Theorems · Theorem · real analysis

ContDiff.comp_contDiffWithinAt

∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} {G : Type u_4} [inst : NontriviallyNormedField 𝕜]
  [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace 𝕜 E] [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F]
  [inst_5 : NormedAddCommGroup G] [inst_6 : NormedSpace 𝕜 G] {t : Set E} {x : E} {n : WithTop ℕ∞} {g : F → G}
  {f : E → F}, ContDiff 𝕜 n g → ContDiffWithinAt 𝕜 n f t x → ContDiffWithinAt 𝕜 n (g ∘ f) t x

Defined in

Mathlib.Analysis.Calculus.ContDiff.Comp

Cited by

4 results in Mathlib

Foundations

Depth 197 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace