Theorems · Theorem · real analysis

DifferentiableOn.diffContOnCl_ball

∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedAddCommGroup F] [inst_3 : NormedSpace 𝕜 E] [inst_4 : NormedSpace 𝕜 F] {f : E → F} {U : Set E} {c : E}
  {R : ℝ}, DifferentiableOn 𝕜 f U → Metric.closedBall c R ⊆ U → DiffContOnCl 𝕜 f (Metric.ball c R)

Defined in

Mathlib.Analysis.Calculus.DiffContOnCl

Cited by

1 results in Mathlib

Foundations

Depth 170 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedAddCommGroupNormedSpaceNormedSpace