∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {H : Type u_3} [inst_3 : TopologicalSpace H] {I : ModelWithCorners 𝕜 E H} {M : Type u_4}
  [inst_4 : TopologicalSpace M] [inst_5 : ChartedSpace H M] {E' : Type u_5} [inst_6 : NormedAddCommGroup E']
  [inst_7 : NormedSpace 𝕜 E'] {H' : Type u_6} [inst_8 : TopologicalSpace H'] {I' : ModelWithCorners 𝕜 E' H'}
  {M' : Type u_7} [inst_9 : TopologicalSpace M'] [inst_10 : ChartedSpace H' M'] {F : Type u_8}
  [inst_11 : NormedAddCommGroup F] [inst_12 : NormedSpace 𝕜 F] {G : Type u_9} [inst_13 : TopologicalSpace G]
  {J : ModelWithCorners 𝕜 F G} {N : Type u_10} [inst_14 : TopologicalSpace N] [inst_15 : ChartedSpace G N]
  {F' : Type u_11} [inst_16 : NormedAddCommGroup F'] [inst_17 : NormedSpace 𝕜 F'] {G' : Type u_12}
  [inst_18 : TopologicalSpace G'] {J' : ModelWithCorners 𝕜 F' G'} {N' : Type u_13} [inst_19 : TopologicalSpace N']
  [inst_20 : ChartedSpace G' N'] {f : M → M'} {x : M} {n : WithTop ℕ∞} {g : N → N'} {y : N},
  ContMDiffAt I I' n f x → ContMDiffAt J J' n g y → ContMDiffAt (I.prod J) (I'.prod J') n (Prod.map f g) (x, y)