Theorems · Theorem · global analysis

DifferentiableAt.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}
  {x : G},
  DifferentiableAt ℝ f x → DifferentiableAt ℝ g x → f x ≠ g x → DifferentiableAt ℝ (fun y => dist (f y) (g y)) x

Defined in

Mathlib.Analysis.InnerProductSpace.Calculus

Cited by

1 results in Mathlib

Foundations

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

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceNormedSpaceNormedAddCommGroupNormedSpace