proposition: Lemma simple_Socle M : mxsimple M -> (M <= Socle)%MS.
proof: Proof. move=> simM; have socM := component_socle sG simM. by rewrite (sumsmx_sup (PackSocle socM)) // PackSocleK component_mx_id. 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)