proposition: Lemma Wedderburn_mulmx0 i j A B : i != j -> (A \in 'R_i)%MS -> (B \in 'R_j)%MS -> A *m B = 0.
proof: Proof. move=> ne_ij RiA RjB; apply: memmx0. by rewrite -(Wedderburn_annihilate ne_ij) mem_mulsmx. 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)