Theorems · Theorem · real analysis
Filter.EventuallyEq.deriv_eq
∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : NormedAddCommGroup F]
[inst_2 : NormedSpace 𝕜 F] {f f₁ : 𝕜 → F} {x : 𝕜}, f₁ =ᶠ[nhds x] f → deriv f₁ x = deriv f x- Defined in
- Mathlib.Analysis.Calculus.Deriv.Basic
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- RingHom.idproof · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- nhdsstatement and proof · cited by 5,554
- ContinuousLinearMapproof · cited by 5,352
- Filter.EventuallyEqstatement and proof · cited by 1,912
- derivstatement · cited by 676
- fderivproof · cited by 398
- Filter.EventuallyEq.fderiv_eqproof · cited by 5
Cited by14
Results whose statement or proof uses this declaration.
- AnalyticAt.analyticOrderAt_sub_eq_one_of_deriv_ne_zeroproof · cited by 3
- Filter.EventuallyEq.derivproof · cited by 3
- Real.deriv2_mul_logproof · cited by 2
- Real.deriv2_qaryEntropyproof · cited by 2
- Real.deriv_Gamma_natproof · cited by 2
- AnalyticAt.analyticOrderAt_deriv_add_oneproof · cited by 2
- DirichletCharacter.deriv_LFunctionTrivChar₁_apply_of_ne_oneproof · cited by 1
- DirichletCharacter.deriv_LFunction_eq_deriv_LSeriesproof · cited by 1
- deriv_norm_ofReal_cpowproof · cited by 1
- deriv_of_notMem_tsupportproof · cited by 1
- ProbabilityTheory.iteratedDeriv_two_cgfproof · cited by 1
- deriv_riemannZeta_eq_neg_inv_sub_sq_addproof · cited by 1