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.
Open Scope Z_scope.
Theorem goal6 (i : Z) (i_1 : Z) (a_1 : addr) (t_2 : addr -> addr) (a : addr) (i_2 : Z) (i_4 : Z) (i_3 : Z) (t : Z -> Z) (t_3 : addr -> addr) (t_1 : Z -> Z) : let x : Z := i + i_1 in let a_2 : addr := shift a_1 0%Z in let a_3 : addr := t_2 a in let a_4 : addr := shift a_3 0%Z in let a_5 : addr := t_2 a_4 in let x_1 : Z := i_1 + i_2 in let a_6 : addr := t_2 (shift a_1 x_1) in let a_7 : addr := shift a_6 0%Z in let a_8 : addr := t_2 a_7 in let a_9 : addr := shift a_8 0%Z in let a_10 : addr := t_2 a_9 in let m : addr -> addr := fun_updt t_2 a_7 a_10 in let x_2 : Z := to_sint32 x in let a_11 : addr := m a in let x_3 : Z := i + i_1 - 2%Z in let a_12 : addr := m (shift a_1 x_3) in ¬ i_4 = i_3 -> i_1 ≤ i_3 -> i_1 ≤ i_4 -> region (base a) ≤ 0%Z -> region (base a_1) ≤ 0%Z -> 2%Z + i_3 ≤ x -> 2%Z + i_4 ≤ x -> framed t_2 -> linked t -> is_sint32 i -> is_sint32 i_1 -> is_sint32 i_2 -> valid_rd t a 1%Z -> valid_rw t a 1%Z -> valid_rw t a_2 2147483646%Z -> separated a 1%Z a_2 2147483646%Z -> separated a_3 4%Z a_2 2147483646%Z -> p_linked_n t t_2 a_3 a_1 i_1 i (Mk_addr 0%Z 0%Z) -> (if decide (a_3 = Mk_addr 0%Z 0%Z) then t_3 = t_2 else t_1 = t ∧ valid_rd t_1 a_4 1%Z ∧ (if decide (a_5 = Mk_addr 0%Z 0%Z) then fun_updt t_2 a a_5 = t_3 ∧ valid_rd t_1 a 1%Z ∧ valid_rw t_1 a 1%Z else a_10 = Mk_addr 0%Z 0%Z ∧ m = t_3 ∧ - 2147483646%Z ≤ i ∧ 2%Z ≤ i ∧ - 2147483648%Z ≤ x ∧ x ≤ 2147483647%Z ∧ 2%Z + i_2 ≤ i ∧ - 2147483646%Z ≤ x_2 ∧ valid_rd t_1 a 1%Z ∧ valid_rw t_1 a_2 2147483646%Z ∧ valid_rd t_1 a_7 1%Z ∧ valid_rw t_1 a_7 1%Z ∧ valid_rw t_1 a_8 4%Z ∧ valid_rd t_1 a_9 1%Z ∧ valid_rd t_1 (shift a_1 (to_sint32 (x_2 - 2%Z))) 1%Z ∧ p_linked_n t_1 t_2 a_6 a_1 x_1 (i - i_2) a_10 ∧ p_linked_n t_1 m a_11 a_1 i_1 (i - 2%Z) a_12 ∧ p_linked_n t_1 m a_11 a_1 i_1 (i - 1%Z) a_10 ∧ p_linked_n t_1 m a_12 a_1 x_3 1%Z a_10)) -> (∀(i_5 : Z), i_1 ≤ i_5 -> i_5 < x -> separated a 1%Z (t_2 (shift a_1 i_5)) 4%Z) -> (∀(i_5 : Z), i_1 ≤ i_5 -> i_5 < x -> separated (t_2 (shift a_1 i_5)) 4%Z a_2 2147483646%Z) -> (∀(i_6 : Z) (i_5 : Z), ¬ i_6 = i_5 -> i_1 ≤ i_5 -> i_1 ≤ i_6 -> i_5 < x -> i_6 < x -> ¬ t_2 (shift a_1 i_6) = t_2 (shift a_1 i_5)) -> (∀(i_6 : Z) (i_5 : Z), ¬ i_6 = i_5 -> i_1 ≤ i_5 -> i_1 ≤ i_6 -> i_5 < x -> i_6 < x -> separated (t_2 (shift a_1 i_6)) 4%Z (t_2 (shift a_1 i_5)) 4%Z) -> separated (t_3 (shift a_1 i_4)) 4%Z (t_3 (shift a_1 i_3)) 4%Z.
Admitted.
