Theorems · Theorem · real analysis
derivWithin_zero_of_not_differentiableWithinAt
∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : AddCommGroup F] [inst_2 : Module 𝕜 F]
[inst_3 : TopologicalSpace F] {f : 𝕜 → F} {x : 𝕜} {s : Set 𝕜}, ¬DifferentiableWithinAt 𝕜 f s x → derivWithin f s x = 0- Defined in
- Mathlib.Analysis.Calculus.Deriv.Basic
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- RingHom.idproof · cited by 18,349
- AddCommGroupstatement and proof · cited by 12,871
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- ContinuousLinearMapproof · cited by 5,352
- DifferentiableWithinAtstatement and proof · cited by 453
- derivWithinstatement · cited by 258
- zero_applyproof · cited by 251
- fderivWithin_zero_of_not_differentiableWithinAtproof · cited by 13
Cited by12
Results whose statement or proof uses this declaration.
- MonotoneOn.derivWithin_nonnegproof · cited by 4
- InformationTheory.rightDeriv_klFunproof · cited by 3
- range_derivWithin_subset_closure_span_imageproof · cited by 3
- derivWithin_zero_of_frequently_memproof · cited by 2
- derivWithin_mul_const_fieldproof · cited by 2
- derivWithin_Ioi_eq_Iciproof · cited by 2
- lineDerivWithin_zero_of_not_lineDifferentiableWithinAtproof · cited by 1
- derivWithin_zero_of_frequently_constproof · cited by 1
- derivWithin.lhopital_zero_nhdsWithin_convexproof · cited by 1
- derivWithin_mem_iffproof · cited by 1
- differentiableWithinAt_of_derivWithin_ne_zeroproof · cited by 1
- InformationTheory.leftDeriv_klFunproof · cited by 1