## lustrec / optim / oversampling / out / typed / g_step_assert_3_Coq.v @ 6a93d814

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1 | 6a93d814 | xthirioux | (* ---------------------------------------------------------- *) |
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2 | (* --- Assertion (file oversampling0_4.c, line 348) --- *) |
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3 | (* ---------------------------------------------------------- *) |
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4 | Require Import ZArith. |
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5 | Require Import Reals. |
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6 | Require Import BuiltIn. |
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7 | Require Import bool.Bool. |
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8 | Require Import int.Int. |
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9 | Require Import int.Abs. |
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10 | Require Import int.ComputerDivision. |
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11 | Require Import real.Real. |
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12 | Require Import real.RealInfix. |
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13 | Require Import real.FromInt. |
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14 | Require Import map.Map. |
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15 | Require Import Qedlib. |
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16 | Require Import Qed. |
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17 | |||

18 | Require Import S_g_mem_pack. |
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19 | Require Import Memory. |
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20 | Require Import Compound. |
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21 | Require Import Axiomatic. |
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22 | Require Import Cint. |
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23 | Require Import Globals. |
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24 | |||

25 | Goal |
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26 | let a := (shift_sint32 ((global (L_last_y_459)%Z)) 0%Z) in |
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27 | forall (t : array Z), |
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28 | forall (t_5 t_4 t_3 t_2 t_1 : farray addr Z), |
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29 | forall (t_6 : farray addr addr), |
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30 | forall (a_2 a_1 : addr), |
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31 | forall (g_1 g : S_g_mem_pack), |
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32 | let a_3 := t_6.[ (shiftfield_F_g_mem_ni_1 a_2) ] in |
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33 | let a_4 := t_6.[ (shiftfield_F_g_mem_ni_0 a_2) ] in |
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34 | let a_5 := t_6.[ (shiftfield_F_f_mem_ni_2 a_4) ] in |
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35 | let a_6 := (shiftfield_F__arrow_reg__first |
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36 | ((shiftfield_F__arrow_mem__reg a_3))) in |
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37 | let x := (t_5.[ a_6 ])%Z in |
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38 | ((IsS_g_mem_pack g)) -> |
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39 | ((IsS_g_mem_pack g_1)) -> |
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40 | ((framed t_6)) -> |
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41 | ((linked t)) -> |
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42 | (a_1 <> a_3) -> |
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43 | ((valid_rw t a_1 1%Z)) -> |
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44 | ((P_valid_g t t_6 a_2)) -> |
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45 | ((((region ((base a_1))%Z)) <= 0)%Z) -> |
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46 | ((((region ((base a_2))%Z)) <= 0)%Z) -> |
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47 | ((separated a_2 3%Z a_1 1%Z)) -> |
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48 | ((P_g_pack1 t_6 t_4 g a_2)) -> |
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49 | ((P_g_pack3 t_6 t_5 g_1 a_2)) -> |
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50 | (a_1 <> a_5) -> |
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51 | (a_3 <> a_5) -> |
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52 | ((separated a_1 1%Z a_4 2%Z)) -> |
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53 | ((separated a_2 3%Z a_4 2%Z)) -> |
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54 | ((separated a_2 3%Z a_3 1%Z)) -> |
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55 | ((separated a_4 2%Z a_3 1%Z)) -> |
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56 | ((is_uint32 x)) -> |
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57 | ((separated a_2 3%Z a_5 1%Z)) -> |
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58 | ((separated a_4 2%Z a_5 1%Z)) -> |
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59 | (itep ((0 = x)%Z) (t_1 = t_5) (t_1 = (t_5.[ a_6 <- (0)%Z ]))) -> |
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60 | (itep ((0 = x)%Z) |
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61 | ((t_1 = t_2) /\ |
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62 | (t_4 = |
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63 | (t_2.[ a <- (t_2.[ (shiftfield_F_g_reg___g_2 |
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64 | ((shiftfield_F_g_mem__reg a_2))) ])%Z ]))) |
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65 | ((t_1 = t_3) /\ (t_4 = (t_3.[ a <- (0)%Z ])))) -> |
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66 | (forall (g_2 : S_g_mem_pack), ((IsS_g_mem_pack g_2)) -> |
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67 | (forall (g_3 : S_g_mem_pack), (P_g_pack0) -> ((IsS_g_mem_pack g_3)) -> |
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68 | ((P_g_pack3 t_6 t_5 g_2 a_2)) -> (P_trans_gA))) -> |
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69 | (forall (g_2 : S_g_mem_pack), ((IsS_g_mem_pack g_2)) -> |
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70 | (forall (g_3 : S_g_mem_pack), ((IsS_g_mem_pack g_3)) -> |
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71 | ((P_g_pack1 t_6 t_1 g_3 a_2)) -> ((P_g_pack3 t_6 t_5 g_2 a_2)) -> |
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72 | ((P_trans_gB g_2 g_3 x)))) -> |
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73 | ((P_trans_gC g_1 g (t_4.[ a ])%Z)). |
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74 | |||

75 | Proof. |
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76 | auto with zarith. |
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77 | Qed. |