proposition: Lemma mxsimple_map (U : 'M_n) : mxsimple rGf U^f -> mxsimple rG U.
proof: Proof. case; rewrite map_mx_eq0 // mxmodule_map // => modU nzU minU. split=> // V modV sVU nzV; rewrite -(map_submx f). by rewrite (minU V^f) //= ?mxmodule_map ?map_mx_eq0 // map_submx. 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)