Theorems · Theorem · real analysis

contDiffWithinAt_snd

∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {n : WithTop ℕ∞}
  {s : Set (E × F)} {p : E × F}, ContDiffWithinAt 𝕜 n Prod.snd s p

The second projection within a domain at a point in a product is C^∞.

Defined in

Mathlib.Analysis.Calculus.ContDiff.Comp

Cited by

5 results in Mathlib

Foundations

Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace