g (conj c * conj a * d * conj b) = conj a * d. Proof. unfold g. rewrite 2 simple_associativity. rewrite <- simple_associativity. rewrite left_inverse. rewrite right_identity. rewrite 2 simple_associativity. rewrite right_inverse. rewrite <- simple_associativity. apply left_identity. Defined.
Require Import Classes.interfaces.abstract_algebra. Require Import Cubical.DPath Cubical.PathSquare. Require Import Pointed.Core Pointed.pSusp. Require Import Homotopy.HSpace.Core. Require Import Homotopy.Suspension. Require Import Homotopy.Join.Core.