Theorems · Theorem · real analysis
derivWithin_of_isOpen
∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : NormedAddCommGroup F]
[inst_2 : NormedSpace 𝕜 F] {f : 𝕜 → F} {x : 𝕜} {s : Set 𝕜}, IsOpen s → x ∈ s → derivWithin f s x = deriv f x- Defined in
- Mathlib.Analysis.Calculus.Deriv.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- derivstatement · cited by 676
- IsOpen.mem_nhdsproof · cited by 470
- derivWithinstatement · cited by 258
- derivWithin_of_mem_nhdsproof · cited by 10
Cited by7
Results whose statement or proof uses this declaration.
- deriv_eqOnproof · cited by 7
- Complex.one_add_cpow_hasFPowerSeriesOnBall_zeroproof · cited by 3
- Set.EqOn.derivproof · cited by 2
- ModularForm.discriminant_qExpansion_coeff_oneproof · cited by 2
- contDiffOn_succ_iff_deriv_of_isOpenproof · cited by 2
- LSeries_iteratedDerivproof · cited by 1
- ContDiffOn.deriv_of_isOpenproof · cited by 0