proposition: Lemma cfConjgSdprod phi y : y \in 'N(K) -> y \in 'N(H) -> (cfSdprod defG phi ^ y = cfSdprod defG (phi ^ y))%CF.
proof: Proof. move=> nKy nHy. have nGy: y \in 'N(G) by rewrite -sub1set -(sdprodW defG) normsM ?sub1set. rewrite -{2}[phi](cfSdprodK defG) cfConjgRes_norm // cfRes_sdprodK //. by rewrite cfker_conjg // -{1}(normP nKy) conjSg cfker_sdprod. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq path) mathcomp(choice fintype div tuple finfun bigop prime order) mathcomp(ssralg ssrnum finset fingroup morphism perm) mathcomp(automorphism quotient action zmodp cyclic center) mathcomp(gproduct commutator gseries nilpotent pgroup) mathcomp(sylow maximal frobenius matrix mxalgebra) mathcomp(mxrepresentation vector algC classfun character) mathcomp(archimedean)