pow — Mathlib

English

A product of monic polynomials is monic.

Русский

Произведение моникных полиномов мон Proceedings моной.

LaTeX

$$$$ m.Monic\left(\prod_{i\in s} P_i\right) \\text{ if } m.Monic(P_i) \text{ for all } i \in s. $$$$

Lean4

protected theorem pow {f : MvPolynomial σ R} {n : ℕ} (hf : m.Monic f) : m.Monic (f ^ n) :=
  by
  nontriviality R
  rw [Monic, leadingCoeff_pow_of_pow_leadingCoeff_ne_zero, hf.leadingCoeff_eq_one, one_pow]
  rw [hf.leadingCoeff_eq_one, one_pow]
  exact one_ne_zero

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