Theorems · Theorem · real analysis
HasDerivWithinAt.deriv_eq_zero
∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : NormedAddCommGroup F]
[inst_2 : NormedSpace 𝕜 F] {f : 𝕜 → F} {x : 𝕜} {s : Set 𝕜},
HasDerivWithinAt f 0 s x → UniqueDiffWithinAt 𝕜 s x → deriv f x = 0- Defined in
- Mathlib.Analysis.Calculus.Deriv.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 170 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- derivstatement · cited by 676
- DifferentiableAtproof · cited by 617
- HasDerivWithinAtstatement and proof · cited by 333
- UniqueDiffWithinAtstatement and proof · cited by 252
- DifferentiableAt.hasDerivAtproof · cited by 114
- HasDerivAt.hasDerivWithinAtproof · cited by 86
- deriv_zero_of_not_differentiableAtproof · cited by 34
- em'proof · cited by 12
Cited by2
Results whose statement or proof uses this declaration.
- deriv2_sqrt_mul_logproof · cited by 1
- deriv_sqrt_mul_logproof · cited by 1