Theorems · Theorem · real analysis

iteratedDerivWithin_fun_const_smul_field

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {F : Type u_2} [inst_1 : NormedAddCommGroup F]
  [inst_2 : NormedSpace 𝕜 F] {n : ℕ} {x : 𝕜} {s : Set 𝕜} {𝕝 : Type u_4} [inst_3 : DivisionSemiring 𝕝]
  [inst_4 : Module 𝕝 F] [SMulCommClass 𝕜 𝕝 F] [ContinuousConstSMul 𝕝 F] (c : 𝕝) (f : 𝕜 → F),
  iteratedDerivWithin n (fun z => c • f z) s x = c • iteratedDerivWithin n f s x

A variant of iteratedDerivWithin_fun_const_smul without differentiability assumption when the scalar multiplication is by division ring elements.

Defined in

Mathlib.Analysis.Calculus.IteratedDeriv.Lemmas

Cited by

2 results in Mathlib

Foundations

Depth 180 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceDivisionSemiringModuleSMulCommClassContinuousConstSMul