∀ {ι : Type u_1} {X : ι → Type u_2} [Finite ι] [inst : (i : ι) → LinearOrder (X i)]
  [inst_1 : (i : ι) → TopologicalSpace (X i)] [∀ (i : ι), OrderTopology (X i)] {a b x : (i : ι) → X i} [Nonempty ι],
  (∀ (i : ι), a i < x i) → (∀ (i : ι), x i < b i) → Set.Ico a b ∈ nhds x