Theorems · Theorem · global analysis

mdifferentiable_prod_module_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] {F₁ : Type u_17} [inst_6 : NormedAddCommGroup F₁]
  [inst_7 : NormedSpace 𝕜 F₁] {F₂ : Type u_18} [inst_8 : NormedAddCommGroup F₂] [inst_9 : NormedSpace 𝕜 F₂]
  (f : M → F₁ × F₂), MDiff f ↔ MDiff (Prod.fst ∘ f) ∧ MDiff (Prod.snd ∘ f)

Defined in

Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions

Cited by

0 results in Mathlib

Foundations

Depth 175 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace