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0dd3af4 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 | 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
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