Theorems · Theorem · functional analysis
ContinuousLinearMap.hasFDerivAt
∀ {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 →L[𝕜] F) {x : E}, HasFDerivAt (⇑f) f x- Defined in
- Mathlib.Analysis.Calculus.FDeriv.Linear
- Cited by
- 38 results in Mathlib
- Foundations
- Depth 166 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- 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
- HasFDerivAtstatement · cited by 350
- ContinuousLinearMap.hasFDerivAtFilterproof · cited by 11
Cited by38
Results whose statement or proof uses this declaration.
- ContinuousLinearMap.differentiableAtproof · cited by 13
- ContinuousLinearMap.fderivproof · cited by 10
- HasDerivAt.real_of_complexproof · cited by 7
- HasFTaylorSeriesUpToOn.continuousLinearMap_compproof · cited by 5
- hasFDerivAt_applyproof · cited by 4
- HasFDerivWithinAt.mul_const'proof · cited by 4
- HasFDerivAt.const_mulproof · cited by 4
- Real.hasFDerivAt_fourierChar_neg_bilinear_rightproof · cited by 3
- intervalIntegral.integral_eq_sub_of_hasDeriv_right_of_leproof · cited by 3
- HasFDerivAt.mul_const'proof · cited by 3
- hasFDerivAt_exp_smul_const_of_mem_ballproof · cited by 3
- HasFDerivAt.continuousAlternatingMap_applyproof · cited by 2