elim ProcS.
elim EXPH4.
elim LmerSn.
elim LmerK.
elim LmerL.
elim LmerRn.
elim CommLRn.
elim CommKL.
elim CommKRn.
elim CommSnK.
elim CommSnL.
elim CommSnRn.
repeat elim A6.
elim
(A6
(D +
(fun d : D =>
seq (ia D r1 d)
(enc H
(mer (seq (Sn_d d e1) (seq (Sn e0) (seq (Sn e1) (S i))))
(mer (K i) (mer (L i) (seq (Rn e0) (R i))))))))).
unfold Y1 in |- *.
pattern (S i) at 1 in |- *.
elim ProcS.
apply refl_equal.
Qed.

(* Specifications: *)
Theorem Lem3 :
forall d : D,
seq (ia Frame c2 (Tuple e0 d))
(enc H
(mer (seq (Tn_d d e0) (seq (Sn e1) (S i)))
(mer
(seq
(alt (seq (ia one int i) (ia Frame s3 (Tuple e0 d)))
(seq (ia one int i) (ia Frame s3 lce)))
(K i)) (mer (L i) (R i))))) = X1 d.