idealX_span — Mathlib

English

For f ∈ Polynomial K and g ∈ Polynomial K with g ≠ 0, the valuation of RatFunc.mk f g equals intValuation f over intValuation g.

Русский

Для f ∈ Polynomial K и g ∈ Polynomial K (g ≠ 0) оценка RatFunc.mk f g равна intValuation f / intValuation g.

LaTeX

$$$ \text{Polynomial}.valuation\;K (\mathrm{RatFunc } K) (\mathrm{RatFunc.mk } f g) = \frac{\mathrm{Polynomial}.intValuation f}{\mathrm{Polynomial}.intValuation g} $$$

Lean4

@[simp]
theorem idealX_span : (idealX K).asIdeal = Ideal.span { X } :=
  rfl

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