Section Backward.
Definition decode_subst (sigma: fin -> exp ag) (N: forall x, normal (sigma x)) (x: fin) :=
match dec_enc (N (F x)) with
| inl  (exist _ n _) => n
| inr _ => 0
end.
End Backward.

Lemma Goldfarb': H10 ⪯ SOU ag 2.