Theorems · Theorem · real analysis

DiffContOnCl.const_smul

∀ {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] {f : E → F} {s : Set E}
  {R : Type u_5} [inst_5 : Semiring R] [inst_6 : Module R F] [SMulCommClass 𝕜 R F] [ContinuousConstSMul R F],
  DiffContOnCl 𝕜 f s → ∀ (c : R), DiffContOnCl 𝕜 (c • f) s

Defined in

Mathlib.Analysis.Calculus.DiffContOnCl

Cited by

0 results in Mathlib

Foundations

Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedAddCommGroupNormedSpaceNormedSpaceSemiringModuleSMulCommClassContinuousConstSMul