Theorems · Theorem · global analysis
gradient_eq_zero_of_not_differentiableAt
∀ {𝕜 : Type u_1} {F : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup F] [inst_2 : InnerProductSpace 𝕜 F]
[inst_3 : CompleteSpace F] {f : F → 𝕜} {x : F}, ¬DifferentiableAt 𝕜 f x → gradient f x = 0- Defined in
- Mathlib.Analysis.Calculus.Gradient.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 186 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.
- DFunLike.coeproof · cited by 62,936
- RingHom.idproof · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- ContinuousLinearMapproof · cited by 5,352
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- CompleteSpacestatement and proof · cited by 2,532
- map_zeroproof · cited by 1,614
- DifferentiableAtstatement and proof · cited by 617
- LinearIsometryEquiv.symmproof · cited by 287
- InnerProductSpace.toDualproof · cited by 45
- gradientstatement · cited by 19
Cited by1
Results whose statement or proof uses this declaration.
- gradient_eq_derivproof · cited by 1