Theorems · Theorem · real analysis

DiffContOnCl.smul_const

∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedAddCommGroup F] [inst_3 : NormedSpace 𝕜 E] [inst_4 : NormedSpace 𝕜 F] {𝕜' : Type u_5}
  [inst_5 : NontriviallyNormedField 𝕜'] [inst_6 : NormedAlgebra 𝕜 𝕜'] [inst_7 : NormedSpace 𝕜' F] [IsScalarTower 𝕜 𝕜' F]
  {c : E → 𝕜'} {s : Set E}, DiffContOnCl 𝕜 c s → ∀ (y : F), DiffContOnCl 𝕜 (fun x => c x • y) s

Defined in

Mathlib.Analysis.Calculus.DiffContOnCl

Cited by

1 results in Mathlib

Foundations

Depth 186 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedAddCommGroupNormedSpaceNormedSpaceNontriviallyNormedFieldNormedAlgebraNormedSpaceIsScalarTower