proposition: Lemma injm_xsdprodm : 'injm xsdprodm = [&& 'injm fH, 'injm fK & fH @* H :&: fK @* K == 1].
proof: Proof. rewrite injm_sdprodm im_sdprodm1 im_sdprodm2 !subG1 /= !ker_restrm !ker_comp. rewrite !morphpre_invm !morphimIim. by rewrite !morphim_injm_eq1 ?subsetIl ?injm_sdpair1 ?injm_sdpair2. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq div) mathcomp(choice fintype bigop finset fingroup morphism) mathcomp(quotient action)