Section IsChar.
Variable gT : finGroupType.
Definition character {G : {set gT}} :=
[qualify a phi : 'CF(G) | [forall i, coord (irr G) i phi \in Cnat]].
Fact character_key G : pred_key (@character G). Proof. by []. Qed.
Canonical character_keyed G := KeyedQualifier (character_key G).
Variable G : {group gT}.
Implicit Types (phi chi xi : 'CF(G)) (i : Iirr G).
Canonical character_addrPred := AddrPred add_char.

Lemma char_sum_irr chi :
chi \is a character -> {r | chi = \sum_(i <- r) 'chi_i}.