{G H : Group} {C : Commutative (@group_sgop G)} (f : GroupIsomorphism G H) : Commutative (@group_sgop H). Proof. unfold Commutative. rapply (equiv_ind f); intro g1. rapply (equiv_ind f); intro g2. refine ((preserves_sg_op _ _)^ @ _ @ (preserves_sg_op _ _)). refine (ap f _). apply C. 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.