proposition: Lemma char_sum_irr chi : chi \is a character -> {r | chi = \sum_(i <- r) 'chi_i}.
proof: Proof. move=> Nchi; apply: sig_eqW; case/char_sum_irrP: Nchi => n {chi}->. elim/big_rec: _ => [|i _ _ [r ->]]; first by exists nil; rewrite big_nil. exists (ncons (n i) i r); rewrite scaler_nat. by elim: {n}(n i) => [|n IHn]; rewrite ?add0r //= big_cons mulrS -addrA IHn. 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)