Theorems · Theorem · real analysis
hasFDerivAt_of_subsingleton
∀ {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] [h : Subsingleton E] (f : E → F) (x : E), HasFDerivAt f 0 x- Defined in
- Mathlib.Analysis.Calculus.FDeriv.Const
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 170 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · 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
- ContinuousLinearMapstatement · cited by 5,352
- Set.mem_univproof · cited by 416
- HasFDerivWithinAtproof · cited by 356
- HasFDerivAtstatement · cited by 350
- Set.Subsingleton.eq_singleton_of_memproof · cited by 16
- hasFDerivWithinAt_univproof · cited by 14
Cited by6
Results whose statement or proof uses this declaration.
- fderiv_norm_smulproof · cited by 2
- differentiable_of_subsingletonproof · cited by 1
- DifferentiableAt.differentiableAt_norm_of_smulproof · cited by 1
- mdifferentiable_of_subsingletonproof · cited by 1
- hasFDerivAt_integral_of_dominated_loc_of_lip'proof · cited by 1
- Subsingleton.conformalAtproof · cited by 0