Theorems · Theorem · global analysis

DifferentiableAt.fderivWithin

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E]
  [inst_3 : TopologicalSpace E] {F : Type u_3} [inst_4 : AddCommGroup F] [inst_5 : Module 𝕜 F]
  [inst_6 : TopologicalSpace F] {f : E → F} {x : E} {s : Set E} [ContinuousAdd E] [ContinuousSMul 𝕜 E] [ContinuousAdd F]
  [ContinuousSMul 𝕜 F] [T2Space F],
  DifferentiableAt 𝕜 f x → UniqueDiffWithinAt 𝕜 s x → fderivWithin 𝕜 f s x = fderiv 𝕜 f x

Defined in

Mathlib.Analysis.Calculus.FDeriv.Basic

Cited by

9 results in Mathlib

Foundations

Depth 170 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldAddCommGroupModuleTopologicalSpaceAddCommGroupModuleTopologicalSpaceContinuousAddContinuousSMulContinuousAddContinuousSMulT2Space