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 contiki_list.Compound.Compound.
Require Import contiki_list.S1_list.S1_list.
Require Import Why3.Cint.Cint.
Require Import contiki_list.Axiomatic.Axiomatic.
Require Import contiki_list.Axiomatic1.Axiomatic1.
Open Scope Z_scope.
Theorem goal16 (t_2 : addr -> addr) (t_3 : addr -> addr) (a_5 : addr) (i_2 : Z) (i_4 : Z) (i_1 : Z) (a_1 : addr) (i : Z) (a : addr) (a_4 : addr) (t : Z -> Z) (a_2 : addr) (t_1 : addr -> R) (a_3 : addr) (i_3 : Z) : let a_6 : addr -> addr := havoc t_2 t_3 (shift a_5 (1%Z + i_2 + i_4 - i_1)) i_1 in let a_7 : addr := t_3 a_1 in let x_1 : Z := i_2 + i_4 in let x_2 : Z := 2147483648%Z + i_1 in let x_4 : Z := i_1 - i_4 in let x_5 : Z := to_sint32 x_4 in let x_6 : Z := i_2 - 1%Z in let a_8 : addr := shift a_5 0%Z in let a_9 : addr := shift a_5 i_2 in let x_7 : Z := i_2 + i_4 - i_1 in let a_10 : addr := shift a_5 x_6 in let x_8 : Z := 1%Z + i_2 in ¬ i_1 = 0%Z -> (i_4 = 0%Z) = (i = 0%Z) -> (0%Z < i_4) = (i = 1%Z) -> a_6 a_1 = a_7 -> i_4 ≤ i_1 -> 0%Z ≤ i_4 -> i_4 < i_1 -> region (base a) ≤ 0%Z -> region (base a_1) ≤ 0%Z -> region (base a_4) ≤ 0%Z -> region (base a_5) ≤ 0%Z -> - 2147483647%Z ≤ i_2 -> i_2 ≤ 2147483646%Z -> - 2147483648%Z ≤ x_1 -> x_1 ≤ 2147483645%Z -> x_1 ≤ 2147483647%Z -> i_1 ≤ 2147483647%Z + i_4 -> i_4 ≤ x_2 -> x_5 ≤ x_2 -> i_1 ≤ 2147483647%Z + x_5 -> framed t_3 -> linked t -> is_sint32 i -> is_sint32 i_1 -> is_sint32 i_2 -> valid_rw t a_1 1%Z -> is_sint32 x_6 -> is_sint32 x_1 -> valid_rw t a_8 2147483646%Z -> valid_rw t a_9 1%Z -> is_sint32 x_7 -> separated a_1 1%Z a_8 2147483646%Z -> separated a_7 4%Z a_8 2147483646%Z -> valid_rd t a_10 1%Z -> p_linked_n t t_3 a a_5 x_7 i_1 a_4 -> p_array_swipe_right a_6 t_3 a_5 x_8 (1%Z + i_2 + i_4) -> p_linked_n t a_6 a a_5 x_7 x_4 a_2 -> p_linked_n t a_6 a_2 a_5 x_8 i_4 a_4 -> p_unchanged t a_6 t_1 t t_3 t_1 a_5 x_7 i_2 -> (if decide (1%Z + i_4 = i_1) then a_3 = a else 1%Z + i_3 + i_4 = i_1 ∧ havoc t_2 t_3 (shift a_5 (i_2 - i_3)) i_1 a_10 = a_3 ∧ - 2147483648%Z ≤ i_3 ∧ i_3 ≤ 2147483647%Z) -> (∀(i_5 : Z), i_5 < x_1 -> x_1 ≤ i_5 + i_1 -> separated a_1 1%Z (t_3 (shift a_5 i_5)) 4%Z) -> (∀(i_5 : Z), i_5 < x_1 -> x_1 ≤ i_5 + i_1 -> separated (t_3 (shift a_5 i_5)) 4%Z a_8 2147483646%Z) -> (∀(i_6 : Z) (i_5 : Z), ¬ i_6 = i_5 -> i_5 < x_1 -> i_6 < x_1 -> x_1 ≤ i_5 + i_1 -> x_1 ≤ i_6 + i_1 -> ¬ t_3 (shift a_5 i_6) = t_3 (shift a_5 i_5)) -> (∀(i_6 : Z) (i_5 : Z), ¬ i_6 = i_5 -> i_5 < x_1 -> i_6 < x_1 -> x_1 ≤ i_5 + i_1 -> x_1 ≤ i_6 + i_1 -> separated (t_3 (shift a_5 i_6)) 4%Z (t_3 (shift a_5 i_5)) 4%Z) -> (∀(i_5 : Z), i_2 < i_5 -> i_5 ≤ x_1 -> separated a_1 1%Z (a_6 (shift a_5 i_5)) 4%Z) -> (∀(i_5 : Z), x_1 ≤ i_5 + i_1 -> i_5 < i + i_2 + i_4 -> separated (a_6 (shift a_5 i_5)) 4%Z a_8 2147483646%Z) -> p_linked_n t (fun_updt a_6 a_9 (a_6 a_10)) a a_5 x_7 (i_1 - 1%Z - i_4) a_3.
Admitted.
