End Isometries.
Section AutVchar.
Variables (u : {rmorphism algC -> algC}) (gT : finGroupType) (G : {group gT}).
Local Notation "alpha ^u" := (cfAut u alpha).
Implicit Type (S : seq 'CF(G)) (phi chi : 'CF(G)).

(* Specifications: *)
Lemma cfAut_zchar S A psi :
cfAut_closed u S -> psi \in 'Z[S, A] -> psi^u \in 'Z[S, A].
Lemma cfAut_vchar A psi : psi \in 'Z[irr G, A] -> psi^u \in 'Z[irr G, A].
Lemma conjC_vcharAut chi x : chi \in 'Z[irr G] -> (u (chi x))^* = u (chi x)^*.
Lemma cfdot_aut_vchar phi chi :
chi \in 'Z[irr G] -> '[phi^u , chi^u] = u '[phi, chi].
Lemma vchar_aut A chi : (chi^u \in 'Z[irr G, A]) = (chi \in 'Z[irr G, A]).
End AutVchar.