Theorems · Theorem · global analysis

DifferentiableWithinAt.norm

∀ (𝕜 : Type u_1) {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [InnerProductSpace 𝕜 E]
  [inst : NormedSpace ℝ E] {G : Type u_4} [inst_2 : NormedAddCommGroup G] [inst_3 : NormedSpace ℝ G] {f : G → E}
  {s : Set G} {x : G}, DifferentiableWithinAt ℝ f s x → f x ≠ 0 → DifferentiableWithinAt ℝ (fun y => ‖f y‖) s x

Defined in

Mathlib.Analysis.InnerProductSpace.Calculus

Cited by

2 results in Mathlib

Foundations

Depth 210 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceNormedSpaceNormedAddCommGroupNormedSpace