Theorems · Theorem · real analysis

HasFDerivWithinAt.restrictScalars

∀ (𝕜 : Type u_1) [inst : NontriviallyNormedField 𝕜] {𝕜' : Type u_2} [inst_1 : NontriviallyNormedField 𝕜']
  [inst_2 : NormedAlgebra 𝕜 𝕜'] {E : Type u_3} [inst_3 : NormedAddCommGroup E] [inst_4 : NormedSpace 𝕜 E]
  [inst_5 : NormedSpace 𝕜' E] [inst_6 : IsScalarTower 𝕜 𝕜' E] {F : Type u_4} [inst_7 : NormedAddCommGroup F]
  [inst_8 : NormedSpace 𝕜 F] [inst_9 : NormedSpace 𝕜' F] [inst_10 : IsScalarTower 𝕜 𝕜' F] {f : E → F} {f' : E →L[𝕜'] F}
  {s : Set E} {x : E}, HasFDerivWithinAt f f' s x → HasFDerivWithinAt f (ContinuousLinearMap.restrictScalars 𝕜 f') s x

Defined in

Mathlib.Analysis.Calculus.FDeriv.RestrictScalars

Cited by

7 results in Mathlib

Foundations

Depth 166 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNontriviallyNormedFieldNormedAlgebraNormedAddCommGroupNormedSpaceNormedSpaceIsScalarTowerNormedAddCommGroupNormedSpaceNormedSpaceIsScalarTower