Theorems · Theorem · global analysis

mvfderivWithin_fun_add

∀ {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] {s : Set M} {g g' : M → F} {x : M},
  MDiffAt[s] g x → MDiffAt[s] g' x → UniqueMDiffAt[s] x → (d[s] fun i => g i + g' i) x = d[s] g x + d[s] g' x

Eta-expanded form of mvfderivWithin_add

Defined in

Mathlib.Geometry.Manifold.MFDeriv.NormedSpace

Cited by

0 results in Mathlib

Foundations

Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceNormedAddCommGroupNormedSpace