charP_iff_charP — Mathlib

English

If R has CharZero, then FreeAlgebra R X has CharZero.

Русский

Если R характеристика ноль, то FreeAlgebra R X характеристика ноль.

LaTeX

$$$( \\text{CharZero}(R) ) \\Rightarrow \\text{CharZero}(\\mathrm{FreeAlgebra}(R,X))$$$

Lean4

theorem charP_iff_charP {K L : Type*} [DivisionRing K] [NonAssocSemiring L] [Nontrivial L] (f : K →+* L) (p : ℕ) :
    CharP K p ↔ CharP L p := by simp only [charP_iff, ← f.injective.eq_iff, map_natCast f, map_zero f]

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