proposition: Lemma ncprod1 : G_ 1 \isog G.
proof: Proof. case: ncprodS => gz isoZ; rewrite isog_sym /= -im_cpair. rewrite mulGSid /=; first by rewrite sub_isog ?injm_cpairg1. rewrite -{3}center_ncprod0 injm_center ?injm_cpair1g //. by rewrite -cpair_center_id center_sub. 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)