∀ {E : Type u_3} {X : Type u_2} {A : Type u_1} [inst : TopologicalSpace E] [inst_1 : TopologicalSpace X]
  [inst_2 : TopologicalSpace A] {p : E → X} (cov : IsCoveringMap p) {f₀ f₁ : C(A, E)} {S : Set A}
  (motive :
    ({ toFun := p, continuous_toFun := ⋯ }.comp f₀).HomotopicRel ({ toFun := p, continuous_toFun := ⋯ }.comp f₁) S →
      Prop)
  (x : ({ toFun := p, continuous_toFun := ⋯ }.comp f₀).HomotopicRel ({ toFun := p, continuous_toFun := ⋯ }.comp f₁) S),
  (∀
      (F :
        ({ toFun := p, continuous_toFun := ⋯ }.comp f₀).HomotopyRel ({ toFun := p, continuous_toFun := ⋯ }.comp f₁) S),
      motive ⋯) →
    motive x