Theorems · Theorem · global analysis
HasFDerivWithinAt.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] {f : E → F} {f' : E →L[𝕜] F} {x : E} {s : Set E} [T1Space E],
s.Subsingleton → HasFDerivWithinAt f f' s x- Defined in
- Mathlib.Analysis.Calculus.FDeriv.Basic
- Cited by
- 1 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.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- AddCommGroupstatement and proof · cited by 12,871
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- ContinuousLinearMapstatement and proof · cited by 5,352
- HasFDerivWithinAtstatement · cited by 356
- Set.Subsingletonstatement and proof · cited by 276
- T1Spacestatement and proof · cited by 275
- Set.Subsingleton.finiteproof · cited by 20
- HasFDerivWithinAt.of_finiteproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- hasFDerivWithinAt_comp_smul_smul_iffproof · cited by 0