Theorems · Theorem · global analysis

DifferentiableOn.dist

∀ (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 : G → E}
  {s : Set G},
  DifferentiableOn ℝ f s →
    DifferentiableOn ℝ g s → (∀ x ∈ s, f x ≠ g x) → DifferentiableOn ℝ (fun y => dist (f y) (g y)) s

Defined in

Mathlib.Analysis.InnerProductSpace.Calculus

Cited by

0 results in Mathlib

Foundations

Depth 212 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceNormedSpaceNormedAddCommGroupNormedSpace