Theorems · Theorem · global analysis

ContDiffAt.norm_sq

∀ (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} {x : G}
  {n : WithTop ℕ∞}, ContDiffAt ℝ n f x → ContDiffAt ℝ n (fun x => ‖f x‖ ^ 2) x

Defined in

Mathlib.Analysis.InnerProductSpace.Calculus

Cited by

3 results in Mathlib

Foundations

Depth 203 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceNormedSpaceNormedAddCommGroupNormedSpace