Theorems · Theorem · global analysis

extDerivWithin_add

∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {n : ℕ}
  {ω₁ ω₂ : E → E [⋀^Fin n]→L[𝕜] F} {s : Set E} {x : E},
  UniqueDiffWithinAt 𝕜 s x →
    DifferentiableWithinAt 𝕜 ω₁ s x →
      DifferentiableWithinAt 𝕜 ω₂ s x → extDerivWithin (ω₁ + ω₂) s x = extDerivWithin ω₁ s x + extDerivWithin ω₂ s x

Defined in

Mathlib.Analysis.Calculus.DifferentialForm.Basic

Cited by

2 results in Mathlib

Foundations

Depth 178 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace