∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] (s : Set X) (t : Set Y)
  (x : { c // s c.1 ∧ t c.2 }), (Homeomorph.Set.prod s t) x = (⟨(↑x).1, ⋯⟩, ⟨(↑x).2, ⋯⟩)