Section Forward.
Variables (E: list deq).
Definition gf n := lambda enc n (var 0).
Definition enc_sol (sigma: nat -> nat) (x: fin) :=
match partition_F_G x with
| inl (exist _ x _) => gf (sigma x)
| inr (exist _ (x,y,z) _) => T (sigma y) (sigma x)
end.

Lemma H10_SU: H10 E -> SOU ag 2 (H10_to_SOU  E).