Theorems · Theorem · real analysis
Differentiable.finsetProd
∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {ι : Type u_2} {𝔸' : Type u_3} [inst_1 : NormedCommRing 𝔸']
[inst_2 : NormedAlgebra 𝕜 𝔸'] {u : Finset ι} {f : ι → 𝕜 → 𝔸'},
(∀ i ∈ u, Differentiable 𝕜 (f i)) → Differentiable 𝕜 (∏ i ∈ u, f i)- Defined in
- Mathlib.Analysis.Calculus.Deriv.Mul
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 191 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Finset.prodstatement · cited by 2,356
- NormedAlgebrastatement and proof · cited by 1,165
- Differentiablestatement and proof · cited by 298
- NormedCommRingstatement and proof · cited by 218
- DifferentiableAt.finsetProdproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Differentiable.finset_prodproof · cited by 0