Theorems · Theorem · global analysis

DifferentiableAt.comp_mdifferentiableWithinAt

∀ {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] {F : Type u_8} [inst_6 : NormedAddCommGroup F]
  [inst_7 : NormedSpace 𝕜 F] {F' : Type u_11} [inst_8 : NormedAddCommGroup F'] [inst_9 : NormedSpace 𝕜 F'] {g : F → F'}
  {f : M → F} {s : Set M} {x : M}, DifferentiableAt 𝕜 g (f x) → MDiffAt[s] f x → MDiffAt[s] (g ∘ f) x

Defined in

Mathlib.Geometry.Manifold.MFDeriv.NormedSpace

Cited by

2 results in Mathlib

Foundations

Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace