Theorems · Theorem · real analysis

ContDiffWithinAt.restrict_scalars

∀ (𝕜 : Type u_1) [inst : NontriviallyNormedField 𝕜] {E : Type uE} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {F : Type uF} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {s : Set E}
  {f : E → F} {x : E} {n : WithTop ℕ∞} {𝕜' : Type u_3} [inst_5 : NontriviallyNormedField 𝕜']
  [inst_6 : NormedAlgebra 𝕜 𝕜'] [inst_7 : NormedSpace 𝕜' E] [IsScalarTower 𝕜 𝕜' E] [inst_9 : NormedSpace 𝕜' F]
  [IsScalarTower 𝕜 𝕜' F], ContDiffWithinAt 𝕜' n f s x → ContDiffWithinAt 𝕜 n f s x

Defined in

Mathlib.Analysis.Calculus.ContDiff.Operations

Cited by

2 results in Mathlib

Foundations

Depth 187 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNontriviallyNormedFieldNormedAlgebraNormedSpaceIsScalarTowerNormedSpaceIsScalarTower