{R : Ring} (x : R) `{IsInvertible R x} : inverse_elem x * x = 1. Proof. apply left_inverse_eq. Defined.
Require Import WildCat. Require Import Spaces.Nat.Core Spaces.Nat.Arithmetic. Require Import Classes.interfaces.abstract_algebra. Require Import Algebra.Groups.Group Algebra.Groups.Subgroup. Require Import Modalities.ReflectiveSubuniverse.