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 should_we_balance.A_thread_variables_properties.A_thread_variables_properties.
Require Import should_we_balance.Compound.Compound.
Require Import Why3.Cint.Cint.
Require Import should_we_balance.A_schedule_cpumask.A_schedule_cpumask.
Open Scope Z_scope.
Theorem goal4 (a_1 : addr) (t_1 : addr -> Z) (t_2 : addr -> addr) (i : Z) (a : addr) (t : Z -> Z) : let a_2 : addr := shift a_1 1%Z in let x : Z := t_1 a_2 in let a_3 : addr := shift a_1 0%Z in let a_4 : addr := t_2 (shift a_1 4%Z) in let a_5 : addr := t_2 a_3 in let a_6 : addr := shift a_5 0%Z in let a_7 : addr := t_2 (shift a_4 0%Z) in let a_8 : addr := shift a_7 0%Z in 0%Z ≤ i -> i < l_size -> 0%Z ≤ x -> x < l_size -> region (base a) ≤ 0%Z -> region (base a_1) ≤ 0%Z -> framed t_2 -> linked t -> is_uint32 i -> valid_rd t a_1 5%Z -> is_uint32 (t_1 (shift a_1 3%Z)) -> is_sint32 x -> valid_rd t a_3 1%Z -> valid_rd t a_4 1%Z -> valid_rd t (t_2 (shift a_1 2%Z)) 2%Z -> valid_rd t a_5 2%Z -> is_sint32 (t_1 (shift a_5 1%Z)) -> valid_rd t a_6 1%Z -> valid_rd t (t_2 a_6) 1%Z -> is_uint8 (t_1 (shift a_7 x)) -> valid_rd t a_8 l_size -> (∀(i_1 : Z), 0%Z ≤ i_1 -> i_1 < l_size -> separated a_8 l_size (shift (t_2 (shift (shift a i_1) 0%Z)) 0%Z) l_size) -> (∀(i_1 : Z), let a_9 : addr := shift a i_1 in 0%Z ≤ i_1 -> i_1 < l_size -> valid_rd t a_9 1%Z ∧ valid_rw t (shift (t_2 (shift a_9 0%Z)) 0%Z) l_size) -> (∀(a_9 : addr), let a_10 : addr := l_sched_group_cpus a_9 in let a_11 : addr := shift (t_2 (shift a_10 0%Z)) 0%Z in valid_rd t a_10 1%Z ∧ valid_rd t a_11 l_size ∧ (∀(i_1 : Z), 0%Z ≤ i_1 -> i_1 < l_size -> separated a_11 l_size (shift (t_2 (shift (shift a i_1) 0%Z)) 0%Z) l_size)) -> (∀(a_9 : addr), let a_10 : addr := l_sched_group_mask a_9 in let a_11 : addr := shift (t_2 (shift a_10 0%Z)) 0%Z in valid_rd t a_10 1%Z ∧ valid_rd t a_11 l_size ∧ (∀(i_1 : Z), 0%Z ≤ i_1 -> i_1 < l_size -> separated a_11 l_size (shift (t_2 (shift (shift a i_1) 0%Z)) 0%Z) l_size)) -> (∀(a_9 : addr), let a_10 : addr := l_group_balance_mask a_9 in let a_11 : addr := shift (t_2 (shift a_10 0%Z)) 0%Z in valid_rd t a_10 1%Z ∧ valid_rd t a_11 l_size ∧ (∀(i_1 : Z), 0%Z ≤ i_1 -> i_1 < l_size -> separated a_11 l_size (shift (t_2 (shift (shift a i_1) 0%Z)) 0%Z) l_size)) -> (∀(i_1 : Z), let a_9 : addr := l_cpu_smt_mask i_1 in let a_10 : addr := shift (t_2 (shift a_9 0%Z)) 0%Z in 0%Z ≤ i_1 -> i_1 < l_size -> valid_rd t a_9 1%Z ∧ valid_rd t a_10 l_size ∧ (∀(i_2 : Z), 0%Z ≤ i_2 -> i_2 < l_size -> separated a_10 l_size (shift (t_2 (shift (shift a i_2) 0%Z)) 0%Z) l_size)) -> valid_rd t a_2 1%Z.
Admitted.
