equiv_path_group@{u v | u < v} {U : Univalence} {G H : Group@{u}} : GroupIsomorphism G H <~> (paths@{v} G H) := equiv_path_group'. Global Instance isequiv_group_left_op {G : Group} : forall (x : G), IsEquiv (x *.). Proof. intro x. srapply isequiv_adjointify. 1: exact (-x *.). all: intro y. all: refine (grp_assoc _ _ _ @ _ @ grp_unit_l y). all: refine (ap (fun x => x * y) _). 1: apply grp_inv_r. apply grp_inv_l. Defined.
Require Import Basics Types HProp HFiber HSet. Require Import Homotopy.IdentitySystems. Require Import (notations) Classes.interfaces.canonical_names. Require Import Pointed.Core. Require Import WildCat. Require Import Spaces.Nat.Core Spaces.Int. Require Import Truncations.Core.