proposition: Lemma subGcfker G i : (G \subset cfker 'chi[G]_i) = (i == 0).
proof: Proof. rewrite -irr_eq1; apply/idP/eqP=> [chiG1 | ->]; last by rewrite cfker_cfun1. apply/cfun_inP=> x Gx; rewrite cfun1E Gx cfker1 ?(subsetP chiG1) ?lin_char1 //. by rewrite lin_irr_der1 (subset_trans (der_sub 1 G)). 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)