Theorems · Theorem · global analysis

MDifferentiableWithinAt.sum

∀ {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'] {s : Set M} {z : M} {ι : Type} {t : Finset ι} {f : ι → M → E'},
  (∀ i ∈ t, MDiffAt[s] (f i) z) → MDiffAt[s] (∑ i ∈ t, f i) z

Defined in

Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions

Cited by

2 results in Mathlib

Foundations

Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceNormedAddCommGroupNormedSpace