proposition: Lemma gen_mx_irr : mx_irreducible rGA.
proof: Proof. apply/mx_irrP; split=> [|U Umod nzU]; first exact: gen_dim_gt0. rewrite -sub1mx -rowval_genK -submx_rowval_gen submx_full //. case/mx_irrP: irrG => _; apply; first by rewrite mxmodule_rowval_gen. rewrite -(inj_eq (can_inj in_genK)) in_gen0. by rewrite -mxrank_eq0 rowval_genK mxrank_eq0. 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)