English
The integral valuation of the power series X equals exp(-1).
Русский
Пусть интегральная valoración ряда X равна exp(-1).
LaTeX
$$$\operatorname{intValuation}(X) = \mathrm{WithZero}.\mathrm{exp}(-1).$$$
Lean4
/-- The integral valuation of the power series `X : K⟦X⟧` equals `(ofAdd -1) : ℤᵐ⁰`. -/
@[simp]
theorem intValuation_X : (idealX K).intValuation X = WithZero.exp (-1 : ℤ) :=
by
rw [← Polynomial.coe_X, ← intValuation_eq_of_coe]
apply intValuation_singleton _ Polynomial.X_ne_zero (by rfl)