English
The exterior derivative of a 0-form given by a constant map equals the corresponding 1-form formed by the derivative of the underlying function.
Русский
Экст_deriv нулевой формы, заданной константой, равен соответствующей 1-форме, полученной из производной функции.
LaTeX
$$$extDeriv (fun x \mapsto ContinuousAlternatingMap.constOfIsEmpty 𝕜 E (Fin 0) (f x)) x = .ofSubsingleton _ _ _ (0 : Fin 1) (fderiv 𝕜 f x)$$$
Lean4
@[simp]
theorem extDerivWithin_univ (ω : E → E [⋀^Fin n]→L[𝕜] F) : extDerivWithin ω univ = extDeriv ω :=
by
ext1 x
rw [extDerivWithin, extDeriv, fderivWithin_univ]