From Stdlib Require Import Strings.String.
From Stdlib Require Import String Ascii.
From Stdlib Require Arith.
From stdpp Require Import base.
From stdpp Require Import fin_maps.
From stdpp Require Import gmap.
From stdpp Require Import base gmultiset.
From Stdlib Require Classical.
From Stdlib Require Import ZArith.
From stdpp.bitvector Require Import definitions tactics.
From Stdlib Require Import Sorting.Sorted.
From Stdlib Require Import Reals.Rbasic_fun.
From Stdlib Require Import Reals.Abstract.ConstructiveAbs.
From Stdlib Require Import Reals.Rdefinitions.
From stdpp Require Import list_relations.
From stdpp Require Import list_numbers.
From stdpp Require Import functions.
From Stdlib Require Import ClassicalEpsilon.
From stdpp Require Import base decidable.
From Stdlib Require Import ZArith.Zeuclid.
From Stdlib Require Import ZArith.Znumtheory.
From stdpp Require Import propset.
From Stdlib Require Import Reals.
Require Import Why3.Base.
Require Import Why3.Qed.Qed.
Require Import Why3.Memory.Memory.
Require Import Why3.Cint.Cint.
Require Import x509_parser.Compound.Compound.
Require Import Why3.Cbits.Cbits.
Open Scope Z_scope.
Lemma goal0 (a_2 : addr) (a : addr) (a_1 : addr) (i_3 : Z) (t_3 : addr -> Z) (t_4 : addr -> Z) (i_4 : Z) (i_2 : Z) (t : Z -> Z) (i : Z) (i_1 : Z) (t_1 : addr -> Z) (t_2 : addr -> Z) : let x : Z := base a_2 in let x_1 : Z := base a in let a_3 : addr := shift a_1 0%Z in let a_4 : addr := shift a_1 1%Z in let a_5 : addr := shift a_2 (1%Z + i_3) in let x_2 : Z := t_3 a_1 in let x_3 : Z := t_4 a_5 in let x_4 : Z := i_3 + i_4 in ¬ i_2 = 0%Z -> ¬ Mk_addr 0%Z 0%Z = a_2 -> ¬ x = x_1 -> 0%Z ≤ i_2 -> region x_1 ≤ 0%Z -> region x ≤ 0%Z -> linked t -> is_uint16 i_2 -> is_uint16 i_3 -> is_uint16 i_4 -> is_sint32 i -> is_sint32 i_1 -> valid_rw t a 1%Z -> is_uint8 (t_1 a_3) -> is_uint8 (t_2 a_4) -> is_uint8 (t_3 a_3) -> is_uint8 (t_4 a_4) -> (if decide (i_1 = 0%Z) then shift a_2 i_3 = a_1 ∧ (if decide (i_4 = 0%Z) then i = - 845%Z else if decide (2%Z ≤ i_4) then valid_rd t a_1 1%Z ∧ (if decide (t_1 a_1 = 0%Z) then t_2 = t_1 ∧ valid_rd t a_5 1%Z ∧ (if decide (bit_test (t_2 a_5) 7%Z) then t_3 = t_2 ∧ (if decide (x_2 = 255%Z) then t_4 = t_3 ∧ (if decide (bit_test x_3 7%Z) then i = - 866%Z else i = 0%Z ∧ - 2147483648%Z ≤ x_4 ∧ x_4 ≤ 2147483647%Z) else i = 0%Z ∧ - 2147483648%Z ≤ x_4 ∧ x_4 ≤ 2147483647%Z) else i = - 860%Z) else t_3 = t_1 ∧ (if decide (x_2 = 255%Z) then t_4 = t_3 ∧ valid_rd t a_5 1%Z ∧ (if decide (bit_test x_3 7%Z) then i = - 866%Z else i = 0%Z ∧ - 2147483648%Z ≤ x_4 ∧ x_4 ≤ 2147483647%Z) else i = 0%Z ∧ - 2147483648%Z ≤ x_4 ∧ x_4 ≤ 2147483647%Z)) else i = 0%Z ∧ - 2147483648%Z ≤ x_4 ∧ x_4 ≤ 2147483647%Z) else i_1 = i) -> (i_1 = 0%Z -> i_4 ≤ i_2) -> (i_1 = 0%Z -> x_4 ≤ i_2) -> (i_1 = 0%Z -> i_3 ≤ i_2 ∧ 2%Z ≤ i_3) -> (0%Z < i_2 -> valid_rd t (shift a_2 0%Z) i_2) -> i_1 = 0%Z ∨ i_1 < 0%Z -> i = 0%Z ∨ i < 0%Z.
Admitted.
