extDerivWithin_add — Mathlib

English

The exterior derivative of the sum ω1 + ω2 is the sum of exterior derivatives: extDeriv(ω1 + ω2) = extDeriv ω1 + extDeriv ω2.

Русский

Производная по 外 extDeriv суммы ω1 и ω2 равна сумме внешних производных.

LaTeX

$$$\text{extDerivWithin}(\omega_1 + \omega_2) = \text{extDerivWithin}(\omega_1) + \text{extDerivWithin}(\omega_2).$$$

Lean4

theorem extDerivWithin_add (hsx : UniqueDiffWithinAt 𝕜 s x) (hω₁ : DifferentiableWithinAt 𝕜 ω₁ s x)
    (hω₂ : DifferentiableWithinAt 𝕜 ω₂ s x) :
    extDerivWithin (ω₁ + ω₂) s x = extDerivWithin ω₁ s x + extDerivWithin ω₂ s x := by
  simp [extDerivWithin, fderivWithin_add hsx hω₁ hω₂, alternatizeUncurryFin_add]

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