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 goal34 (i_1 : Z) (i_2 : Z) (t_4 : addr -> addr) (a_3 : addr) (a_4 : addr) (t_2 : addr -> addr) (a_2 : addr) (a : addr) (a_1 : addr) (i : Z) (t_3 : addr -> addr) (i_3 : Z) (t : Z -> Z) (t_1 : addr -> R) : let x : Z := i_1 - 1%Z in let x_1 : Z := i_1 + i_2 - 1%Z in let x_2 : Z := l_index_of t_4 a_3 a_4 x x_1 in let a_5 : addr -> addr := havoc t_2 (fun_updt (fun_updt t_4 a_2 a) (shift (t_4 (shift a_4 (x_2 - 1%Z))) 0%Z) a_1) (shift a_4 x_2) (i_1 + i_2 - 1%Z - x_2) in let a_6 : addr := shift a_4 x in let x_3 : Z := 1%Z + i in let a_7 : addr -> addr := havoc t_3 a_5 a_6 x_3 in let a_8 : addr := a_7 a_2 in let a_9 : addr := a_5 a_2 in let x_4 : Z := i_1 + i_2 in let x_5 : Z := i + i_1 in let x_6 : Z := 1%Z + x_2 in let a_10 : addr := shift a_3 0%Z in let a_11 : addr := shift a_4 0%Z in let a_12 : addr := t_4 a_2 in let a_13 : addr -> addr := fun_updt (fun_updt a_7 a_10 a_8) a_6 a_3 in let a_14 : addr -> addr := fun_updt a_13 a_2 a_3 in let a_15 : addr := t_4 (shift a_4 i_3) in let x_7 : Z := l_index_of t_4 a_15 a_4 x x_1 in ¬ Mk_addr 0%Z 0%Z = a_3 -> a_8 = a_9 -> 0%Z < i_1 -> 0%Z ≤ i_2 -> region (base a_2) ≤ 0%Z -> region (base a_3) ≤ 0%Z -> region (base a_4) ≤ 0%Z -> x_2 < x_4 -> i_2 ≤ 2147483645%Z -> i_1 ≤ 2147483647%Z -> - 2147483647%Z ≤ x_4 -> x_5 ≤ 2147483646%Z -> x_4 ≤ 2147483646%Z -> x_4 ≤ 2147483648%Z -> i_1 ≤ x_6 -> framed t_4 -> linked t -> is_sint32 i -> is_sint32 i_1 -> is_sint32 i_2 -> valid_rd t a_2 1%Z -> valid_rw t a_2 1%Z -> valid_rw t a_3 4%Z -> separated a_2 1%Z a_3 4%Z -> is_sint32 x -> valid_rw t a_10 1%Z -> valid_rw t a_11 2147483646%Z -> separated a_2 1%Z a_11 2147483646%Z -> separated a_3 4%Z a_11 2147483646%Z -> separated a_12 4%Z a_11 2147483646%Z -> valid_rw t a_6 1%Z -> valid_rw t a_6 i_2 -> p_linked_n t t_4 a_12 a_4 x i_2 (Mk_addr 0%Z 0%Z) -> is_sint32 x_2 -> separated a_9 4%Z a_11 2147483646%Z -> eqs1_list (load_s1_list a_3 t_1 a_5) (load_s1_list a_3 t_1 t_4) -> p_linked_n t a_5 a_9 a_4 x i (Mk_addr 0%Z 0%Z) -> p_linked_n t a_5 a_9 a_4 x i_2 (Mk_addr 0%Z 0%Z) -> p_unchanged t a_5 t_1 t t_4 t_1 a_4 x x_1 -> separated a_8 4%Z a_11 2147483646%Z -> p_array_swipe_right a_7 a_5 a_4 i_1 x_5 -> p_linked_n t a_7 a_9 a_4 i_1 i (Mk_addr 0%Z 0%Z) -> p_unchanged t a_14 t_1 t a_13 t_1 a_4 x x_5 -> (if decide (x_6 = x_4) then i_2 = i else x_3 = i_2 ∧ - 2147483648%Z ≤ i) -> (if decide (i_2 = i) then x_6 = x_4 ∧ (∀(i_4 : Z), i_1 ≤ 1%Z + i_4 -> 2%Z + i_4 ≤ x_4 -> is_sint32 i_4 -> ¬ t_4 (shift a_4 i_4) = a_3) else a_15 = a_3 ∧ i_1 ≤ 1%Z + i_3 ∧ 2%Z + i_3 ≤ x_4 ∧ i_1 ≤ 1%Z + x_7 ∧ 2%Z + x_7 ≤ x_4) -> (∀(i_4 : Z), i_1 ≤ 1%Z + i_4 -> 2%Z + i_4 ≤ x_4 -> ¬ t_4 (shift a_4 i_4) = a_3) -> (∀(i_4 : Z), i_1 ≤ 1%Z + i_4 -> 2%Z + i_4 ≤ x_4 -> separated a_2 1%Z (t_4 (shift a_4 i_4)) 4%Z) -> (∀(i_4 : Z), i_1 ≤ 1%Z + i_4 -> 2%Z + i_4 ≤ x_4 -> separated (t_4 (shift a_4 i_4)) 4%Z a_11 2147483646%Z) -> (∀(i_4 : Z), let a_16 : addr := t_4 (shift a_4 i_4) in ¬ a_16 = a_3 -> i_1 ≤ 1%Z + i_4 -> 2%Z + i_4 ≤ x_4 -> separated a_3 4%Z a_16 4%Z) -> (∀(i_5 : Z) (i_4 : Z), ¬ i_5 = i_4 -> i_1 ≤ 1%Z + i_4 -> i_1 ≤ 1%Z + i_5 -> 2%Z + i_4 ≤ x_4 -> 2%Z + i_5 ≤ x_4 -> ¬ t_4 (shift a_4 i_5) = t_4 (shift a_4 i_4)) -> (∀(i_5 : Z) (i_4 : Z), ¬ i_5 = i_4 -> i_1 ≤ 1%Z + i_4 -> i_1 ≤ 1%Z + i_5 -> 2%Z + i_4 ≤ x_4 -> 2%Z + i_5 ≤ x_4 -> separated (t_4 (shift a_4 i_5)) 4%Z (t_4 (shift a_4 i_4)) 4%Z) -> (∀(i_4 : Z), i_1 ≤ 1%Z + i_4 -> 2%Z + i_4 ≤ x_4 -> ¬ a_5 (shift a_4 i_4) = a_3) -> (∀(i_4 : Z), i_1 ≤ 1%Z + i_4 -> 2%Z + i_4 ≤ x_5 -> separated a_2 1%Z (a_5 (shift a_4 i_4)) 4%Z) -> (∀(i_4 : Z), i_1 ≤ 1%Z + i_4 -> 2%Z + i_4 ≤ x_4 -> separated a_2 1%Z (a_5 (shift a_4 i_4)) 4%Z) -> (∀(i_4 : Z), i_1 ≤ 1%Z + i_4 -> 2%Z + i_4 ≤ x_4 -> separated a_3 4%Z (a_5 (shift a_4 i_4)) 4%Z) -> (∀(i_4 : Z), i_1 ≤ 1%Z + i_4 -> 2%Z + i_4 ≤ x_5 -> separated (a_5 (shift a_4 i_4)) 4%Z a_11 2147483646%Z) -> (∀(i_4 : Z), i_1 ≤ 1%Z + i_4 -> 2%Z + i_4 ≤ x_4 -> separated (a_5 (shift a_4 i_4)) 4%Z a_11 2147483646%Z) -> (∀(i_5 : Z) (i_4 : Z), ¬ i_5 = i_4 -> i_1 ≤ 1%Z + i_4 -> i_1 ≤ 1%Z + i_5 -> 2%Z + i_4 ≤ x_5 -> 2%Z + i_5 ≤ x_5 -> ¬ a_5 (shift a_4 i_5) = a_5 (shift a_4 i_4)) -> (∀(i_5 : Z) (i_4 : Z), ¬ i_5 = i_4 -> i_1 ≤ 1%Z + i_4 -> i_1 ≤ 1%Z + i_5 -> 2%Z + i_4 ≤ x_4 -> 2%Z + i_5 ≤ x_4 -> ¬ a_5 (shift a_4 i_5) = a_5 (shift a_4 i_4)) -> (∀(i_4 : Z), i_1 ≤ i_4 -> i_4 < x_5 -> separated a_2 1%Z (a_7 (shift a_4 i_4)) 4%Z) -> (∀(i_4 : Z), i_1 ≤ i_4 -> i_4 < x_5 -> separated (a_7 (shift a_4 i_4)) 4%Z a_11 2147483646%Z) -> (∀(i_5 : Z) (i_4 : Z), ¬ i_5 = i_4 -> i_1 ≤ 1%Z + i_4 -> i_1 ≤ 1%Z + i_5 -> 2%Z + i_4 ≤ x_5 -> 2%Z + i_5 ≤ x_5 -> separated (a_5 (shift a_4 i_5)) 4%Z (a_5 (shift a_4 i_4)) 4%Z) -> (∀(i_5 : Z) (i_4 : Z), ¬ i_5 = i_4 -> i_1 ≤ 1%Z + i_4 -> i_1 ≤ 1%Z + i_5 -> 2%Z + i_4 ≤ x_4 -> 2%Z + i_5 ≤ x_4 -> separated (a_5 (shift a_4 i_5)) 4%Z (a_5 (shift a_4 i_4)) 4%Z) -> (∀(i_5 : Z) (i_4 : Z), ¬ i_5 = i_4 -> i_4 < x_5 -> i_5 < x_5 -> i_1 ≤ 1%Z + i_4 -> i_1 ≤ 1%Z + i_5 -> ¬ a_7 (shift a_4 i_5) = a_7 (shift a_4 i_4)) -> (∀(i_5 : Z) (i_4 : Z), ¬ i_5 = i_4 -> i_1 ≤ i_4 -> i_1 ≤ i_5 -> i_4 < x_5 -> i_5 < x_5 -> separated (a_7 (shift a_4 i_5)) 4%Z (a_7 (shift a_4 i_4)) 4%Z) -> p_linked_n t a_14 a_3 a_4 x (1%Z + i_2) (Mk_addr 0%Z 0%Z).
Admitted.
