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lustrec / optim / oversampling / out / typed / g_step_assert_5_Coq.v @ 6a93d814

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(* ---------------------------------------------------------- *)
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(* --- Assertion (file oversampling0_4.c, line 358)       --- *)
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(* ---------------------------------------------------------- *)
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Require Import ZArith.
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Require Import Reals.
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Require Import BuiltIn.
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Require Import bool.Bool.
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Require Import int.Int.
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Require Import int.Abs.
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Require Import int.ComputerDivision.
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Require Import real.Real.
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Require Import real.RealInfix.
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Require Import real.FromInt.
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Require Import map.Map.
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Require Import Qedlib.
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Require Import Qed.
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Require Import S_g_mem_pack.
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Require Import Memory.
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Require Import Cint.
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Require Import Compound.
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Require Import Axiomatic.
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Require Import Globals.
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Require Import S_f_mem_pack.
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Goal
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  let a := (shift_sint32 ((global (L_cpt_458)%Z)) 0%Z) in
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  let a_1 := (shift_sint32 ((global (L_last_y_459)%Z)) 0%Z) in
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  forall (i_5 i_4 i_3 i_2 i_1 i : Z),
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  forall (t : array Z),
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  forall (t_7 t_6 t_5 t_4 t_3 t_2 t_1 : farray addr Z),
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  forall (t_8 : farray addr addr),
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  forall (a_3 a_2 : addr),
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  forall (g_1 g : S_g_mem_pack),
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  let a_4 := t_8.[ (shiftfield_F_g_mem_ni_1 a_3) ] in
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  let a_5 := t_8.[ (shiftfield_F_g_mem_ni_0 a_3) ] in
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  let a_6 := t_8.[ (shiftfield_F_f_mem_ni_2 a_5) ] in
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  let x := (t_6.[ a_1 ])%Z in
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  let a_7 := (shiftfield_F__arrow_reg__first
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               ((shiftfield_F__arrow_mem__reg a_4))) in
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  let x_1 := (t_7.[ a_7 ])%Z in
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  let m := (((t_6.[ a <- (i)%Z ]).[ a_1 <- (i_1)%Z ]).[ (shiftfield_F_f_reg___f_2
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                                                          ((shiftfield_F_f_mem__reg
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                                                             a_5))) <- 
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            (i_3)%Z ]).[ (shiftfield_F__arrow_reg__first
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                           ((shiftfield_F__arrow_mem__reg a_6))) <- (i_4)%Z ] in
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  let x_2 := (m.[ a_1 ])%Z in
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  ((IsS_g_mem_pack g)) ->
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  ((IsS_g_mem_pack g_1)) ->
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  ((framed t_8)) ->
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  ((linked t)) ->
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  ((is_uint32 i_2%Z)) ->
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  (a_2 <> a_4) ->
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  ((valid_rw t a_2 1%Z)) ->
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  ((P_valid_g t t_8 a_3)) ->
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  ((((region ((base a_2))%Z)) <= 0)%Z) ->
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  ((((region ((base a_3))%Z)) <= 0)%Z) ->
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  ((separated a_3 3%Z a_2 1%Z)) ->
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  ((P_g_pack3 t_8 t_7 g_1 a_3)) ->
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  (a_2 <> a_6) ->
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  (a_4 <> a_6) ->
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  (a <> a_6) ->
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  (a_1 <> a_6) ->
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  ((P_valid_f ((t.[ (L_cpt_458)%Z <- (1)%Z ]).[ (L_last_y_459)%Z <- (1)%Z ])
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     t_8 a_5)) ->
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  ((separated a_2 1%Z a_5 2%Z)) ->
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  ((separated a_3 3%Z a_5 2%Z)) ->
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  ((separated a_3 3%Z a_4 1%Z)) ->
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  ((separated a_5 2%Z a_4 1%Z)) ->
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  ((is_sint32 x)) ->
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  ((separated a_5 2%Z a 1%Z)) ->
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  ((separated a_5 2%Z a_1 1%Z)) ->
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  ((is_uint32 x_1)) ->
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  ((separated a_3 3%Z a_6 1%Z)) ->
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  ((separated a_5 2%Z a_6 1%Z)) ->
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  (itep ((0 = x_1)%Z) (t_1 = t_7) (t_1 = (t_7.[ a_7 <- (0)%Z ]))) ->
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  (itep ((0 = i_2)%Z) (t_4 = t_6)
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   ((t_4 = t_5) /\ (t_6 = (t_5.[ a_1 <- (i_5)%Z ])))) ->
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  (itep ((0 = x_1)%Z)
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   ((t_1 = t_2) /\
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    (t_4 =
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     (t_2.[ a_1 <- (t_2.[ (shiftfield_F_g_reg___g_2
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                            ((shiftfield_F_g_mem__reg a_3))) ])%Z ])))
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   ((t_1 = t_3) /\ (t_4 = (t_3.[ a_1 <- (0)%Z ])))) ->
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  ((P_g_pack2 t_8 m g a_3)) ->
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  (forall (g_2 : S_g_mem_pack), ((IsS_g_mem_pack g_2)) ->
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   (forall (g_3 : S_g_mem_pack), (P_g_pack0) -> ((IsS_g_mem_pack g_3)) ->
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    ((P_g_pack3 t_8 t_7 g_2 a_3)) -> (P_trans_gA))) ->
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  (forall (g_2 : S_g_mem_pack), ((IsS_g_mem_pack g_2)) ->
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   (forall (g_3 : S_g_mem_pack), ((IsS_g_mem_pack g_3)) ->
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    ((P_g_pack1 t_8 t_4 g_3 a_3)) -> ((P_g_pack3 t_8 t_7 g_2 a_3)) ->
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    ((P_trans_gC g_2 g_3 (t_4.[ a_1 ])%Z)))) ->
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  (forall (g_2 : S_g_mem_pack), ((IsS_g_mem_pack g_2)) ->
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   (forall (g_3 : S_g_mem_pack), ((IsS_g_mem_pack g_3)) ->
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    ((P_g_pack1 t_8 t_1 g_3 a_3)) -> ((P_g_pack3 t_8 t_7 g_2 a_3)) ->
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    ((P_trans_gB g_2 g_3 x_1)))) ->
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  (forall (g_2 : S_g_mem_pack), ((IsS_g_mem_pack g_2)) ->
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   (forall (g_3 : S_g_mem_pack), ((IsS_g_mem_pack g_3)) ->
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    ((P_g_pack1 t_8 t_6 g_3 a_3)) -> ((P_g_pack3 t_8 t_7 g_2 a_3)) ->
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    ((P_trans_gD i_2%Z i_5%Z g_2 g_3 x)))) ->
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  (forall (f : S_f_mem_pack), ((IsS_f_mem_pack f)) ->
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   (forall (f_1 : S_f_mem_pack), ((IsS_f_mem_pack f_1)) ->
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    ((P_f_pack2 t_8 t_6 f a_5)) -> ((P_f_pack2 t_8 m f_1 a_5)) ->
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    ((P_trans_fF x f f_1 x_2 (m.[ a ])%Z)))) ->
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  ((P_trans_gE i_2%Z i_5%Z g_1 g x_2)).
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Proof.
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  auto with zarith.
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Qed.
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