monic_of_d_eq_one — Mathlib

English

Let R be a semiring. The constant-1 polynomial, i.e. the polynomial obtained from coefficients (0,0,0,1), is monic in R[X].

Русский

Пусть R — полупрямой; константный полином 1 над R[X] моничен.

LaTeX

$$$\\forall R [\\mathrm{Semiring}\, R]: (1) \\text{ is monic in } R[X].$$$

Lean4

theorem monic_of_d_eq_one (ha : P.a = 0) (hb : P.b = 0) (hc : P.c = 0) (hd : P.d = 1) : P.toPoly.Monic := by
  rw [Monic, leadingCoeff_of_c_eq_zero ha hb hc, hd]

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