proposition: Lemma map_regular_subseries U i (modU : mx_subseries (regular_repr aF G) U) (modUf : mx_subseries (regular_repr rF G) [seq M^f | M <- U]) : mx_rsim (map_repr f (subseries_repr i modU)) (subseries_repr i modUf).
proof: Proof. set mf := map _ in modUf *; rewrite /subseries_repr. do 2!move: (mx_subseries_module' _ _) (mx_subseries_module _ _). have mf_i V: nth 0^f (mf V) i = (V`_i)^f. case: (ltnP i (size V)) => [ltiV | leVi]; first exact: nth_map. by rewrite !nth_default ?size_map. rewrite -(map_mx0 f) mf_i (mf_i (0 :: U)) => modUi'f modUif modUi' modUi. by apply: map_section_repr; apply: map_regular_repr. 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)