Theorems · Theorem · global analysis
HasFDerivAt.continuousAt
∀ {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} [ContinuousAdd E] [ContinuousSMul 𝕜 E]
[ContinuousAdd F] [ContinuousSMul 𝕜 F], HasFDerivAt f f' x → ContinuousAt f x- Defined in
- Mathlib.Analysis.Calculus.FDeriv.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 167 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.
- 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
- le_rflproof · cited by 1,558
- ContinuousSMulstatement and proof · cited by 1,016
- ContinuousAddstatement and proof · cited by 777
- ContinuousAtstatement · cited by 697
- HasFDerivAtstatement and proof · cited by 350
- HasFDerivAtFilter.tendsto_nhdsproof · cited by 4
Cited by8
Results whose statement or proof uses this declaration.
- HasFDerivAt.compproof · cited by 50
- DifferentiableAt.continuousAtproof · cited by 28
- HasDerivAt.comp_hasFDerivAtproof · cited by 20
- HasStrictFDerivAt.continuousAtproof · cited by 5
- continuousAt_jacobiTheta₂proof · cited by 3
- HasFDerivWithinAt.comp_hasFDerivAtproof · cited by 2
- HasDerivWithinAt.comp_hasFDerivAtproof · cited by 1
- HasFDerivAt.iterateproof · cited by 1