Theorems · Theorem · real analysis
HasDerivAt.congr_of_eventuallyEq
∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : NormedAddCommGroup F]
[inst_2 : NormedSpace 𝕜 F] {f f₁ : 𝕜 → F} {f' : F} {x : 𝕜}, HasDerivAt f f' x → f₁ =ᶠ[nhds x] f → HasDerivAt f₁ f' x- Defined in
- Mathlib.Analysis.Calculus.Deriv.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 167 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- 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
- Filter.EventuallyEqstatement and proof · cited by 1,912
- HasDerivAtstatement and proof · cited by 493
- Filter.EventuallyEq.filter_monoproof · cited by 59
- pure_le_nhdsproof · cited by 39
- Filter.EventuallyEq.prodMapproof · cited by 10
- HasDerivAtFilter.congr_of_eventuallyEqproof · cited by 3
Cited by8
Results whose statement or proof uses this declaration.
- Filter.EventuallyEq.hasDerivAt_iffproof · cited by 4
- hasDerivAt_ofReal_cpow_const'proof · cited by 2
- expNegInvGlue.hasDerivAt_polynomial_eval_inv_mulproof · cited by 2
- MeasureTheory.integral_Ioi_deriv_mul_eq_subproof · cited by 1
- intervalIntegral.integral_eq_sub_of_hasDerivAt_of_tendstoproof · cited by 1
- MeasureTheory.integral_Iic_deriv_mul_eq_subproof · cited by 1
- Derivative.normalizedDerivOfComplex_slashproof · cited by 1
- not_differentiableAt_of_local_left_inverse_hasDerivAt_zeroproof · cited by 0