C_div — Mathlib

English

In a polynomial ring over a field, the coefficient-wise inverse equals the coefficient of the inverse unit: coeff of u⁻¹ at n equals (coeff of u at n)⁻¹.

Русский

В полиномной кольце над полем коэффициентный инверс равен коэффициенту обратной единицы: (coeff u⁻¹)_n = (coeff u_n)⁻¹.

LaTeX

$$ (u : R[X]) .coeff n)⁻¹ = (u⁻¹ : R[X]).coeff n$$

Lean4

theorem C_div : C (a / b) = C a / C b := by rw [div_C, ← C_mul, div_eq_mul_inv]

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