Theorems · Theorem · real analysis
HasDerivWithinAt.continuousWithinAt
∀ {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} {s : Set 𝕜},
HasDerivWithinAt f f' s x → ContinuousWithinAt f s x- Defined in
- Mathlib.Analysis.Calculus.Deriv.Basic
- Cited by
- 11 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.
Cites8
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
- ContinuousWithinAtstatement · cited by 512
- HasDerivWithinAtstatement and proof · cited by 333
- inf_le_leftproof · cited by 286
- HasDerivAtFilter.tendsto_nhdsproof · cited by 2
Cited by11
Results whose statement or proof uses this declaration.
- HasDerivWithinAt.scompproof · cited by 7
- HasDerivWithinAt.nonneg_of_monotoneOnproof · cited by 4
- HasDerivWithinAt.continuousOnproof · cited by 4
- norm_image_sub_le_of_norm_deriv_le_segment'proof · cited by 4
- exists_hasDerivWithinAt_eq_of_gt_of_ltproof · cited by 2
- intervalIntegral.integral_deriv_mul_eq_sub_of_hasDerivWithinAtproof · cited by 1
- IsIntegralCurveOn.continuousWithinAtproof · cited by 1
- intervalIntegral.integral_smul_deriv_eq_deriv_smul_of_hasDerivWithinAtproof · cited by 1
- intervalIntegral.integral_mul_deriv_eq_deriv_mul_of_hasDerivWithinAtproof · cited by 1
- IsIntegralCurveOn.continuousOnproof · cited by 0
- domain_mvtproof · cited by 0