| import Mathlib | |
| namespace OAI | |
| open scoped symmDiff | |
| namespace SimpleAmenable | |
| noncomputable def FolnerAmenable (G : Type*) [Group G] : Prop := by | |
| classical | |
| exact ∀ K : Finset G, ∀ ε : ℝ, 0 < ε → | |
| ∃ D : Finset G, D.Nonempty ∧ ∀ g ∈ K, | |
| (((D.image (fun d => g * d)) ∆ D).card : ℝ) < ε * D.card | |
| def MainStatement : Prop := ∃ (G : Type) (_ : Group G), | |
| Infinite G ∧ Group.IsFinitelyPresented G ∧ IsSimpleGroup G ∧ FolnerAmenable G | |
| end SimpleAmenable | |
| end OAI | |