Canonical char_semiringPred := SemiringPred mul_char.
End IsChar.
Prenex Implicits character.
Arguments char_reprP {gT G phi}.
Section AutChar.
Variables (gT : finGroupType) (G : {group gT}).
Implicit Type u : {rmorphism algC -> algC}.
Implicit Type chi : 'CF(G).

(* Specifications: *)
Lemma cfRepr_map u n (rG : mx_representation algCF G n) :
cfRepr (map_repr u rG) = cfAut u (cfRepr rG).
Lemma cfConjC_char chi : (chi^*%CF \is a character) = (chi \is a character).
Lemma lin_char_prod I r (P : pred I) (x : I -> gT) :
(forall i, P i -> x i \in G) ->
xi (\prod_(i <- r | P i) x i)%g = \prod_(i <- r | P i) xi (x i).