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.Axiomatic1.Axiomatic1.
Open Scope Z_scope.
Theorem goal20 (i : Z) (i_1 : Z) (a_1 : addr) (t_4 : addr -> addr) (a : addr) (t_3 : addr -> addr) (i_2 : Z) (t : Z -> Z) (t_5 : addr -> addr) (t_2 : addr -> addr) (t_1 : addr -> R) : let x : Z := i + i_1 in let a_2 : addr := shift a_1 0%Z in let a_3 : addr := t_4 a in let a_4 : addr := t_3 a in let a_5 : addr := shift a_4 0%Z in let a_6 : addr := shift a_1 i_1 in let x_1 : Z := i - 1%Z in let a_7 : addr := shift a_3 0%Z in let a_8 : addr := t_4 a_6 in ¬ i = 1%Z -> 0%Z < i -> 0%Z ≤ i_1 -> i_1 ≤ i_2 -> region (base a) ≤ 0%Z -> region (base a_1) ≤ 0%Z -> 2%Z + i_2 ≤ x -> framed t_4 -> 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_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_4 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_5 = t_4 else a_3 = a_4 ∧ fun_updt t_3 a (t_3 a_5) = t_5 ∧ havoc t_2 t_4 a_6 x_1 = t_3 ∧ - 2147483647%Z ≤ i ∧ valid_rd t a_5 1%Z ∧ valid_rd t a_7 1%Z ∧ separated a_4 4%Z a_2 2147483646%Z ∧ p_unchanged t t_3 t_1 t t_4 t_1 a_1 i_1 i_1 ∧ p_array_swipe_left t_3 t_4 a_1 i_1 (i + i_1 - 1%Z) ∧ p_linked_n t t_3 (t_3 a_7) a_1 i_1 x_1 (Mk_addr 0%Z 0%Z) ∧ p_linked_n t t_3 a_8 a_1 i_1 0%Z a_3 ∧ p_linked_n t t_3 (t_4 a_7) a_1 i_1 x_1 (Mk_addr 0%Z 0%Z) ∧ p_linked_n t t_4 a_8 a_1 i_1 0%Z a_3 ∧ (∀(i_3 : Z), i_1 ≤ i_3 -> 2%Z + i_3 ≤ x -> ¬ t_3 (shift a_1 i_3) = a_3) ∧ (∀(i_3 : Z), i_1 ≤ i_3 -> 2%Z + i_3 ≤ x -> separated a 1%Z (t_3 (shift a_1 i_3)) 4%Z) ∧ (∀(i_3 : Z), i_1 ≤ i_3 -> 2%Z + i_3 ≤ x -> separated a_3 4%Z (t_3 (shift a_1 i_3)) 4%Z) ∧ (∀(i_3 : Z), i_1 ≤ i_3 -> 2%Z + i_3 ≤ x -> separated (t_3 (shift a_1 i_3)) 4%Z a_2 2147483646%Z) ∧ (∀(i_4 : Z) (i_3 : Z), ¬ i_4 = i_3 -> i_1 ≤ i_3 -> i_1 ≤ i_4 -> 2%Z + i_3 ≤ x -> 2%Z + i_4 ≤ x -> ¬ t_3 (shift a_1 i_4) = t_3 (shift a_1 i_3)) ∧ (∀(i_3 : Z), i_1 ≤ i_3 -> 2%Z + i_3 ≤ x -> p_linked_n t t_3 (t_3 (shift a_1 i_3)) a_1 i_3 (i + i_1 - 1%Z - i_3) (Mk_addr 0%Z 0%Z)) ∧ (∀(i_4 : Z) (i_3 : Z), ¬ i_4 = i_3 -> i_1 ≤ i_3 -> i_1 ≤ i_4 -> 2%Z + i_3 ≤ x -> 2%Z + i_4 ≤ x -> separated (t_3 (shift a_1 i_4)) 4%Z (t_3 (shift a_1 i_3)) 4%Z)) -> (∀(i_3 : Z), i_1 ≤ i_3 -> i_3 < x -> separated a 1%Z (t_4 (shift a_1 i_3)) 4%Z) -> (∀(i_3 : Z), i_1 ≤ i_3 -> i_3 < x -> separated (t_4 (shift a_1 i_3)) 4%Z a_2 2147483646%Z) -> (∀(i_4 : Z) (i_3 : Z), ¬ i_4 = i_3 -> i_1 ≤ i_3 -> i_1 ≤ i_4 -> i_3 < x -> i_4 < x -> ¬ t_4 (shift a_1 i_4) = t_4 (shift a_1 i_3)) -> (∀(i_4 : Z) (i_3 : Z), ¬ i_4 = i_3 -> i_1 ≤ i_3 -> i_1 ≤ i_4 -> i_3 < x -> i_4 < x -> separated (t_4 (shift a_1 i_4)) 4%Z (t_4 (shift a_1 i_3)) 4%Z) -> separated (t_5 (shift a_1 i_2)) 4%Z a_2 2147483646%Z.
Admitted.
