Theorems · Theorem · real analysis
HasDerivAt.continuousOn
∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : NormedAddCommGroup F]
[inst_2 : NormedSpace 𝕜 F] {s : Set 𝕜} {f f' : 𝕜 → F}, (∀ x ∈ s, HasDerivAt f (f' x) x) → ContinuousOn f s- Defined in
- Mathlib.Analysis.Calculus.Deriv.Basic
- Cited by
- 4 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.
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
- ContinuousOnstatement · cited by 1,411
- HasDerivAtstatement and proof · cited by 493
- ContinuousAt.continuousWithinAtproof · cited by 102
- HasDerivAt.continuousAtproof · cited by 28
Cited by4
Results whose statement or proof uses this declaration.
- intervalIntegral.integral_eq_sub_of_hasDerivAtproof · cited by 11
- intervalIntegral.integral_deriv_smul_deriv_compproof · cited by 2
- MeasureTheory.measurable_resolventproof · cited by 2
- ODE_solution_unique_of_mem_Iooproof · cited by 2