Ostmann.primes).Infinite := | |
| Ostmann.inverseGoldbach A B hA hB | |
| /-- Theorem 2.3, the two-infinite-summand formulation. -/ | |
| theorem two_infinite_summands (A B : Set ℕ) (hA : A.Infinite) (hB : B.Infinite) : | |
| ¬ (Ostmann.sumset A B ∆ Ostmann.primes).Finite := by | |
| intro hfinite | |
| exact Ostmann.twoInfiniteSummandsImpossible A B hA hB | |
| ((Ostmann.finite_symmDiff_iff A B).mp hfinite) | |
| end OstmannPaper | |
| end OAI | |