Theorems · Theorem · global analysis
HasGradientAt.gradient
∀ {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} {f' x : F}, HasGradientAt f f' x → gradient f x = f'- Defined in
- Mathlib.Analysis.Calculus.Gradient.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 189 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NormedAddCommGroupstatement and proof · cited by 15,752
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- CompleteSpacestatement and proof · cited by 2,532
- HasGradientAtstatement and proof · cited by 24
- gradientstatement · cited by 19
- DifferentiableAt.hasGradientAtproof · cited by 2
- HasGradientAt.differentiableAtproof · cited by 1
- HasGradientAt.uniqueproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- gradient_eqproof · cited by 0