∀ {n : WithTop ℕ∞} {𝕜 : Type u_5} [inst : NontriviallyNormedField 𝕜] {E : Type u_6} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {E' : Type u_7} [inst_3 : NormedAddCommGroup E'] [inst_4 : NormedSpace 𝕜 E'] {H : Type u_8}
  [inst_5 : TopologicalSpace H] {I : ModelWithCorners 𝕜 E H} {H' : Type u_9} [inst_6 : TopologicalSpace H']
  {I' : ModelWithCorners 𝕜 E' H'} (M : Type u_10) [inst_7 : TopologicalSpace M] [inst_8 : ChartedSpace H M]
  [IsManifold I n M] (M' : Type u_11) [inst_10 : TopologicalSpace M'] [inst_11 : ChartedSpace H' M']
  [IsManifold I' n M'], IsManifold (I.prod I') n (M × M')