proposition: Lemma hom_component_mx f : (compU <= dom_hom_mx f)%MS -> (compU *m f <= compU)%MS.
proof: Proof. move=> hom_f. have [I W /= simW defW _] := hom_mxsemisimple component_mx_semisimple hom_f. rewrite -defW; apply/sumsmx_subP=> i _; apply: mx_iso_component. by apply: hom_component_mx_iso hom_f _ => //; rewrite -defW (sumsmx_sup i). 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)