Theorems · Theorem · real analysis
iteratedDerivWithin_of_isOpen_eq_iterate
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {F : Type u_2} [inst_1 : NormedAddCommGroup F]
[inst_2 : NormedSpace 𝕜 F] {n : ℕ} {f : 𝕜 → F} {s : Set 𝕜},
IsOpen s → Set.EqOn (iteratedDerivWithin n f s) (deriv^[n] f) s- Cited by
- 2 results in Mathlib
- Foundations
- Depth 183 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- IsOpenstatement and proof · cited by 2,400
- Nat.iteratestatement and proof · cited by 740
- derivstatement and proof · cited by 676
- Set.EqOnstatement and proof · cited by 603
- iteratedDerivWithinstatement · cited by 122
- Set.EqOn.transproof · cited by 13
- iteratedDeriv_eq_iterateproof · cited by 8
- iteratedDerivWithin_of_isOpenproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- iteratedDerivWithin_one_divproof · cited by 0
- iteratedDerivWithin_zpowproof · cited by 0