∀ {ι : Type u_2} {X : ι → Type u_1} {Y : ι → Type u_3} [inst : (i : ι) → TopologicalSpace (X i)]
  [inst_1 : (i : ι) → TopologicalSpace (Y i)] (h : (i : ι) → ContinuousMap.HomotopyEquiv (X i) (Y i)),
  (ContinuousMap.piMap fun i => (h i).invFun.comp (h i).toFun).Homotopic
    (ContinuousMap.piMap fun i => ContinuousMap.id (X i))