## lustrec / optim / oversampling / out / typed / g_step_assert_2_Coq.v @ 6a93d814

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1 | 6a93d814 | xthirioux | (* ---------------------------------------------------------- *) |
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2 | (* --- Assertion (file oversampling0_4.c, line 342) --- *) |
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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 | |||

24 | Goal |
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25 | forall (t : array Z), |
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26 | forall (t_2 t_1 : farray addr Z), |
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27 | forall (t_3 : farray addr addr), |
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28 | forall (a_1 a : addr), |
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29 | forall (g_1 g : S_g_mem_pack), |
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30 | let a_2 := t_3.[ (shiftfield_F_g_mem_ni_1 a_1) ] in |
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31 | let a_3 := t_3.[ (shiftfield_F_g_mem_ni_0 a_1) ] in |
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32 | let a_4 := t_3.[ (shiftfield_F_f_mem_ni_2 a_3) ] in |
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33 | let a_5 := (shiftfield_F__arrow_reg__first |
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34 | ((shiftfield_F__arrow_mem__reg a_2))) in |
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35 | let x := (t_2.[ a_5 ])%Z in |
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36 | ((IsS_g_mem_pack g)) -> |
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37 | ((IsS_g_mem_pack g_1)) -> |
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38 | ((framed t_3)) -> |
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39 | ((linked t)) -> |
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40 | (a <> a_2) -> |
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41 | ((valid_rw t a 1%Z)) -> |
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42 | ((P_valid_g t t_3 a_1)) -> |
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43 | ((((region ((base a))%Z)) <= 0)%Z) -> |
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44 | ((((region ((base a_1))%Z)) <= 0)%Z) -> |
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45 | ((separated a_1 3%Z a 1%Z)) -> |
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46 | ((P_g_pack1 t_3 t_1 g a_1)) -> |
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47 | ((P_g_pack3 t_3 t_2 g_1 a_1)) -> |
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48 | (a <> a_4) -> |
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49 | (a_2 <> a_4) -> |
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50 | ((separated a 1%Z a_3 2%Z)) -> |
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51 | ((separated a_1 3%Z a_3 2%Z)) -> |
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52 | ((separated a_1 3%Z a_2 1%Z)) -> |
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53 | ((separated a_3 2%Z a_2 1%Z)) -> |
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54 | ((is_uint32 x)) -> |
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55 | ((separated a_1 3%Z a_4 1%Z)) -> |
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56 | ((separated a_3 2%Z a_4 1%Z)) -> |
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57 | (itep ((0 = x)%Z) (t_1 = t_2) (t_1 = (t_2.[ a_5 <- (0)%Z ]))) -> |
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58 | (forall (g_2 : S_g_mem_pack), ((IsS_g_mem_pack g_2)) -> |
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59 | (forall (g_3 : S_g_mem_pack), (P_g_pack0) -> ((IsS_g_mem_pack g_3)) -> |
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60 | ((P_g_pack3 t_3 t_2 g_2 a_1)) -> (P_trans_gA))) -> |
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61 | ((P_trans_gB g_1 g x)). |
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62 | |||

63 | Proof. |
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64 | auto with zarith. |
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65 | Qed. |