∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_5} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {E' : Type u_6} [inst_3 : NormedAddCommGroup E'] [inst_4 : NormedSpace 𝕜 E'] {H : Type u_7}
  [inst_5 : TopologicalSpace H] {H' : Type u_8} [inst_6 : TopologicalSpace H'] {I : ModelWithCorners 𝕜 E H}
  {I' : ModelWithCorners 𝕜 E' H'} {M : Type u_10} [inst_7 : TopologicalSpace M] [inst_8 : ChartedSpace H M]
  {M' : Type u_9} [inst_9 : TopologicalSpace M'] [inst_10 : ChartedSpace H' M'] {F : Type u_2}
  [inst_11 : NormedAddCommGroup F] [inst_12 : NormedSpace 𝕜 F] {G : Type u_3} [inst_13 : TopologicalSpace G]
  {J : ModelWithCorners 𝕜 F G} {N : Type u_4} [inst_14 : TopologicalSpace N] [inst_15 : ChartedSpace G N]
  {n : WithTop ℕ∞} (f : ContMDiffMap J I N M n) (g : ContMDiffMap J I' N M' n),
  ContMDiff J (I.prod I') n fun x => (↑f x, g x)