|
1
|
(* ---------------------------------------------------------- *)
|
|
2
|
(* --- Assertion (file oversampling0_4.c, line 175) --- *)
|
|
3
|
(* ---------------------------------------------------------- *)
|
|
4
|
Require Import ZArith.
|
|
5
|
Require Import Reals.
|
|
6
|
Require Import BuiltIn.
|
|
7
|
Require Import bool.Bool.
|
|
8
|
Require Import int.Int.
|
|
9
|
Require Import int.Abs.
|
|
10
|
Require Import int.ComputerDivision.
|
|
11
|
Require Import real.Real.
|
|
12
|
Require Import real.RealInfix.
|
|
13
|
Require Import real.FromInt.
|
|
14
|
Require Import map.Map.
|
|
15
|
Require Import Qedlib.
|
|
16
|
Require Import Qed.
|
|
17
|
|
|
18
|
Require Import S_f_mem_pack.
|
|
19
|
Require Import Memory.
|
|
20
|
Require Import Cint.
|
|
21
|
Require Import Compound.
|
|
22
|
Require Import Axiomatic.
|
|
23
|
|
|
24
|
Goal
|
|
25
|
forall (i_1 i : Z),
|
|
26
|
forall (t : array Z),
|
|
27
|
forall (t_2 t_1 : farray addr Z),
|
|
28
|
forall (t_3 : farray addr addr),
|
|
29
|
forall (a_2 a_1 a : addr),
|
|
30
|
forall (f_1 f : S_f_mem_pack),
|
|
31
|
let a_3 := t_3.[ (shiftfield_F_f_mem_ni_2 a_2) ] in
|
|
32
|
let x := (1%Z + i_1%Z)%Z in
|
|
33
|
let m := t_2.[ a_1 <- x ] in
|
|
34
|
let a_4 := (shiftfield_F__arrow_reg__first
|
|
35
|
((shiftfield_F__arrow_mem__reg a_3))) in
|
|
36
|
let x_1 := (m.[ a_4 ])%Z in
|
|
37
|
let x_2 := (1%Z + i%Z)%Z in
|
|
38
|
let m_1 := t_1.[ a <- x_2 ] in
|
|
39
|
let a_5 := (shiftfield_F_f_reg___f_2 ((shiftfield_F_f_mem__reg a_2))) in
|
|
40
|
let m_2 := m_1.[ a_5 <- x_2 ] in
|
|
41
|
let x_3 := (t_1.[ a_1 ])%Z in
|
|
42
|
(a <> a_1) ->
|
|
43
|
((IsS_f_mem_pack f)) ->
|
|
44
|
((IsS_f_mem_pack f_1)) ->
|
|
45
|
((framed t_3)) ->
|
|
46
|
((linked t)) ->
|
|
47
|
((is_sint32 i%Z)) ->
|
|
48
|
((is_sint32 i_1%Z)) ->
|
|
49
|
(a <> a_3) ->
|
|
50
|
(a_1 <> a_3) ->
|
|
51
|
((valid_rw t a 1%Z)) ->
|
|
52
|
((valid_rw t a_1 1%Z)) ->
|
|
53
|
((P_valid_f t t_3 a_2)) ->
|
|
54
|
((((region ((base a))%Z)) <= 0)%Z) ->
|
|
55
|
((((region ((base a_1))%Z)) <= 0)%Z) ->
|
|
56
|
((((region ((base a_2))%Z)) <= 0)%Z) ->
|
|
57
|
((separated a_2 2%Z a 1%Z)) ->
|
|
58
|
((separated a_2 2%Z a_1 1%Z)) ->
|
|
59
|
((P_f_pack2 t_3 t_2 f_1 a_2)) ->
|
|
60
|
((separated a_2 2%Z a_3 1%Z)) ->
|
|
61
|
((is_uint32 x_1)) ->
|
|
62
|
((P_f_pack2 t_3 m_2 f a_2)) ->
|
|
63
|
(itep ((0 = x_1)%Z) (t_1 = m) (t_1 = (m.[ a_4 <- (0)%Z ]))) ->
|
|
64
|
(itep ((0 = x_1)%Z) ((i = (t_1.[ a_5 ]))%Z) ((0 = i)%Z)) ->
|
|
65
|
(forall (f_2 : S_f_mem_pack), ((IsS_f_mem_pack f_2)) ->
|
|
66
|
(forall (f_3 : S_f_mem_pack), (P_f_pack0) -> ((IsS_f_mem_pack f_3)) ->
|
|
67
|
((P_f_pack2 t_3 t_2 f_2 a_2)) -> (P_trans_fA))) ->
|
|
68
|
(forall (f_2 : S_f_mem_pack), ((IsS_f_mem_pack f_2)) ->
|
|
69
|
(forall (f_3 : S_f_mem_pack), (P_f_pack0) -> ((IsS_f_mem_pack f_3)) ->
|
|
70
|
((P_f_pack2 t_3 t_2 f_2 a_2)) -> ((P_trans_fB i_1%Z x)))) ->
|
|
71
|
(forall (f_2 : S_f_mem_pack), ((IsS_f_mem_pack f_2)) ->
|
|
72
|
(forall (f_3 : S_f_mem_pack), ((IsS_f_mem_pack f_3)) ->
|
|
73
|
((P_f_pack1 t_3 t_1 f_3 a_2)) -> ((P_f_pack2 t_3 t_2 f_2 a_2)) ->
|
|
74
|
((P_trans_fD i_1%Z f_2 f_3 x_3 i%Z)))) ->
|
|
75
|
(forall (f_2 : S_f_mem_pack), ((IsS_f_mem_pack f_2)) ->
|
|
76
|
(forall (f_3 : S_f_mem_pack), ((IsS_f_mem_pack f_3)) ->
|
|
77
|
((P_f_pack2 t_3 t_2 f_2 a_2)) -> ((P_f_pack1 t_3 m_1 f_3 a_2)) ->
|
|
78
|
((P_trans_fE i_1%Z f_2 f_3 (m_1.[ a_1 ])%Z x_2)))) ->
|
|
79
|
(forall (f_2 : S_f_mem_pack), ((IsS_f_mem_pack f_2)) ->
|
|
80
|
(forall (f_3 : S_f_mem_pack), ((IsS_f_mem_pack f_3)) ->
|
|
81
|
((P_f_pack1 t_3 t_1 f_3 a_2)) -> ((P_f_pack2 t_3 t_2 f_2 a_2)) ->
|
|
82
|
((P_trans_fC i_1%Z f_2 f_3 x_3 x_1)))) ->
|
|
83
|
((P_trans_fF i_1%Z f_1 f (m_2.[ a_1 ])%Z (m_2.[ a ])%Z)).
|
|
84
|
|