Section InverseTransport.

(* Lemma 26(1) in [1] *)
Lemma iipc2_St_soundness {xs tSs tPs t1 t2 t3 n1 n2 n3} :
iipc2 (Gamma0 ++ map Ut (map (fun x : nat => poly_var (x + zt)) xs) ++ map St tSs ++ map Pt tPs) (St (t1, t2, t3)) ->
Forall encodes_sum tSs -> encodes_nat t1 n1 -> encodes_nat t2 n2 -> encodes_nat t3 n3 -> n1 + n2 = n3.