proposition: Lemma im_cfclass_Iirr i : H <| G -> perm_eq [seq 'chi_j | j in cfclass_Iirr G i] ('chi_i ^: G)%CF.
proof: Proof. move=> nsHG; have UchiG := cfclass_uniq 'chi_i nsHG. apply: uniq_perm; rewrite ?(map_inj_uniq irr_inj) ?enum_uniq // => phi. apply/imageP/idP=> [[j iGj ->] | /cfclassP[y]]; first by rewrite -cfclass_IirrE. by exists (conjg_Iirr i y); rewrite ?imset_f ?conjg_IirrE. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq path) mathcomp(choice fintype div tuple finfun bigop prime order) mathcomp(ssralg ssrnum finset fingroup morphism perm) mathcomp(automorphism quotient action zmodp cyclic center) mathcomp(gproduct commutator gseries nilpotent pgroup) mathcomp(sylow maximal frobenius matrix mxalgebra) mathcomp(mxrepresentation vector algC classfun character) mathcomp(archimedean)