Theorems · Theorem · real analysis
differentiableAt_iff_restrictScalars
∀ (𝕜 : Type u_1) [inst : NontriviallyNormedField 𝕜] {𝕜' : Type u_2} [inst_1 : NontriviallyNormedField 𝕜']
[inst_2 : NormedAlgebra 𝕜 𝕜'] {E : Type u_3} [inst_3 : NormedAddCommGroup E] [inst_4 : NormedSpace 𝕜 E]
[inst_5 : NormedSpace 𝕜' E] [inst_6 : IsScalarTower 𝕜 𝕜' E] {F : Type u_4} [inst_7 : NormedAddCommGroup F]
[inst_8 : NormedSpace 𝕜 F] [inst_9 : NormedSpace 𝕜' F] [inst_10 : IsScalarTower 𝕜 𝕜' F] {f : E → F} {x : E},
DifferentiableAt 𝕜 f x → (DifferentiableAt 𝕜' f x ↔ ∃ g', ContinuousLinearMap.restrictScalars 𝕜 g' = fderiv 𝕜 f x)- Cited by
- 2 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.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHom.idstatement and proof · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- ContinuousLinearMapstatement and proof · cited by 5,352
- Set.univproof · cited by 3,945
- IsScalarTowerstatement and proof · cited by 3,896
- NormedAlgebrastatement and proof · cited by 1,165
- DifferentiableAtstatement and proof · cited by 617
- DifferentiableWithinAtproof · cited by 453
- fderivstatement and proof · cited by 398
- DifferentiableAt.differentiableWithinAtproof · cited by 96
Cited by2
Results whose statement or proof uses this declaration.
- differentiableAt_complex_iff_differentiableAt_realproof · cited by 1
- conformalAt_iff_differentiableAt_or_differentiableAt_comp_conjproof · cited by 0