proposition: Lemma irr_comp_id (M : 'M_nG) (modM : mxmodule aG M) (iM : sG) : mxsimple aG M -> (M <= iM)%MS -> irr_comp (submod_repr modM) = iM.
proof: Proof. move=> simM sMiM; rewrite -[iM]irr_reprK. apply/esym/irr_comp_rsim/mx_rsim_iso/component_mx_iso => //. exact: socle_simple. 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)