proposition: Lemma lin_char_der1 : G^`(1)%g \subset cfker xi.
proof: Proof. rewrite gen_subG /=; apply/subsetP=> _ /imset2P[x y Gx Gy ->]. rewrite cfkerEchar // inE groupR //= !lin_charM ?lin_charV ?in_group //. by rewrite mulrCA mulKf ?mulVf ?lin_char_neq0 // lin_char1. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype choice ssrnat seq) mathcomp(path div fintype tuple finfun bigop prime order) mathcomp(ssralg poly finset gproduct fingroup morphism) mathcomp(perm automorphism quotient finalg action zmodp) mathcomp(commutator cyclic center pgroup nilpotent sylow) mathcomp(abelian matrix mxalgebra mxpoly mxrepresentation) mathcomp(vector ssrnum algC classfun archimedean)