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 contiki_list.Compound.Compound.
Require Import contiki_list.S1_list.S1_list.
Require Import contiki_list.Axiomatic.Axiomatic.
Require Import contiki_list.A_Index_of_item.A_Index_of_item.
Require Import contiki_list.Axiomatic1.Axiomatic1.
Open Scope Z_scope.
Theorem goal28 (t_3 : addr -> addr) (a : addr) (a_1 : addr) (i_1 : Z) (i : Z) (t_2 : addr -> addr) (t : Z -> Z) (t_1 : addr -> R) : let a_2 : addr := t_3 a in let a_3 : addr := shift a_1 i_1 in let x : Z := i - 1%Z in let a_4 : addr -> addr := havoc t_2 t_3 a_3 x in let a_5 : addr := a_4 a in let a_6 : addr := shift a_1 0%Z in let x_1 : Z := i + i_1 in let x_2 : Z := l_index_of t_3 a_2 a_1 i_1 x_1 in let a_7 : addr := t_3 a_3 in ¬ a_2 = Mk_addr 0%Z 0%Z -> a_5 = a_2 -> 0%Z < i -> 0%Z ≤ i -> 0%Z ≤ i_1 -> region (base a) ≤ 0%Z -> region (base a_1) ≤ 0%Z -> region (base a_2) ≤ 0%Z -> i ≤ 2147483645%Z -> framed t_3 -> linked t -> is_sint32 i -> is_sint32 i_1 -> valid_rd t a 1%Z -> valid_rw t a 1%Z -> valid_rw t a_6 2147483646%Z -> ¬ invalid t a_3 x -> separated a 1%Z a_6 2147483646%Z -> separated a_2 4%Z a_6 2147483646%Z -> p_linked_n t t_3 a_2 a_1 i_1 i (Mk_addr 0%Z 0%Z) -> is_sint32 x_2 -> p_linked_n t t_3 a_7 a_1 i_1 0%Z a_2 -> separated a_5 4%Z a_6 2147483646%Z -> p_array_swipe_left a_4 t_3 a_1 i_1 (i + i_1 - 1%Z) -> p_linked_n t a_4 a_7 a_1 i_1 0%Z a_2 -> p_linked_n t a_4 (a_4 (shift a_2 0%Z)) a_1 i_1 x (Mk_addr 0%Z 0%Z) -> p_unchanged t a_4 t_1 t t_3 t_1 a_1 i_1 i_1 -> (∀(i_2 : Z), i_1 ≤ i_2 -> i_2 < x_1 -> separated a 1%Z (t_3 (shift a_1 i_2)) 4%Z) -> (∀(i_2 : Z), i_1 ≤ i_2 -> i_2 < x_1 -> separated (t_3 (shift a_1 i_2)) 4%Z a_6 2147483646%Z) -> (∀(i_2 : Z), i_1 ≤ i_2 -> 2%Z + i_2 ≤ x_1 -> ¬ a_4 (shift a_1 i_2) = a_2) -> (∀(i_2 : Z), let a_8 : addr := t_3 (shift a_1 i_2) in ¬ a_8 = a_2 -> i_1 ≤ i_2 -> i_2 < x_1 -> separated a_2 4%Z a_8 4%Z) -> (∀(i_3 : Z) (i_2 : Z), ¬ i_3 = i_2 -> i_1 ≤ i_2 -> i_1 ≤ i_3 -> i_2 < x_1 -> i_3 < x_1 -> ¬ t_3 (shift a_1 i_3) = t_3 (shift a_1 i_2)) -> (∀(i_2 : Z), i_1 ≤ i_2 -> 2%Z + i_2 ≤ x_1 -> separated a 1%Z (a_4 (shift a_1 i_2)) 4%Z) -> (∀(i_2 : Z), i_1 ≤ i_2 -> 2%Z + i_2 ≤ x_1 -> separated a_2 4%Z (a_4 (shift a_1 i_2)) 4%Z) -> (∀(i_2 : Z), i_1 ≤ i_2 -> 2%Z + i_2 ≤ x_1 -> separated (a_4 (shift a_1 i_2)) 4%Z a_6 2147483646%Z) -> (∀(i_3 : Z) (i_2 : Z), ¬ i_3 = i_2 -> i_1 ≤ i_2 -> i_1 ≤ i_3 -> i_2 < x_1 -> i_3 < x_1 -> separated (t_3 (shift a_1 i_3)) 4%Z (t_3 (shift a_1 i_2)) 4%Z) -> (∀(i_3 : Z) (i_2 : Z), ¬ i_3 = i_2 -> i_1 ≤ i_2 -> i_1 ≤ i_3 -> 2%Z + i_2 ≤ x_1 -> 2%Z + i_3 ≤ x_1 -> ¬ a_4 (shift a_1 i_3) = a_4 (shift a_1 i_2)) -> (∀(i_3 : Z) (i_2 : Z), ¬ i_3 = i_2 -> i_1 ≤ i_2 -> i_1 ≤ i_3 -> 2%Z + i_2 ≤ x_1 -> 2%Z + i_3 ≤ x_1 -> separated (a_4 (shift a_1 i_3)) 4%Z (a_4 (shift a_1 i_2)) 4%Z) -> included a_3 x a 1%Z ∨ included a_3 x (shift a_1 x_2) (i + i_1 - x_2) ∨ included a_3 x (shift (t_3 (shift a_1 (x_2 - 1%Z))) 0%Z) 1%Z.
Admitted.
