Theorems · Theorem · functional analysis

fderivWithin_zero_of_not_differentiableWithinAt

∀ {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},
  ¬DifferentiableWithinAt 𝕜 f s x → fderivWithin 𝕜 f s x = 0

Defined in

Mathlib.Analysis.Calculus.FDeriv.Defs

Cited by

13 results in Mathlib

Foundations

Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldAddCommGroupModuleTopologicalSpaceAddCommGroupModuleTopologicalSpace