Theorems · Theorem · global analysis

contMDiff_sum_map

∀ {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] {M' : Type u_16} [inst_6 : TopologicalSpace M']
  [inst_7 : ChartedSpace H M'] {n : WithTop ℕ∞} {E' : Type u_17} [inst_8 : NormedAddCommGroup E']
  [inst_9 : NormedSpace 𝕜 E'] {H' : Type u_18} [inst_10 : TopologicalSpace H'] {J : ModelWithCorners 𝕜 E' H'}
  {N : Type u_20} {N' : Type u_21} [inst_11 : TopologicalSpace N] [inst_12 : TopologicalSpace N']
  [inst_13 : ChartedSpace H' N] [inst_14 : ChartedSpace H' N'] {f : M → N} {g : M' → N'},
  ContMDiff I J n (Sum.map f g) ↔ ContMDiff I J n f ∧ ContMDiff I J n g

Defined in

Mathlib.Geometry.Manifold.ContMDiff.Constructions

Cited by

0 results in Mathlib

Foundations

Depth 207 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceTopologicalSpaceChartedSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceTopologicalSpaceChartedSpaceChartedSpace