Theorems · Theorem · real analysis
hasFDerivWithinAt_singleton
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E]
[inst_3 : TopologicalSpace E] {F : Type u_3} [inst_4 : AddCommGroup F] [inst_5 : Module 𝕜 F]
[inst_6 : TopologicalSpace F] (f : E → F) (x : E), HasFDerivWithinAt f 0 {x} x- Defined in
- Mathlib.Analysis.Calculus.FDeriv.Const
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- AddCommGroupstatement and proof · cited by 12,871
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Filterproof · cited by 8,121
- nhdsproof · cited by 5,554
- ContinuousLinearMapstatement · cited by 5,352
- Bot.botproof · cited by 4,720
- Filter.NeBotproof · cited by 853
- Filter.principalproof · cited by 740
Cited by2
Results whose statement or proof uses this declaration.
- hasFDerivAt_of_subsingletonproof · cited by 6
- differentiableOn_singletonproof · cited by 1