Theorems · Theorem · real analysis

Differentiable.smul_const

∀ {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] {𝕜' : Type u_5}
  [inst_5 : NormedRing 𝕜'] [inst_6 : NormedAlgebra 𝕜 𝕜'] [inst_7 : Module 𝕜' F] [IsBoundedSMul 𝕜' F]
  [IsScalarTower 𝕜 𝕜' F] {c : E → 𝕜'}, Differentiable 𝕜 c → ∀ (f : F), Differentiable 𝕜 fun y => c y • f

Defined in

Mathlib.Analysis.Calculus.FDeriv.Mul

Cited by

5 results in Mathlib

Foundations

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

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedRingNormedAlgebraModuleIsBoundedSMulIsScalarTower