Theorems · Theorem · real analysis

curveIntegralFun_restrictScalars

∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {a b : E} {ω : E → E →L[𝕜] F}
  {γ : Path a b} {𝕝 : Type u_4} [inst_5 : RCLike 𝕝] [inst_6 : NormedSpace 𝕝 F] [inst_7 : NormedSpace 𝕝 E]
  [inst_8 : LinearMap.CompatibleSMul E F 𝕝 𝕜],
  curveIntegralFun (fun t => ContinuousLinearMap.restrictScalars 𝕝 (ω t)) γ = curveIntegralFun ω γ

Defined in

Mathlib.MeasureTheory.Integral.CurveIntegral.Basic

Cited by

2 results in Mathlib

Foundations

Depth 168 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceRCLikeNormedSpaceNormedSpaceLinearMap.CompatibleSMul