∀ {α : Type u_1} (U : Set (α × α)) (a : (Set α × Set α) × Set α × Set α)
  (motive : a ∈ entourageProd (hausdorffEntourage U) (hausdorffEntourage U) → Prop)
  (h : a ∈ entourageProd (hausdorffEntourage U) (hausdorffEntourage U)),
  (∀ (h₁ : (a.1.1, a.2.1) ∈ hausdorffEntourage U) (h₂ : (a.1.2, a.2.2) ∈ hausdorffEntourage U), motive ⋯) → motive h