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 goal27 (t_3 : addr -> addr) (a_1 : addr) (a : addr) (i_1 : Z) (i_2 : Z) (i_3 : Z) (a_2 : addr) (t_2 : addr -> addr) (t : Z -> Z) (i : Z) (t_1 : addr -> R) : let a_3 : addr := t_3 a_1 in let a_4 : addr := shift a 0%Z in let a_5 : addr := t_3 a_4 in let x : Z := i_1 + i_2 in let x_2 : Z := i_3 - i_2 in let x_3 : Z := to_sint32 x_2 in let a_6 : addr := shift a_2 0%Z in let x_4 : Z := l_index_of t_3 a_5 a_2 i_2 x in let x_5 : Z := 1%Z + i_3 in let x_7 : Z := 2%Z + i_3 in let a_7 : addr := shift a_2 x_5 in let x_8 : Z := i_1 + i_2 - 2%Z - i_3 in let a_8 : addr := t_3 (shift a_2 i_2) in let x_9 : Z := 1%Z + i_3 - i_2 in let a_9 : addr -> addr := havoc t_2 t_3 a_7 x_8 in let a_10 : addr := a_9 a_1 in ¬ a_3 = Mk_addr 0%Z 0%Z -> ¬ a_5 = Mk_addr 0%Z 0%Z -> ¬ a_5 = a_3 -> 0%Z ≤ i_1 -> 0%Z ≤ i_2 -> i_2 ≤ i_3 -> i_3 ≤ x -> region (base a_1) ≤ 0%Z -> region (base a_2) ≤ 0%Z -> region (base a_5) ≤ 0%Z -> i_1 ≤ 2147483645%Z -> i_3 ≤ 2147483646%Z -> i_2 ≤ 2147483648%Z + i_3 -> i_3 ≤ 2147483647%Z + i_2 -> x_3 ≤ 2147483648%Z + i_1 -> i_1 ≤ 2147483647%Z + x_3 -> - 2147483647%Z ≤ to_sint32 (i_1 - x_3) -> framed t_3 -> linked t -> is_sint32 i -> is_sint32 i_1 -> is_sint32 i_2 -> is_sint32 i_3 -> valid_rd t a_1 1%Z -> valid_rw t a_1 1%Z -> valid_rd t a_4 1%Z -> valid_rw t a_6 2147483646%Z -> separated a_1 1%Z a_6 2147483646%Z -> separated a_3 4%Z a_6 2147483646%Z -> p_linked_n t t_3 a_3 a_2 i_2 i_1 (Mk_addr 0%Z 0%Z) -> p_unchanged t t_3 t_1 t t_3 t_1 a_2 i_2 i_3 -> is_sint32 x_4 -> p_linked_n t t_3 a a_2 i_3 1%Z a_5 -> p_linked_n t t_3 a_3 a_2 i_2 x_2 a -> p_linked_n t t_3 a_5 a_2 x_5 (i_1 + i_2 - 1%Z - i_3) (Mk_addr 0%Z 0%Z) -> i_2 ≤ x_5 ∧ x_7 ≤ x ∧ ¬ invalid t a_7 x_8 ∧ p_linked_n t t_3 a_8 a_2 i_2 x_9 a_5 ∨ a_10 = a_3 ∧ i_2 ≤ x_5 ∧ x_7 ≤ x ∧ ¬ invalid t a_7 x_8 ∧ p_linked_n t t_3 a_8 a_2 i_2 x_9 a_5 ∧ separated a_10 4%Z a_6 2147483646%Z ∧ p_array_swipe_left a_9 t_3 a_2 x_5 (i_1 + i_2 - 1%Z) ∧ p_linked_n t a_9 a_8 a_2 i_2 x_9 a_5 ∧ p_linked_n t a_9 (a_9 (shift a_5 0%Z)) a_2 x_5 x_8 (Mk_addr 0%Z 0%Z) ∧ p_unchanged t a_9 t_1 t t_3 t_1 a_2 i_2 x_5 ∧ (∀(i_4 : Z), i_2 ≤ i_4 -> 2%Z + i_4 ≤ x -> ¬ a_9 (shift a_2 i_4) = a_5) ∧ (∀(i_4 : Z), i_2 ≤ i_4 -> 2%Z + i_4 ≤ x -> separated a_1 1%Z (a_9 (shift a_2 i_4)) 4%Z) ∧ (∀(i_4 : Z), i_2 ≤ i_4 -> 2%Z + i_4 ≤ x -> separated a_5 4%Z (a_9 (shift a_2 i_4)) 4%Z) ∧ (∀(i_4 : Z), i_2 ≤ i_4 -> 2%Z + i_4 ≤ x -> separated (a_9 (shift a_2 i_4)) 4%Z a_6 2147483646%Z) ∧ (∀(i_5 : Z) (i_4 : Z), ¬ i_5 = i_4 -> i_2 ≤ i_4 -> i_2 ≤ i_5 -> 2%Z + i_4 ≤ x -> 2%Z + i_5 ≤ x -> ¬ a_9 (shift a_2 i_5) = a_9 (shift a_2 i_4)) ∧ (∀(i_5 : Z) (i_4 : Z), ¬ i_5 = i_4 -> i_2 ≤ i_4 -> i_2 ≤ i_5 -> 2%Z + i_4 ≤ x -> 2%Z + i_5 ≤ x -> separated (a_9 (shift a_2 i_5)) 4%Z (a_9 (shift a_2 i_4)) 4%Z) -> (∀(i_4 : Z), i_2 ≤ i_4 -> i_4 ≤ i_3 -> ¬ t_3 (shift a_2 i_4) = a_5) -> (∀(i_4 : Z), i_2 ≤ i_4 -> i_4 < x -> separated a_1 1%Z (t_3 (shift a_2 i_4)) 4%Z) -> (∀(i_4 : Z), i_2 ≤ i_4 -> i_4 < i_3 -> separated a_5 4%Z (t_3 (shift a_2 i_4)) 4%Z) -> (∀(i_4 : Z), i_2 ≤ i_4 -> i_4 < x -> separated (t_3 (shift a_2 i_4)) 4%Z a_6 2147483646%Z) -> (∀(i_4 : Z), let a_11 : addr := t_3 (shift a_2 i_4) in ¬ a_11 = a_5 -> i_2 ≤ i_4 -> i_4 < x -> separated a_5 4%Z a_11 4%Z) -> (∀(i_5 : Z) (i_4 : Z), ¬ i_5 = i_4 -> i_2 ≤ i_4 -> i_2 ≤ i_5 -> i_4 < x -> i_5 < x -> ¬ t_3 (shift a_2 i_5) = t_3 (shift a_2 i_4)) -> (∀(i_5 : Z) (i_4 : Z), ¬ i_5 = i_4 -> i_2 ≤ i_4 -> i_2 ≤ i_5 -> i_4 < x -> i_5 < x -> separated (t_3 (shift a_2 i_5)) 4%Z (t_3 (shift a_2 i_4)) 4%Z) -> included a_7 x_8 a_1 1%Z ∨ included a_7 x_8 (shift a_2 x_4) (i_1 + i_2 - x_4) ∨ included a_7 x_8 (shift (t_3 (shift a_2 (x_4 - 1%Z))) 0%Z) 1%Z.
Admitted.
