proposition: Lemma char_reprP phi : reflect (exists rG : representation algC G, phi = cfRepr rG) (phi \is a character).
proof: Proof. apply: (iffP char_sum_irrP) => [[n ->] | [[n rG] ->]]; last first. exists (fun i => standard_irr_coef rG (socle_of_Iirr i)). by rewrite -cfRepr_standard (cfRepr_sim (mx_rsim_standard rG)). exists (\big[dadd_grepr/grepr0]_i muln_grepr (Representation 'Chi_i) (n i)). rewrite cfRepr_dsum; apply: eq_bigr => i _. by rewrite cfRepr_muln irrRepr scaler_nat. 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)