proposition: Lemma cyclic_mx_module u : mxmodule (cyclic_mx u).
proof: Proof. apply/mxmoduleP=> x Gx; apply/row_subP=> i; rewrite row_mul. have [A E_A ->{i}] := @cyclic_mxP u _ (row_sub i _); rewrite -mulmxA. by apply/cyclic_mxP; exists (A *m rG x); rewrite ?envelop_mxM ?envelop_mx_id. 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)