∀ {E : Type u_1} {X : Type u_2} [inst : TopologicalSpace E] [inst_1 : TopologicalSpace X] (f : E → X) (G : Type u_3)
  [inst_2 : Group G] [inst_3 : MulAction G E],
  IsQuotientCoveringMap f G ↔
    Topology.IsQuotientMap f ∧
      ContinuousConstSMul G E ∧
        (∀ {e₁ e₂ : E}, f e₁ = f e₂ ↔ e₁ ∈ MulAction.orbit G e₂) ∧
          ∀ (e : E), ∃ U ∈ nhds e, ∀ (g : G), ((fun x => g • x) '' U ∩ U).Nonempty → g = 1