Theorems · Theorem · real analysis
CPolynomialOn.contDiffOn
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {F : Type v} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {f : E → F}
{s : Set E}, CPolynomialOn 𝕜 f s → ∀ {n : WithTop ℕ∞}, ContDiffOn 𝕜 n f sA polynomial function is infinitely differentiable.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 197 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Set.ofPredproof · cited by 6,101
- ENatstatement and proof · cited by 4,985
- WithTopstatement and proof · cited by 3,754
- IsOpenproof · cited by 2,400
- ContDiffOnstatement and proof · cited by 294
- AnalyticOnNhdproof · cited by 206
- CPolynomialOnstatement and proof · cited by 29
- CPolynomialAtproof · cited by 28
Cited by1
Results whose statement or proof uses this declaration.
- CPolynomialAt.contDiffAtproof · cited by 1