proposition: Lemma rsim_regular_submod : {U : 'M_nG & {modU : mxmodule aG U & mx_rsim rG (submod_repr modU)}}.
proof: Proof. have [V [modV eqG'V]] := rsim_regular_factmod. have [U modU defVU dxVU] := mx_Maschke F'G modV (submx1 V). exists U; exists modU; apply: mx_rsim_trans eqG'V _. by apply: mx_rsim_factmod; rewrite ?mxdirectE /= addsmxC // addnC. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq path) mathcomp(div choice fintype tuple finfun bigop prime) mathcomp(ssralg poly polydiv finset fingroup morphism) mathcomp(perm automorphism quotient finalg action zmodp) mathcomp(commutator cyclic center pgroup matrix mxalgebra) mathcomp(mxpoly)