Theorems · Theorem · global analysis
DifferentiableAt.fun_add_iff_left
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {F : Type u_3} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {f g : E → F}
{x : E}, DifferentiableAt 𝕜 g x → (DifferentiableAt 𝕜 (fun i => f i + g i) x ↔ DifferentiableAt 𝕜 f x)Eta-expanded form of DifferentiableAt.add_iff_left
- Defined in
- Mathlib.Analysis.Calculus.FDeriv.Add
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NormedAddCommGroupstatement · cited by 15,752
- NormedSpacestatement · cited by 12,499
- NontriviallyNormedFieldstatement · cited by 8,742
- DifferentiableAtstatement · cited by 617
- DifferentiableAt.add_iff_leftproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Real.differentiableAt_binEntropy_iff_ne_zero_oneproof · cited by 1