proposition: Lemma hom_component_mx_iso f V : mxsimple V -> (compU <= dom_hom_mx f)%MS -> (V <= compU *m f)%MS -> mx_iso U V.
proof: Proof. have [I [W isoUW ->]] := component_mx_def => simV homWf sVWf. have [i _ _|i _ ] := hom_mxsemisimple_iso simV _ homWf sVWf. exact: mx_iso_simple (simU). exact: mx_iso_trans. 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)