Theorems · Theorem · global analysis
HasGradientAtFilter.hasDerivAtFilter
∀ {𝕜 : Type u_1} [inst : RCLike 𝕜] {g : 𝕜 → 𝕜} {g' u : 𝕜} {L' : Filter 𝕜},
HasGradientAtFilter g g' u L' → HasDerivAtFilter g ((starRingEnd 𝕜) g') (L' ×ˢ pure u)- Defined in
- Mathlib.Analysis.Calculus.Gradient.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 185 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- RingHomstatement · cited by 10,189
- Filterstatement and proof · cited by 8,121
- RCLikestatement and proof · cited by 2,829
- SProd.sprodstatement · cited by 1,750
- starRingEndstatement · cited by 671
- HasDerivAtFilterstatement · cited by 63
- HasGradientAtFilterstatement and proof · cited by 10
Cited by1
Results whose statement or proof uses this declaration.
- HasGradientAtFilter.hasDerivAtFilter'proof · cited by 0