Theorems · Theorem · global analysis

HasFDerivWithinAt.unique_on

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E]
  [inst_3 : TopologicalSpace E] [ContinuousAdd E] [ContinuousSMul 𝕜 E] {F : Type u_3} [inst_6 : AddCommGroup F]
  [inst_7 : Module 𝕜 F] [inst_8 : TopologicalSpace F] [ContinuousAdd F] [ContinuousSMul 𝕜 F] {f : E → F}
  {f' f₁' : E →L[𝕜] F} {x : E} {s : Set E} [T2Space F],
  HasFDerivWithinAt f f' s x → HasFDerivWithinAt f f₁' s x → Set.EqOn (⇑f') (⇑f₁') (tangentConeAt 𝕜 s x)

If f' and f₁' are two derivatives of f within s at x, then they are equal on the tangent cone to s at x

Defined in

Mathlib.Analysis.Calculus.FDeriv.Basic

Cited by

1 results in Mathlib

Foundations

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

Assumes

NontriviallyNormedFieldAddCommGroupModuleTopologicalSpaceContinuousAddContinuousSMulAddCommGroupModuleTopologicalSpaceContinuousAddContinuousSMulT2Space