proposition: Lemma cfkerE chi : chi \is a character -> cfker chi = G :&: \bigcap_(i in irr_constt chi) cfker 'chi_i.
proof: Proof. move=> Nchi; rewrite cfkerEchar //; apply/setP=> x; rewrite !inE. apply: andb_id2l => Gx; rewrite {1 2}[chi]cfun_sum_constt !sum_cfunE. apply/eqP/bigcapP=> [Kx i Ci | Kx]; last first. by apply: eq_bigr => i /Kx Kx_i; rewrite !cfunE cfker1. rewrite cfkerEirr inE /= -(inj_eq (mulfI Ci)). have:= (normC_sum_upper _ Kx) i; rewrite !cfunE => -> // {Ci}i _. have chi_i_ge0: 0 <= '[chi, 'chi_i]. by rewrite natr_ge0 ?Cnat_cfdot_char_irr. by rewrite !cfunE normrM (normr_idP _) ?ler_wpM2l ?char1_ge_norm ?irr_char. 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)