proposition: Lemma lemma2 : f (conj c * conj a * d * conj b) = (-d) * conj b.
proof: Proof. unfold f. rewrite 2 factorneg_r. rewrite 3 simple_associativity. rewrite <- distropp. rewrite (right_inverse (a * c)). rewrite (left_identity d). symmetry. apply factorneg_l. Defined.
imports: Classes.interfaces.abstract_algebra Cubical Pointed.Core Pointed.pSusp Homotopy.HSpace.Core Homotopy.Suspension Homotopy.Join.Core