Theorems · Theorem · real analysis

contDiffOn_prod_iff

∀ {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] {s : Set E} {n : WithTop ℕ∞} (f : E → F × G),
  ContDiffOn 𝕜 n f s ↔ ContDiffOn 𝕜 n (Prod.fst ∘ f) s ∧ ContDiffOn 𝕜 n (Prod.snd ∘ f) s

Defined in

Mathlib.Analysis.Calculus.ContDiff.Comp

Cited by

0 results in Mathlib

Foundations

Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace