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Theorems · Theorem · real analysis

ContDiffWithinAt.snd

∀ {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} {x : E},
  ContDiffWithinAt 𝕜 n f s x → ContDiffWithinAt 𝕜 n (fun x => (f x).2) s x

Postcomposing f with Prod.snd is C^n at x

Defined in
Mathlib.Analysis.Calculus.ContDiff.Comp
Cited by
1 results in Mathlib
Foundations
Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

contDiffWithinAt_prod_iff · cited by 0contDiffWithinAt_prod_iffSet · cited by 53352SetNormedAddCommGroup · cited by 15752NormedAddCommGroupNormedSpace · cited by 12499NormedSpaceNontriviallyNormedField · cited by 8742NontriviallyNormedFieldENat · cited by 4985ENatWithTop · cited by 3754WithTopContDiffWithinAt · cited by 283ContDiffWithinAtSet.mapsTo_image · cited by 71Set.mapsTo_imageContDiffWithinAt.comp · cited by 18ContDiffWithinAt.compcontDiffWithinAt_snd · cited by 5contDiffWithinAt_sndContDiffWithinAt.sndCITED BYCITES

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Cited by1

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