finite_of_fg_torsion — Mathlib

English

A finitely generated commutative group that is torsion is finite.

Русский

Конечная коммутативная группа, тождественная, тождественный торсион, конечна.

LaTeX

$$$[CommGroup G] \land [Group.FG G] \land [Monoid.IsTorsion G] \Rightarrow Finite G$$$

Lean4

theorem finite_of_fg_torsion [CommGroup G] [Group.FG G] (hG : Monoid.IsTorsion G) : Finite G :=
  @Finite.of_equiv _ _ (AddCommGroup.finite_of_fg_torsion (Additive G) hG) Multiplicative.ofAdd

Похожие утверждения