proposition: Lemma Wedderburn_sum_id : \sum_i 'e_i = 1%:M.
proof: Proof. rewrite -linear_sum; apply: canLR mxvecK _. have: (1%:M \in R_G)%MS := envelop_mx1 aG. rewrite -Wedderburn_sum; case/(sub_dsumsmx Wedderburn_direct) => e Re -> _. apply: eq_bigr => i _; have dxR := mxdirect_sumsP Wedderburn_direct i (erefl _). rewrite (bigD1 i) // mulmxDl proj_mx_id ?Re // proj_mx_0 ?addr0 //=. by rewrite summx_sub // => j ne_ji; rewrite (sumsmx_sup j) ?Re. 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)