intValuation_X — Mathlib

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)

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