## lustrec / optim / oversampling / out / typed / g_step_assert_4_Coq.v @ 6a93d814

History | View | Annotate | Download (2.95 KB)

1 |
(* ---------------------------------------------------------- *) |
---|---|

2 |
(* --- Assertion (file oversampling0_4.c, line 355) --- *) |

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_g_mem_pack. |

19 |
Require Import Memory. |

20 |
Require Import Cint. |

21 |
Require Import Compound. |

22 |
Require Import Axiomatic. |

23 |
Require Import Globals. |

24 | |

25 |
Goal |

26 |
let a := (shift_sint32 ((global (L_last_y_459)%Z)) 0%Z) in |

27 |
forall (i_1 i : Z), |

28 |
forall (t : array Z), |

29 |
forall (t_7 t_6 t_5 t_4 t_3 t_2 t_1 : farray addr Z), |

30 |
forall (t_8 : farray addr addr), |

31 |
forall (a_2 a_1 : addr), |

32 |
forall (g_1 g : S_g_mem_pack), |

33 |
let a_3 := t_8.[ (shiftfield_F_g_mem_ni_1 a_2) ] in |

34 |
let a_4 := t_8.[ (shiftfield_F_g_mem_ni_0 a_2) ] in |

35 |
let a_5 := t_8.[ (shiftfield_F_f_mem_ni_2 a_4) ] in |

36 |
let x := (t_6.[ a ])%Z in |

37 |
let a_6 := (shiftfield_F__arrow_reg__first |

38 |
((shiftfield_F__arrow_mem__reg a_3))) in |

39 |
let x_1 := (t_7.[ a_6 ])%Z in |

40 |
((IsS_g_mem_pack g)) -> |

41 |
((IsS_g_mem_pack g_1)) -> |

42 |
((framed t_8)) -> |

43 |
((linked t)) -> |

44 |
((is_uint32 i%Z)) -> |

45 |
(a_1 <> a_3) -> |

46 |
((valid_rw t a_1 1%Z)) -> |

47 |
((P_valid_g t t_8 a_2)) -> |

48 |
((((region ((base a_1))%Z)) <= 0)%Z) -> |

49 |
((((region ((base a_2))%Z)) <= 0)%Z) -> |

50 |
((separated a_2 3%Z a_1 1%Z)) -> |

51 |
((P_g_pack1 t_8 t_6 g a_2)) -> |

52 |
((P_g_pack3 t_8 t_7 g_1 a_2)) -> |

53 |
(a_1 <> a_5) -> |

54 |
(a_3 <> a_5) -> |

55 |
((separated a_1 1%Z a_4 2%Z)) -> |

56 |
((separated a_2 3%Z a_4 2%Z)) -> |

57 |
((separated a_2 3%Z a_3 1%Z)) -> |

58 |
((separated a_4 2%Z a_3 1%Z)) -> |

59 |
((is_sint32 x)) -> |

60 |
((is_uint32 x_1)) -> |

61 |
((separated a_2 3%Z a_5 1%Z)) -> |

62 |
((separated a_4 2%Z a_5 1%Z)) -> |

63 |
(itep ((0 = x_1)%Z) (t_1 = t_7) (t_1 = (t_7.[ a_6 <- (0)%Z ]))) -> |

64 |
(itep ((0 = i)%Z) (t_4 = t_6) |

65 |
((t_4 = t_5) /\ (t_6 = (t_5.[ a <- (i_1)%Z ])))) -> |

66 |
(itep ((0 = x_1)%Z) |

67 |
((t_1 = t_2) /\ |

68 |
(t_4 = |

69 |
(t_2.[ a <- (t_2.[ (shiftfield_F_g_reg___g_2 |

70 |
((shiftfield_F_g_mem__reg a_2))) ])%Z ]))) |

71 |
((t_1 = t_3) /\ (t_4 = (t_3.[ a <- (0)%Z ])))) -> |

72 |
(forall (g_2 : S_g_mem_pack), ((IsS_g_mem_pack g_2)) -> |

73 |
(forall (g_3 : S_g_mem_pack), (P_g_pack0) -> ((IsS_g_mem_pack g_3)) -> |

74 |
((P_g_pack3 t_8 t_7 g_2 a_2)) -> (P_trans_gA))) -> |

75 |
(forall (g_2 : S_g_mem_pack), ((IsS_g_mem_pack g_2)) -> |

76 |
(forall (g_3 : S_g_mem_pack), ((IsS_g_mem_pack g_3)) -> |

77 |
((P_g_pack1 t_8 t_4 g_3 a_2)) -> ((P_g_pack3 t_8 t_7 g_2 a_2)) -> |

78 |
((P_trans_gC g_2 g_3 (t_4.[ a ])%Z)))) -> |

79 |
(forall (g_2 : S_g_mem_pack), ((IsS_g_mem_pack g_2)) -> |

80 |
(forall (g_3 : S_g_mem_pack), ((IsS_g_mem_pack g_3)) -> |

81 |
((P_g_pack1 t_8 t_1 g_3 a_2)) -> ((P_g_pack3 t_8 t_7 g_2 a_2)) -> |

82 |
((P_trans_gB g_2 g_3 x_1)))) -> |

83 |
((P_trans_gD i%Z i_1%Z g_1 g x)). |

84 | |

85 |
Proof. |

86 |
auto with zarith. |

87 |
Qed. |

88 |