Theorems · Theorem · global analysis

fderivWithin_comp_add_left

∀ {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 : E → F}
  {x : E} {s : Set E} (a : E), fderivWithin 𝕜 (fun x => f (a + x)) s x = fderivWithin 𝕜 f (a +ᵥ s) (a + x)

Defined in

Mathlib.Analysis.Calculus.FDeriv.Add

Cited by

3 results in Mathlib

Foundations

Depth 168 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace