(* Note: other isometry lemmas, and the dot product lemmas for orthogonal     *)
(* and orthonormal sequences are in vcharacter, because we need the 'Z[S]     *)
(* notation for the isometry domains. Alternatively, this could be moved to   *)
(* cfun.                                                                      *)
Arguments orthoP {gT G phi psi}.
Arguments orthoPl {gT G phi S}.
Arguments orthoPr {gT G S psi}.
Arguments orthogonalP {gT G S R}.
Arguments pairwise_orthogonalP {gT G S}.
Arguments orthonormalP {gT G S}.
Section CfunOrder.
Variables (gT : finGroupType) (G : {group gT}) (phi : 'CF(G)).

(* Specifications: *)
Lemma dvdn_cforderP n :
reflect {in G, forall x, phi x ^+ n = 1} (#[phi]%CF %| n)%N.
Lemma dvdn_cforder n : (#[phi]%CF %| n) = (phi ^+ n == 1).
Lemma exp_cforder : phi ^+ #[phi]%CF = 1.
End MorphOrder.