Theorems · Theorem · functional analysis
fderivWithin_univ
∀ {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}, fderivWithin 𝕜 f Set.univ = fderiv 𝕜 f- Defined in
- Mathlib.Analysis.Calculus.FDeriv.Defs
- Cited by
- 29 results in Mathlib
- Foundations
- Depth 81 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.
- DFunLike.coeproof · 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
- Set.univstatement and proof · cited by 3,945
- fderivstatement · cited by 398
- fderivWithinstatement and proof · cited by 357
- ContinuousLinearMap.extproof · cited by 320
- fderiv_defproof · cited by 5
Cited by29
Results whose statement or proof uses this declaration.
- iteratedFDerivWithin_univproof · cited by 19
- derivWithin_univproof · cited by 11
- fderiv_fun_constproof · cited by 6
- fderivWithin_eq_fderivproof · cited by 6
- Filter.EventuallyEq.fderiv_eqproof · cited by 5
- iteratedFDeriv_succ_apply_rightproof · cited by 4
- ContinuousLinearEquiv.comp_fderivproof · cited by 3
- fderivWithin_of_mem_nhdsproof · cited by 3
- fderiv_comp_smulproof · cited by 2
- VectorField.lieBracketWithin_univproof · cited by 2
- differentiableAt_iff_restrictScalarsproof · cited by 2
- ContinuousLinearEquiv.comp_right_fderivproof · cited by 1