∀ {A : Type u_2} {B : Type u_3} {C : Type u_4} {D : Type u_5} [inst : Monoid A] [inst_1 : Monoid B] [inst_2 : Monoid C]
  [inst_3 : Monoid D] [inst_4 : TopologicalSpace A] [inst_5 : TopologicalSpace B] [inst_6 : TopologicalSpace C]
  [inst_7 : TopologicalSpace D] (f : A →ₜ* C) (g : B →ₜ* D) (i : A × B), (f.prodMap g) i = (f i.1, g i.2)