Theorems · Theorem · global analysis

DifferentiableAt.add

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {F : Type u_3} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {f g : E → F}
  {x : E}, DifferentiableAt 𝕜 f x → DifferentiableAt 𝕜 g x → DifferentiableAt 𝕜 (f + g) x

Defined in

Mathlib.Analysis.Calculus.FDeriv.Add

Cited by

8 results in Mathlib

Foundations

Depth 167 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace