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

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(* ---------------------------------------------------------- *) |
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(* --- Instance of 'Pre-condition (file oversampling0_4.c, line 149) in 'f_step'' in 'g_step' at call 'f_step' (file oversampling0_4.c, line 357) |

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--- *) |

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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 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_g_mem_pack. |

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Goal |

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

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forall (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_2 a_1 : addr), |

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

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

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

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

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let a_6 := (shiftfield_F__arrow_reg__first |

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((shiftfield_F__arrow_mem__reg a_3))) in |

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

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((framed t_8)) -> |

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((linked t)) -> |

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((is_uint32 i%Z)) -> |

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(a_1 <> a_3) -> |

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

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((P_valid_g t t_8 a_2)) -> |

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

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

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

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(a_1 <> a_5) -> |

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(a_3 <> a_5) -> |

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

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

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

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

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((is_sint32 x)) -> |

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((is_uint32 x_1)) -> |

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

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

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

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

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((t_4 = t_5) /\ (t_6 = (t_5.[ a <- (i_1)%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 <- (t_2.[ (shiftfield_F_g_reg___g_2 |

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

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

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(forall (g : S_g_mem_pack), ((IsS_g_mem_pack g)) -> |

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(forall (g_1 : S_g_mem_pack), (P_g_pack0) -> ((IsS_g_mem_pack g_1)) -> |

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((P_g_pack3 t_8 t_7 g a_2)) -> (P_trans_gA))) -> |

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(forall (g : S_g_mem_pack), ((IsS_g_mem_pack g)) -> |

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(forall (g_1 : S_g_mem_pack), ((IsS_g_mem_pack g_1)) -> |

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((P_g_pack1 t_8 t_4 g_1 a_2)) -> ((P_g_pack3 t_8 t_7 g a_2)) -> |

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((P_trans_gC g g_1 (t_4.[ a ])%Z)))) -> |

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(forall (g : S_g_mem_pack), ((IsS_g_mem_pack g)) -> |

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(forall (g_1 : S_g_mem_pack), ((IsS_g_mem_pack g_1)) -> |

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((P_g_pack1 t_8 t_1 g_1 a_2)) -> ((P_g_pack3 t_8 t_7 g a_2)) -> |

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((P_trans_gB g g_1 x_1)))) -> |

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(forall (g : S_g_mem_pack), ((IsS_g_mem_pack g)) -> |

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(forall (g_1 : S_g_mem_pack), ((IsS_g_mem_pack g_1)) -> |

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((P_g_pack1 t_8 t_6 g_1 a_2)) -> ((P_g_pack3 t_8 t_7 g a_2)) -> |

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((P_trans_gD i%Z i_1%Z g g_1 x)))) -> |

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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_4)). |

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Proof. |

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auto with zarith. |

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Qed. |

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