Theorems · Theorem · global analysis
HasGradientAt.hasDerivAt
∀ {𝕜 : Type u_1} [inst : RCLike 𝕜] {g : 𝕜 → 𝕜} {g' u : 𝕜}, HasGradientAt g g' u → HasDerivAt g ((starRingEnd 𝕜) g') u- Defined in
- Mathlib.Analysis.Calculus.Gradient.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 187 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RCLike
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- RingHomstatement · cited by 10,189
- one_mulproof · cited by 2,841
- RCLikestatement and proof · cited by 2,829
- starRingEndstatement and proof · cited by 671
- HasDerivAtstatement · cited by 493
- HasDerivAt.congr_simpproof · cited by 82
- InnerProductSpace.toDualproof · cited by 45
- HasGradientAtstatement and proof · cited by 24
- hasGradientAt_iff_hasFDerivAtproof · cited by 5
- hasFDerivAt_iff_hasDerivAtproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- gradient_eq_derivproof · cited by 1
- HasGradientAt.hasDerivAt'proof · cited by 0