intro.
unfold X1 at 1 in |- *.
elim (EXPH4 (seq (Sn_d d e0) (seq (Sn e1) (S i))) (K i) (L i) (R i) H).
elim LmerSnd.
elim LmerK.
elim LmerL.
pattern (R i) at 2 3 5 8 in |- *.
elim ProcR.
elim LmerRn.
elim CommLRn.
elim CommKL.
elim CommKRn.
elim ProcSn_d.
elim A5.
elim Comms2K.
elim Comms2Rn.
elim Comms2L.
repeat elim A6.
repeat elim A6'.
elim SC7.
apply refl_equal.
Qed.

Theorem Lem4 :
forall d : D,
alt
(seq (ia one int i)
(enc H
(mer (seq (ia Frame s3 (Tuple e0 d)) (K i))
(mer (seq (Tn_d d e0) (seq (Sn e1) (S i))) (mer (L i) (R i))))))
(seq (ia one int i)
(enc H
(mer (seq (ia Frame s3 lce) (K i))
(mer (seq (Tn_d d e0) (seq (Sn e1) (S i))) (mer (L i) (R i)))))) =
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)))).