Definition HTrue_inv1 l i ys xs : Prop :=
      Zlength l = 16 /\ exists ints, l=map Vint ints /\
               forall j, 0<=j<16 -> exists xj,
                Znth j xs = Vint xj
                /\ (j<i -> exists yj, Znth j ys = Vint yj /\
                                      Znth j l = Vint (Int.add yj xj))
                /\ (i<=j ->  Znth j l = Vint xj).Definition htrue_loop1_statement:=
Sfor (Sset _i (Econst_int (Int.repr 0) tint))
     (Ebinop Olt (Etempvar _i tint) (Econst_int (Int.repr 16) tint) tint)
     (Ssequence
        (Sset _t'17
           (Ederef
              (Ebinop Oadd (Evar _x (tarray tuint 16)) (Etempvar _i tint)
                 (tptr tuint)) tuint))
        (Ssequence
           (Sset _t'18
              (Ederef
                 (Ebinop Oadd (Evar _y (tarray tuint 16)) (Etempvar _i tint)
                    (tptr tuint)) tuint))
           (Sassign
              (Ederef
                 (Ebinop Oadd (Evar _x (tarray tuint 16)) (Etempvar _i tint)
                    (tptr tuint)) tuint)
              (Ebinop Oadd (Etempvar _t'17 tuint) (Etempvar _t'18 tuint)
                 tuint))))
     (Sset _i
        (Ebinop Oadd (Etempvar _i tint) (Econst_int (Int.repr 1) tint) tint)).(*June 4th, 2017 (loptop): 1.4s*)

(* Fragment:
       FOR(i,4) {
        x[5*i] -= ld32(c+4*i);
        x[6+i] -= ld32(in+4*i);
       }*)
Definition HTrue_loop2_statement :=
Sfor (Sset _i (Econst_int (Int.repr 0) tint))
     (Ebinop Olt (Etempvar _i tint) (Econst_int (Int.repr 4) tint) tint)
     (Ssequence
        (Ssequence
           (Scall (Some _t'9)
              (Evar _ld32
                 (Tfunction (Tcons (tptr tuchar) Tnil) tuint cc_default))
              [Ebinop Oadd (Etempvar _c (tptr tuchar))
                 (Ebinop Omul (Econst_int (Int.repr 4) tint)
                    (Etempvar _i tint) tint) (tptr tuchar)])
           (Ssequence
              (Sset _t'16
                 (Ederef
                    (Ebinop Oadd (Evar _x (tarray tuint 16))
                       (Ebinop Omul (Econst_int (Int.repr 5) tint)
                          (Etempvar _i tint) tint) (tptr tuint)) tuint))
              (Sassign
                 (Ederef
                    (Ebinop Oadd (Evar _x (tarray tuint 16))
                       (Ebinop Omul (Econst_int (Int.repr 5) tint)
                          (Etempvar _i tint) tint) (tptr tuint)) tuint)
                 (Ebinop Osub (Etempvar _t'16 tuint) (Etempvar _t'9 tuint)
                    tuint))))
        (Ssequence
           (Scall (Some _t'10)
              (Evar _ld32
                 (Tfunction (Tcons (tptr tuchar) Tnil) tuint cc_default))
              [Ebinop Oadd (Etempvar _in (tptr tuchar))
                 (Ebinop Omul (Econst_int (Int.repr 4) tint)
                    (Etempvar _i tint) tint) (tptr tuchar)])
           (Ssequence
              (Sset _t'15
                 (Ederef
                    (Ebinop Oadd (Evar _x (tarray tuint 16))
                       (Ebinop Oadd (Econst_int (Int.repr 6) tint)
                          (Etempvar _i tint) tint) (tptr tuint)) tuint))
              (Sassign
                 (Ederef
                    (Ebinop Oadd (Evar _x (tarray tuint 16))
                       (Ebinop Oadd (Econst_int (Int.repr 6) tint)
                          (Etempvar _i tint) tint) (tptr tuint)) tuint)
                 (Ebinop Osub (Etempvar _t'15 tuint) (Etempvar _t'10 tuint)
                    tuint)))))
     (Sset _i
        (Ebinop Oadd (Etempvar _i tint) (Econst_int (Int.repr 1) tint) tint)).Fixpoint hPosLoop2 (n:nat) (sumlist: list int) (C Nonce: SixteenByte): list int :=
       match n with
         O => sumlist
       | S m => let j:= Z.of_nat m in
                let s := hPosLoop2 m sumlist C Nonce in
                let five := Int.sub (Znth (5*j) sumlist) (littleendian (Select16Q C j)) in
                let six := Int.sub (Znth (6+j) sumlist) (littleendian (Select16Q Nonce j)) in
                upd_Znth (6+j) (upd_Znth (5*j) s five) six
       end.(*June 4th, 2017 (laptop: Finished transaction in 4.418 secs (3.784u,0.004s) (successful)*)

Definition UpdateOut (l: list val) (i:Z) (xi:int) :=
         (sublist 0 i l) ++ QuadByte2ValList (littleendian_invert xi) ++ sublist (i+4) (Zlength l) l.

Lemma UpdateOut_Zlength l i xi: 0<=i -> i + 4 <= Zlength l -> Zlength (UpdateOut l i xi) = Zlength l.