Local Open Scope logic.
Definition i_8_16_inv F x z c b m nonce k zbytes gv: environ -> mpred :=
EX i:_,
(PROP  ()
LOCAL  (temp _u (Vint (fst (ZZ zbytes (Z.to_nat (i-8)))));
lvar _x (Tarray tuchar 64 noattr) x;
lvar _z (Tarray tuchar 16 noattr) z; temp _c c; temp _m m;
temp _b b; temp _n nonce; temp _k k; gvars gv)
SEP  (F; data_at Tsh (Tarray tuchar 16 noattr) (Bl2VL (snd (ZZ zbytes (Z.to_nat (i-8))))) z)).
Definition for_loop_statement:=
Sfor (Sset _i (Econst_int (Int.repr 8) tint))
(Ebinop Olt (Etempvar _i tuint) (Econst_int (Int.repr 16) tint) tint)
(Ssequence
(Ssequence
(Sset _t'5
(Ederef
(Ebinop Oadd (Evar _z (tarray tuchar 16))
(Etempvar _i tuint) (tptr tuchar)) tuchar))
(Sset _u
(Ebinop Oadd (Etempvar _u tuint)
(Ecast (Etempvar _t'5 tuchar) tuint) tuint)))
(Ssequence
(Sassign
(Ederef
(Ebinop Oadd (Evar _z (tarray tuchar 16))
(Etempvar _i tuint) (tptr tuchar)) tuchar)
(Etempvar _u tuint))
(Sset _u
(Ebinop Oshr (Etempvar _u tuint) (Econst_int (Int.repr 8) tint)
tuint))))
(Sset _i
(Ebinop Oadd (Etempvar _i tuint) (Econst_int (Int.repr 1) tint) tuint)).
Definition null_or_offset x q y :=
match x with
Vint i => i=Int.zero /\ y=nullval
| Vptr _ _ => y=offset_val q x
| _ => False
end.
Definition byte_at x i mbytes :=
match x with
Vint _ => Byte.zero
| _ => Znth i mbytes
end.

Lemma bxorlist_snoc x q y b l mbytes xbytes
(M:null_or_offset x q y )
(X: bxorlist (bytes_at x q (Zlength l) mbytes)
(sublist 0 (Zlength l) xbytes) = Some l):
0<= q -> Zlength l < Zlength xbytes ->  q+ Zlength l < Zlength mbytes ->
b = Byte.xor (byte_at x (Zlength l + q) mbytes)
(Znth (Zlength l) xbytes) ->
bxorlist (bytes_at x q (Zlength l  + 1) mbytes)
(sublist 0 (Zlength l  + 1) xbytes) = Some (l ++ [b]).