Section AutChar.
Variables (gT : finGroupType) (G : {group gT}).
Implicit Type u : {rmorphism algC -> algC}.
Implicit Type chi : 'CF(G).

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).