Theorems · Theorem · real analysis

curveIntegral_sub

∀ {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}
  {ω₁ ω₂ : E → E →L[𝕜] F} {γ : Path a b},
  CurveIntegrable ω₁ γ →
    CurveIntegrable ω₂ γ → curveIntegral (ω₁ - ω₂) γ = ∫ᶜ (x : E) in γ, ω₁ x - ∫ᶜ (x : E) in γ, ω₂ x

Defined in

Mathlib.MeasureTheory.Integral.CurveIntegral.Basic

Cited by

1 results in Mathlib

Foundations

Depth 258 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace