| import Mathlib | |
| namespace OAI | |
| open scoped Pointwise symmDiff | |
| namespace Ostmann | |
| def primes : Set ℕ := {n | Nat.Prime n} | |
| abbrev sumset (A B : Set ℕ) : Set ℕ := A + B | |
| def EventuallyPrimeSumset (A B : Set ℕ) : Prop := | |
| ∃ N : ℕ, ∀ n, N ≤ n → (n ∈ sumset A B ↔ n.Prime) | |
| def TwoInfiniteSummandsImpossible : Prop := | |
| ∀ A B : Set ℕ, A.Infinite → B.Infinite → ¬ EventuallyPrimeSumset A B | |
| def InverseGoldbach : Prop := | |
| ∀ A B : Set ℕ, A.Nontrivial → B.Nontrivial → | |
| Set.Infinite (@symmDiff (Set ℕ) | |
| (@SemilatticeSup.toMax (Set ℕ) | |
| (@Lattice.toSemilatticeSup (Set ℕ) | |
| (@CompleteLattice.toLattice (Set ℕ) | |
| (@CompleteBooleanAlgebra.toCompleteLattice (Set ℕ) | |
| (@CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra (Set ℕ) | |
| (@Set.instCompleteAtomicBooleanAlgebra ℕ)))))) | |
| Set.instSDiff (sumset A B) primes) | |
| theorem inverseGoldbach : InverseGoldbach := by | |
| sorry | |
| theorem twoInfiniteSummandsImpossible : TwoInfiniteSummandsImpossible := by | |
| sorry | |
| end Ostmann | |
| end OAI | |