proposition: Lemma morphim_mx_abs_irr : mx_absolutely_irreducible rG = mx_absolutely_irreducible rGf.
proof: Proof. have fG_onto: f @* G \subset restrm sGD f @* G. by rewrite morphim_restrm setIid. rewrite -(morphpre_mx_abs_irr _ fG_onto); congr (_ && (_ == _)). by rewrite /enveloping_algebra_mx /= morphpre_restrm (setIidPl _). 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)