Theorems · Theorem · real analysis

Differentiable.fun_mul

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {𝔸 : Type u_5} [inst_3 : NormedRing 𝔸] [inst_4 : NormedAlgebra 𝕜 𝔸] {a b : E → 𝔸},
  Differentiable 𝕜 a → Differentiable 𝕜 b → Differentiable 𝕜 fun i => a i * b i

Eta-expanded form of Differentiable.mul

Defined in

Mathlib.Analysis.Calculus.FDeriv.Mul

Cited by

2 results in Mathlib

Foundations

Depth 185 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedRingNormedAlgebra