proposition: Lemma Wedderburn_direct : mxdirect (\sum_i 'R_i)%MS.
proof: Proof. apply/mxdirectP; rewrite /= sums_R mxrankMfree ?gring_free //. rewrite (mxdirectP (Socle_direct sG)); apply: eq_bigr=> i _ /=. by rewrite genmxE mxrankMfree ?gring_free. 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)