proposition: Lemma injm_cpairg1 : 'injm cpairg1.
proof: Proof. rewrite /cpairg1; case: restrmP => _ [_ -> _ _]. rewrite ker_comp ker_in_cprod; apply/subsetP=> x; rewrite 5!inE /=. by case/and3P=> _ Zx; rewrite inE eq_sym (inv_eq invgK) invg1 morph_injm_eq1. Qed.
imports: mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq div) mathcomp(fintype bigop finset fingroup morphism perm) mathcomp(automorphism quotient action gproduct gfunctor) mathcomp(cyclic)