all — Mathlib

English

Let R be a ring with CharP R p and t ∈ ℕ. If t is invertible in R and R is nontrivial, then ringChar R does not divide t.

Русский

Пусть R — кольцо с CharP R p и t ∈ ℕ. Если t обратим в R и R не тривиально, то ringChar R не делит t.

LaTeX

$${t : ℕ} [Invertible (t : R)] [Nontrivial R] : ringChar R ∤ t$$

Lean4

/-- When two is invertible in a ring, every element is `Odd`. -/
@[simp low]
theorem all [Ring R] [Invertible (2 : R)] (a : R) : Odd a :=
  .of_isUnit_two (isUnit_of_invertible _) _

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