Theorems · Theorem · global analysis

contMDiff_prod_iff

∀ {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_11}
  [inst_11 : NormedAddCommGroup F'] [inst_12 : NormedSpace 𝕜 F'] {G' : Type u_12} [inst_13 : TopologicalSpace G']
  {J' : ModelWithCorners 𝕜 F' G'} {N' : Type u_13} [inst_14 : TopologicalSpace N'] [inst_15 : ChartedSpace G' N']
  {n : WithTop ℕ∞} (f : M → M' × N'),
  ContMDiff I (I'.prod J') n f ↔ ContMDiff I I' n (Prod.fst ∘ f) ∧ ContMDiff I J' n (Prod.snd ∘ f)

Defined in

Mathlib.Geometry.Manifold.ContMDiff.Constructions

Cited by

1 results in Mathlib

Foundations

Depth 205 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpace