Theorems · Theorem · real analysis
HasDerivAt.continuousAt
∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : NormedAddCommGroup F]
[inst_2 : NormedSpace 𝕜 F] {f : 𝕜 → F} {f' : F} {x : 𝕜}, HasDerivAt f f' x → ContinuousAt f x- Defined in
- Mathlib.Analysis.Calculus.Deriv.Basic
- Cited by
- 28 results in Mathlib
- Foundations
- Depth 168 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- le_rflproof · cited by 1,558
- ContinuousAtstatement · cited by 697
- HasDerivAtstatement and proof · cited by 493
- HasDerivAtFilter.tendsto_nhdsproof · cited by 2
Cited by28
Results whose statement or proof uses this declaration.
- HasDerivAt.compproof · cited by 43
- HasDerivAt.scompproof · cited by 11
- MeasureTheory.integral_Ioi_of_hasDerivAt_of_tendsto'proof · cited by 7
- HasDerivAt.lhopital_zero_right_on_Iooproof · cited by 5
- MeasureTheory.integral_Ioi_of_hasDerivAt_of_tendstoproof · cited by 5
- HasDerivAt.continuousOnproof · cited by 4
- MeasureTheory.integrableOn_Ioi_deriv_of_nonneg'proof · cited by 4
- MeasureTheory.integral_Iic_of_hasDerivAt_of_tendstoproof · cited by 3
- MeasureTheory.integrableOn_Ioi_deriv_of_nonnegproof · cited by 3
- intervalIntegral.integral_deriv_smul_comp'proof · cited by 3
- exists_hasDerivAt_eq_zero'proof · cited by 3
- MeasureTheory.integral_Iic_of_hasDerivAt_of_tendsto'proof · cited by 2