Fact Zchar_key : pred_key Zchar.Canonical Zchar_keyed := KeyedPred Zchar_key.Fact Zchar_zmod : zmod_closed Zchar.Canonical Zchar_opprPred := OpprPred Zchar_zmod.Canonical Zchar_addrPred := AddrPred Zchar_zmod.Canonical Zchar_zmodPred := ZmodPred Zchar_zmod.Notation "''Z[' S , A ]" := (Zchar S A)
  (at level 8, format "''Z[' S ,  A ]") : group_scope.Canonical vchar_mulrPred := MulrPred vchar_mulr_closed.Canonical vchar_smulrPred := SmulrPred vchar_mulr_closed.Canonical vchar_semiringPred := SemiringPred vchar_mulr_closed.Canonical vchar_subringPred := SubringPred vchar_mulr_closed.

Lemma map_orthonormal : orthonormal (map nu S).