Theorems · Theorem · global analysis
Differentiable.differentiableOn
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E]
[inst_3 : TopologicalSpace E] {F : Type u_3} [inst_4 : AddCommGroup F] [inst_5 : Module 𝕜 F]
[inst_6 : TopologicalSpace F] {f : E → F} {s : Set E}, Differentiable 𝕜 f → DifferentiableOn 𝕜 f s- Defined in
- Mathlib.Analysis.Calculus.FDeriv.Basic
- Cited by
- 40 results in Mathlib
- Foundations
- Depth 165 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.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- DifferentiableOnstatement · cited by 419
- Differentiablestatement and proof · cited by 298
- Set.subset_univproof · cited by 228
- DifferentiableOn.monoproof · cited by 39
- differentiableOn_univproof · cited by 10
Cited by40
Results whose statement or proof uses this declaration.
- Differentiable.diffContOnClproof · cited by 15
- differentiableOn_idproof · cited by 13
- differentiableOn_constproof · cited by 12
- Differentiable.comp_differentiableOnproof · cited by 6
- Complex.Gamma_mul_Gamma_add_halfproof · cited by 2
- differentiableAt_iteratedDerivWithin_cexpproof · cited by 2
- Real.differentiableOn_mul_logproof · cited by 2
- ContinuousLinearEquiv.differentiableOnproof · cited by 1
- GaussianFourier.integral_cexp_neg_mul_sq_add_real_mul_Iproof · cited by 1
- InnerProductSpace.HarmonicOnNhd.exists_analyticOnNhd_univ_re_eqproof · cited by 1
- ContinuousAffineMap.differentiableOnproof · cited by 1
- Differentiable.isExactOn_univproof · cited by 1