{E : Type u_1} →
  {X : Type u_2} →
    {A : Type u_3} →
      [inst : TopologicalSpace E] →
        [inst_1 : TopologicalSpace X] →
          [inst_2 : TopologicalSpace A] →
            {p : E → X} →
              IsCoveringMap p →
                (H : C(↑unitInterval × A, X)) →
                  (f : C(A, E)) → (∀ (a : A), H (0, a) = p (f a)) → C(↑unitInterval × A, E)