| import Mathlib | |
| namespace OAI | |
| namespace UniversalFInfinity | |
| universe u | |
| def HasTypeFInfinity (G : Type u) [Group G] : Prop := | |
| ∃ (X : Type u) (_ : TopologicalSpace X) (_ : T2Space X) | |
| (_ : ConnectedSpace X) (cw : Topology.CWComplex (Set.univ : Set X)), | |
| (∀ n : ℕ, Finite (cw.cell n)) ∧ | |
| (∃ x : X, Nonempty (FundamentalGroup X x ≃* G)) ∧ | |
| ∃ (E : Type u) (_ : TopologicalSpace E) (_ : ContractibleSpace E) | |
| (p : E → X), Function.Surjective p ∧ IsCoveringMap p | |
| end UniversalFInfinity | |
| end OAI | |